International Nuclear Information System (INIS)
Guo, Yu; Luo, Albert C.J.
2015-01-01
In this paper, analytically predicted are complex periodic motions in the periodically forced, damped, hardening Duffing oscillator through discrete implicit maps of the corresponding differential equations. Bifurcation trees of periodic motions to chaos in such a hardening Duffing oscillator are obtained. The stability and bifurcation analysis of periodic motion in the bifurcation trees is carried out by eigenvalue analysis. The solutions of all discrete nodes of periodic motions are computed by the mapping structures of discrete implicit mapping. The frequency-amplitude characteristics of periodic motions are computed that are based on the discrete Fourier series. Thus, the bifurcation trees of periodic motions are also presented through frequency-amplitude curves. Finally, based on the analytical predictions, the initial conditions of periodic motions are selected, and numerical simulations of periodic motions are carried out for comparison of numerical and analytical predictions. The harmonic amplitude spectrums are also given for the approximate analytical expressions of periodic motions, which can also be used for comparison with experimental measurement. This study will give a better understanding of complex periodic motions in the hardening Duffing oscillator.
Bifurcation of forced periodic oscillations for equations with Preisach hysteresis
International Nuclear Information System (INIS)
Krasnosel'skii, A; Rachinskii, D
2005-01-01
We study oscillations in resonant systems under periodic forcing. The systems depend on a scalar parameter and have the form of simple pendulum type equations with ferromagnetic friction represented by the Preisach hysteresis nonlinearity. If for some parameter value the period of free oscillations of the principal linear part of the system coincides with the period of the forcing term, then one may expect the existence of unbounded branches of periodic solutions for nearby parameter values. We present conditions for the existence and nonexistence of such branches and estimates of their number
Han, Qun; Xu, Wei; Sun, Jian-Qiao
2016-09-01
The stochastic response of nonlinear oscillators under periodic and Gaussian white noise excitations is studied with the generalized cell mapping based on short-time Gaussian approximation (GCM/STGA) method. The solutions of the transition probability density functions over a small fraction of the period are constructed by the STGA scheme in order to construct the GCM over one complete period. Both the transient and steady-state probability density functions (PDFs) of a smooth and discontinuous (SD) oscillator are computed to illustrate the application of the method. The accuracy of the results is verified by direct Monte Carlo simulations. The transient responses show the evolution of the PDFs from being Gaussian to non-Gaussian. The effect of a chaotic saddle on the stochastic response is also studied. The stochastic P-bifurcation in terms of the steady-state PDFs occurs with the decrease of the smoothness parameter, which corresponds to the deterministic pitchfork bifurcation.
Bifurcation analysis of delay-induced periodic oscillations
Green, K.
2010-01-01
In this paper we consider a generic differential equation with a cubic nonlinearity and delay. This system, in the absence of delay, is known to undergo an oscillatory instability. The addition of the delay is shown to result in the creation of a number of periodic solutions with constant amplitude
Energy Technology Data Exchange (ETDEWEB)
Emelianova, Yu.P., E-mail: yuliaem@gmail.com [Department of Electronics and Instrumentation, Saratov State Technical University, Polytechnicheskaya 77, Saratov 410054 (Russian Federation); Kuznetsov, A.P., E-mail: apkuz@rambler.ru [Kotel' nikov' s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, Zelyenaya 38, Saratov 410019 (Russian Federation); Turukina, L.V., E-mail: lvtur@rambler.ru [Kotel' nikov' s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, Zelyenaya 38, Saratov 410019 (Russian Federation); Institute for Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24-25, 14476 Potsdam (Germany)
2014-01-10
The dynamics of the four dissipatively coupled van der Pol oscillators is considered. Lyapunov chart is presented in the parameter plane. Its arrangement is discussed. We discuss the bifurcations of tori in the system at large frequency detuning of the oscillators. Here are quasi-periodic saddle-node, Hopf and Neimark–Sacker bifurcations. The effect of increase of the threshold for the “amplitude death” regime and the possibilities of complete and partial broadband synchronization are revealed.
Bifurcation and Nonlinear Oscillations.
1980-09-28
Structural stability and bifurcation theory. pp. 549-560 in Dinamical Systems (Ed. MI. Peixoto), Academic Press, 1973. [211 J. Sotomayor, Generic one...Dynamical Systems Brown University ELECTP" 71, Providence, R. I. 02912 1EC 2 4 1980j //C -*)’ Septabe-4., 1980 / -A + This research was supported in...problems are discussed. The first one deals with the characterization of the flow for a periodic planar system which is the perturbation of an autonomous
International Nuclear Information System (INIS)
Luo, G.W.; Lv, X.H.; Ma, L.
2008-01-01
A two-degree-of-freedom plastic impact oscillator with a frictional slider is considered. Dynamics of the plastic impact oscillator are analyzed by a three-dimensional map, which describes free flight and sticking solutions of two masses of the system, between impacts, supplemented by transition conditions at the instants of impacts. Piecewise property and singularity are found to exist in the impact Poincare map. The piecewise property of the map is caused by the transitions of free flight and sticking motions of two masses immediately after the impact, and the singularity of the map is generated via the grazing contact of two masses immediately before the impact. These properties of the map have been shown to exhibit particular types of sliding and grazing bifurcations of periodic-impact motions under parameter variation. The influence of piecewise property, grazing singularity and parameter variation on dynamics of the vibro-impact system is analyzed. The global bifurcation diagrams of before-impact velocity as a function of the excitation frequency are plotted to predict much of the qualitative behavior of the system. The global bifurcations of period-N single-impact motions of the plastic impact oscillator are found to exhibit extensive and systematic characteristics. Dynamics of the impact oscillator, in the elastic impact case, is also analyzed. This type of impact is modelled by using the conditions of conservation of momentum and an instantaneous coefficient of restitution rule. The differences in periodic-impact motions and bifurcations are found by making a comparison between dynamic behaviors of the plastic and elastic impact oscillators with a frictional slider. The best progression of the plastic impact oscillator is found to occur in period-1 single-impact sticking motion with large impact velocity. The largest progression of the elastic impact oscillator occurs in period-1 multi-impact motion. The simulative results show that the plastic impact
Heteroclinic Bifurcation Behaviors of a Duffing Oscillator with Delayed Feedback
Directory of Open Access Journals (Sweden)
Shao-Fang Wen
2018-01-01
Full Text Available The heteroclinic bifurcation and chaos of a Duffing oscillator with forcing excitation under both delayed displacement feedback and delayed velocity feedback are studied by Melnikov method. The Melnikov function is analytically established to detect the necessary conditions for generating chaos. Through the analysis of the analytical necessary conditions, we find that the influences of the delayed displacement feedback and delayed velocity feedback are separable. Then the influences of the displacement and velocity feedback parameters on heteroclinic bifurcation and threshold value of chaotic motion are investigated individually. In order to verify the correctness of the analytical conditions, the Duffing oscillator is also investigated by numerical iterative method. The bifurcation curves and the largest Lyapunov exponents are provided and compared. From the analysis of the numerical simulation results, it could be found that two types of period-doubling bifurcations occur in the Duffing oscillator, so that there are two paths leading to the chaos in this oscillator. The typical dynamical responses, including time histories, phase portraits, and Poincare maps, are all carried out to verify the conclusions. The results reveal some new phenomena, which is useful to design or control this kind of system.
Bifurcations and Crises in a Shape Memory Oscillator
Directory of Open Access Journals (Sweden)
Luciano G. Machado
2004-01-01
Full Text Available The remarkable properties of shape memory alloys have been motivating the interest in applications in different areas varying from biomedical to aerospace hardware. The dynamical response of systems composed by shape memory actuators presents nonlinear characteristics and a very rich behavior, showing periodic, quasi-periodic and chaotic responses. This contribution analyses some aspects related to bifurcation phenomenon in a shape memory oscillator where the restitution force is described by a polynomial constitutive model. The term bifurcation is used to describe qualitative changes that occur in the orbit structure of a system, as a consequence of parameter changes, being related to chaos. Numerical simulations show that the response of the shape memory oscillator presents period doubling cascades, direct and reverse, and crises.
Bifurcation and category learning in network models of oscillating cortex
Baird, Bill
1990-06-01
A genetic model of oscillating cortex, which assumes “minimal” coupling justified by known anatomy, is shown to function as an associative memory, using previously developed theory. The network has explicit excitatory neurons with local inhibitory interneuron feedback that forms a set of nonlinear oscillators coupled only by long-range excitatory connections. Using a local Hebb-like learning rule for primary and higher-order synapses at the ends of the long-range connections, the system learns to store the kinds of oscillation amplitude patterns observed in olfactory and visual cortex. In olfaction, these patterns “emerge” during respiration by a pattern forming phase transition which we characterize in the model as a multiple Hopf bifurcation. We argue that these bifurcations play an important role in the operation of real digital computers and neural networks, and we use bifurcation theory to derive learning rules which analytically guarantee CAM storage of continuous periodic sequences-capacity: N/2 Fourier components for an N-node network-no “spurious” attractors.
Bursting oscillations, bifurcation and synchronization in neuronal systems
Energy Technology Data Exchange (ETDEWEB)
Wang Haixia [School of Science, Nanjing University of Science and Technology, Nanjing 210094 (China); Wang Qingyun, E-mail: drwangqy@gmail.com [Department of Dynamics and Control, Beihang University, Beijing 100191 (China); Lu Qishao [Department of Dynamics and Control, Beihang University, Beijing 100191 (China)
2011-08-15
Highlights: > We investigate bursting oscillations and related bifurcation in the modified Morris-Lecar neuron. > Two types of fast-slow bursters are analyzed in detail. > We show the properties of some crucial bifurcation points. > Synchronization transition and the neural excitability are explored in the coupled bursters. - Abstract: This paper investigates bursting oscillations and related bifurcation in the modified Morris-Lecar neuron. It is shown that for some appropriate parameters, the modified Morris-Lecar neuron can exhibit two types of fast-slow bursters, that is 'circle/fold cycle' bursting and 'subHopf/homoclinic' bursting with class 1 and class 2 neural excitability, which have different neuro-computational properties. By means of the analysis of fast-slow dynamics and phase plane, we explore bifurcation mechanisms associated with the two types of bursters. Furthermore, the properties of some crucial bifurcation points, which can determine the type of the burster, are studied by the stability and bifurcation theory. In addition, we investigate the influence of the coupling strength on synchronization transition and the neural excitability in two electrically coupled bursters with the same bursting type. More interestingly, the multi-time-scale synchronization transition phenomenon is found as the coupling strength varies.
Local and global bifurcations at infinity in models of glycolytic oscillations
DEFF Research Database (Denmark)
Sturis, Jeppe; Brøns, Morten
1997-01-01
We investigate two models of glycolytic oscillations. Each model consists of two coupled nonlinear ordinary differential equations. Both models are found to have a saddle point at infinity and to exhibit a saddle-node bifurcation at infinity, giving rise to a second saddle and a stable node...... at infinity. Depending on model parameters, a stable limit cycle may blow up to infinite period and amplitude and disappear in the bifurcation, and after the bifurcation, the stable node at infinity then attracts all trajectories. Alternatively, the stable node at infinity may coexist with either a stable...... sink (not at infinity) or a stable limit cycle. This limit cycle may then disappear in a heteroclinic bifurcation at infinity in which the unstable manifold from one saddle at infinity joins the stable manifold of the other saddle at infinity. These results explain prior reports for one of the models...
Quasi-period oscillations of relay feedback systems
International Nuclear Information System (INIS)
Wen Guilin; Wang Qingguo; Lee, T.H.
2007-01-01
This paper presents an analytical method for investigation of the existence and stability of quasi-period oscillations (torus solutions) for a class of relay feedback systems. The idea is to analyze Poincare map from one switching surface to the next based on the Hopf bifurcation theory of maps. It is shown that there exist quasi-period oscillations in certain relay feedback systems
Synchronization of diffusively coupled oscillators near the homoclinic bifurcation
International Nuclear Information System (INIS)
Postnov, D.; Han, Seung Kee; Kook, Hyungtae
1998-09-01
It has been known that a diffusive coupling between two limit cycle oscillations typically leads to the inphase synchronization and also that it is the only stable state in the weak coupling limit. Recently, however, it has been shown that the coupling of the same nature can result in the distinctive dephased synchronization when the limit cycles are close to the homoclinic bifurcation, which often occurs especially for the neuronal oscillators. In this paper we propose a simple physical model using the modified van der Pol equation, which unfolds the generic synchronization behaviors of the latter kind and in which one may readily observe changes in the synchronization behaviors between the distinctive regimes as well. The dephasing mechanism is analyzed both qualitatively and quantitatively in the weak coupling limit. A general form of coupling is introduced and the synchronization behaviors over a wide range of the coupling parameters are explored to construct the phase diagram using the bifurcation analysis. (author)
Chaotic behavior of current-carrying plasmas in external periodic oscillations
Energy Technology Data Exchange (ETDEWEB)
Ohno, Noriyasu; Tanaka, Masayoshi; Komori, Akio; Kawai, Yoshinobu
1989-01-01
A set of cascading bifurcations and a chaotic state in the presence of an external periodic oscillation are experimentally investigated in a current-carrying plasma. The measured bifurcation sequence leading to chaos, which is controlled by changing plasma densities and the frequencies of external oscillations, is in qualitative agreement with a theory which describes anharmonic systems in periodic fields. (author).
Multiple bifurcations and periodic 'bubbling' in a delay population model
International Nuclear Information System (INIS)
Peng Mingshu
2005-01-01
In this paper, the flip bifurcation and periodic doubling bifurcations of a discrete population model without delay influence is firstly studied and the phenomenon of Feigenbaum's cascade of periodic doublings is also observed. Secondly, we explored the Neimark-Sacker bifurcation in the delay population model (two-dimension discrete dynamical systems) and the unique stable closed invariant curve which bifurcates from the nontrivial fixed point. Finally, a computer-assisted study for the delay population model is also delved into. Our computer simulation shows that the introduction of delay effect in a nonlinear difference equation derived from the logistic map leads to much richer dynamic behavior, such as stable node → stable focus → an lower-dimensional closed invariant curve (quasi-periodic solution, limit cycle) or/and stable periodic solutions → chaotic attractor by cascading bubbles (the combination of potential period doubling and reverse period-doubling) and the sudden change between two different attractors, etc
Perturbed period-doubling bifurcation. I. Theory
DEFF Research Database (Denmark)
Svensmark, Henrik; Samuelsen, Mogens Rugholm
1990-01-01
-defined way that is a function of the amplitude and the frequency of the signal. New scaling laws between the amplitude of the signal and the detuning δ are found; these scaling laws apply to a variety of quantities, e.g., to the shift of the bifurcation point. It is also found that the stability...... of a microwave-driven Josephson junction confirm the theory. Results should be of interest in parametric-amplification studies....
Effect of various periodic forces on Duffing oscillator
Indian Academy of Sciences (India)
Bifurcations and chaos in the ubiquitous Duffing oscillator equation with different external periodic forces are studied numerically. The external periodic forces considered are sine wave, square wave, rectified sine wave, symmetric saw-tooth wave, asymmetric saw-tooth wave, rectangular wave with amplitude-dependent ...
Chaos and bifurcations in periodic windows observed in plasmas
International Nuclear Information System (INIS)
Qin, J.; Wang, L.; Yuan, D.P.; Gao, P.; Zhang, B.Z.
1989-01-01
We report the experimental observations of deterministic chaos in a steady-state plasma which is not driven by any extra periodic forces. Two routes to chaos have been found, period-doubling and intermittent chaos. The fine structures in chaos such as periodic windows and bifurcations in windows have also been observed
International Nuclear Information System (INIS)
Song Yongli; Tadé, Moses O; Zhang Tonghua
2009-01-01
In this paper, a delayed neural network with unidirectional coupling is considered which consists of two two-dimensional nonlinear differential equation systems with exponential decay where one system receives a delayed input from the other system. Some parameter regions are given for conditional/absolute stability and Hopf bifurcations by using the theory of functional differential equations. Conditions ensuring the stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the centre manifold theorem. We also investigate the spatio-temporal patterns of bifurcating periodic oscillations by using the symmetric bifurcation theory of delay-differential equations combined with representation theory of Lie groups. Then the global continuation of phase-locked periodic solutions is investigated. Numerical simulations are given to illustrate the results obtained
Border-Collision Bifurcations and Chaotic Oscillations in a Piecewise-Smooth Dynamical System
DEFF Research Database (Denmark)
Zhusubaliyev, Z.T.; Soukhoterin, E.A.; Mosekilde, Erik
2002-01-01
Many problems of engineering and applied science result in the consideration of piecewise-smooth dynamical systems. Examples are relay and pulse-width control systems, impact oscillators, power converters, and various electronic circuits with piecewise-smooth characteristics. The subject...... of investigation in the present paper is the dynamical model of a constant voltage converter which represents a three-dimensional piecewise-smooth system of nonautonomous differential equations. A specific type of phenomena that arise in the dynamics of piecewise-smooth systems are the so-called border......-collision bifurcations. The paper contains a detailed analysis of this type of bifurcational transition in the dynamics of the voltage converter, in particular, the merging and subsequent disappearance of cycles of different types, change of solution type, and period-doubling, -tripling, -quadrupling and -quintupling...
Bifurcation analysis of delay-induced resonances of the El-Niño Southern Oscillation.
Krauskopf, Bernd; Sieber, Jan
2014-09-08
Models of global climate phenomena of low to intermediate complexity are very useful for providing an understanding at a conceptual level. An important aspect of such models is the presence of a number of feedback loops that feature considerable delay times, usually due to the time it takes to transport energy (for example, in the form of hot/cold air or water) around the globe. In this paper, we demonstrate how one can perform a bifurcation analysis of the behaviour of a periodically forced system with delay in dependence on key parameters. As an example, we consider the El-Niño Southern Oscillation (ENSO), which is a sea-surface temperature (SST) oscillation on a multi-year scale in the basin of the Pacific Ocean. One can think of ENSO as being generated by an interplay between two feedback effects, one positive and one negative, which act only after some delay that is determined by the speed of transport of SST anomalies across the Pacific. We perform here a case study of a simple delayed-feedback oscillator model for ENSO, which is parametrically forced by annual variation. More specifically, we use numerical bifurcation analysis tools to explore directly regions of delay-induced resonances and other stability boundaries in this delay-differential equation model for ENSO.
Bifurcations of a periodically forced microbial continuous culture model with restrained growth rate
Ren, Jingli; Yuan, Qigang
2017-08-01
A three dimensional microbial continuous culture model with a restrained microbial growth rate is studied in this paper. Two types of dilution rates are considered to investigate the dynamic behaviors of the model. For the unforced system, fold bifurcation and Hopf bifurcation are detected, and numerical simulations reveal that the system undergoes degenerate Hopf bifurcation. When the system is periodically forced, bifurcation diagrams for periodic solutions of period-one and period-two are given by researching the Poincaré map, corresponding to different bifurcation cases in the unforced system. Stable and unstable quasiperiodic solutions are obtained by Neimark-Sacker bifurcation with different parameter values. Periodic solutions of various periods can occur or disappear and even change their stability, when the Poincaré map of the forced system undergoes Neimark-Sacker bifurcation, flip bifurcation, and fold bifurcation. Chaotic attractors generated by a cascade of period doublings and some phase portraits are given at last.
Yu, Yue; Zhang, Zhengdi; Han, Xiujing
2018-03-01
In this work, we aim to demonstrate the novel routes to periodic and chaotic bursting, i.e., the different bursting dynamics via delayed pitchfork bifurcations around stable attractors, in the classical controlled Lü system. First, by computing the corresponding characteristic polynomial, we determine where some critical values about bifurcation behaviors appear in the Lü system. Moreover, the transition mechanism among different stable attractors has been introduced including homoclinic-type connections or chaotic attractors. Secondly, taking advantage of the above analytical results, we carry out a study of the mechanism for bursting dynamics in the Lü system with slowly periodic variation of certain control parameter. A distinct delayed supercritical pitchfork bifurcation behavior can be discussed when the control item passes through bifurcation points periodically. This delayed dynamical behavior may terminate at different parameter areas, which leads to different spiking modes around different stable attractors (equilibriums, limit cycles, or chaotic attractors). In particular, the chaotic attractor may appear by Shilnikov connections or chaos boundary crisis, which leads to the occurrence of impressive chaotic bursting oscillations. Our findings enrich the study of bursting dynamics and deepen the understanding of some similar sorts of delayed bursting phenomena. Finally, some numerical simulations are included to illustrate the validity of our study.
Baird, Bill
1986-08-01
A neural network model describing pattern recognition in the rabbit olfactory bulb is analysed to explain the changes in neural activity observed experimentally during classical Pavlovian conditioning. EEG activity recorded from an 8×8 arry of 64 electrodes directly on the surface on the bulb shows distinct spatial patterns of oscillation that correspond to the animal's recognition of different conditioned odors and change with conditioning to new odors. The model may be considered a variant of Hopfield's model of continuous analog neural dynamics. Excitatory and inhibitory cell types in the bulb and the anatomical architecture of their connection requires a nonsymmetric coupling matrix. As the mean input level rises during each breath of the animal, the system bifurcates from homogenous equilibrium to a spatially patterned oscillation. The theory of multiple Hopf bifurcations is employed to find coupled equations for the amplitudes of these unstable oscillatory modes independent of frequency. This allows a view of stored periodic attractors as fixed points of a gradient vector field and thereby recovers the more familiar dynamical systems picture of associative memory.
International Nuclear Information System (INIS)
Ji, J.C.; Zhang, N.
2009-01-01
Non-resonant bifurcations of codimension two may appear in the controlled van der Pol-Duffing oscillator when two critical time delays corresponding to a double Hopf bifurcation have the same value. With the aid of centre manifold theorem and the method of multiple scales, the non-resonant response and two types of primary resonances of the forced van der Pol-Duffing oscillator at non-resonant bifurcations of codimension two are investigated by studying the possible solutions and their stability of the four-dimensional ordinary differential equations on the centre manifold. It is shown that the non-resonant response of the forced oscillator may exhibit quasi-periodic motions on a two- or three-dimensional (2D or 3D) torus. The primary resonant responses admit single and mixed solutions and may exhibit periodic motions or quasi-periodic motions on a 2D torus. Illustrative examples are presented to interpret the dynamics of the controlled system in terms of two dummy unfolding parameters and exemplify the periodic and quasi-periodic motions. The analytical predictions are found to be in good agreement with the results of numerical integration of the original delay differential equation.
Fully developed turbulence via Feigenbaum's period-doubling bifurcations
International Nuclear Information System (INIS)
Duong-van, M.
1987-08-01
Since its publication in 1978, Feigenbaum's predictions of the onset of turbulence via period-doubling bifurcations have been thoroughly borne out experimentally. In this paper, Feigenbaum's theory is extended into the regime in which we expect to see fully developed turbulence. We develop a method of averaging that imposes correlations in the fluctuating system generated by this map. With this averaging method, the field variable is obtained by coarse-graining, while microscopic fluctuations are preserved in all averaging scales. Fully developed turbulence will be shown to be a result of microscopic fluctuations with proper averaging. Furthermore, this model preserves Feigenbaum's results on the physics of bifurcations at the onset of turbulence while yielding additional physics both at the onset of turbulence and in the fully developed turbulence regime
A Method to Determine Oscillation Emergence Bifurcation in Time-Delayed LTI System with Single Lag
Directory of Open Access Journals (Sweden)
Yu Xiaodan
2014-01-01
Full Text Available One type of bifurcation named oscillation emergence bifurcation (OEB found in time-delayed linear time invariant (abbr. LTI systems is fully studied. The definition of OEB is initially put forward according to the eigenvalue variation. It is revealed that a real eigenvalue splits into a pair of conjugated complex eigenvalues when an OEB occurs, which means the number of the system eigenvalues will increase by one and a new oscillation mode will emerge. Next, a method to determine OEB bifurcation in the time-delayed LTI system with single lag is developed based on Lambert W function. A one-dimensional (1-dim time-delayed system is firstly employed to explain the mechanism of OEB bifurcation. Then, methods to determine the OEB bifurcation in 1-dim, 2-dim, and high-dimension time-delayed LTI systems are derived. Finally, simulation results validate the correctness and effectiveness of the presented method. Since OEB bifurcation occurs with a new oscillation mode emerging, work of this paper is useful to explore the complex phenomena and the stability of time-delayed dynamic systems.
Experimental bifurcation analysis of an impact oscillator – Determining stability
DEFF Research Database (Denmark)
Bureau, Emil; Schilder, Frank; Elmegård, Michael
2014-01-01
We propose and investigate three different methods for assessing stability of dynamical equilibrium states during experimental bifurcation analysis, using a control-based continuation method. The idea is to modify or turn off the control at an equilibrium state and study the resulting behavior...
Bifurcation study of phase oscillator systems with attractive and repulsive interaction
Burylko, Oleksandr; Kazanovich, Yakov; Borisyuk, Roman
2014-08-01
We study a model of globally coupled phase oscillators that contains two groups of oscillators with positive (synchronizing) and negative (desynchronizing) incoming connections for the first and second groups, respectively. This model was previously studied by Hong and Strogatz (the Hong-Strogatz model) in the case of a large number of oscillators. We consider a generalized Hong-Strogatz model with a constant phase shift in coupling. Our approach is based on the study of invariant manifolds and bifurcation analysis of the system. In the case of zero phase shift, various invariant manifolds are analytically described and a new dynamical mode is found. In the case of a nonzero phase shift we obtained a set of bifurcation diagrams for various systems with three or four oscillators. It is shown that in these cases system dynamics can be complex enough and include multistability and chaotic oscillations.
Hydrodynamic bifurcation in electro-osmotically driven periodic flows
Morozov, Alexander; Marenduzzo, Davide; Larson, Ronald G.
2018-06-01
In this paper, we report an inertial instability that occurs in electro-osmotically driven channel flows. We assume that the charge motion under the influence of an externally applied electric field is confined to a small vicinity of the channel walls that, effectively, drives a bulk flow through a prescribed slip velocity at the boundaries. Here, we study spatially periodic wall velocity modulations in a two-dimensional straight channel numerically. At low slip velocities, the bulk flow consists of a set of vortices along each wall that are left-right symmetric, while at sufficiently high slip velocities, this flow loses its stability through a supercritical bifurcation. Surprisingly, the flow state that bifurcates from a left-right symmetric base flow has a rather strong mean component along the channel, which is similar to pressure-driven velocity profiles. The instability sets in at rather small Reynolds numbers of about 20-30, and we discuss its potential applications in microfluidic devices.
International Nuclear Information System (INIS)
Jiang Yu; Lozada-Cassou, M.; Vinet, A.
2003-01-01
The spatiotemporal dynamics of networks based on a ring of coupled oscillators with regular shortcuts beyond the nearest-neighbor couplings is studied by using master stability equations and numerical simulations. The generic criterion for dynamic synchronization has been extended to arbitrary network topologies with zero row-sum. The symmetry-breaking oscillation patterns that resulted from the Hopf bifurcation from synchronous states are analyzed by the symmetry group theory
Directory of Open Access Journals (Sweden)
Rong Haiwu
2014-01-01
Full Text Available The erosion of the safe basins and chaotic motions of a nonlinear vibroimpact oscillator under both harmonic and bounded random noise is studied. Using the Melnikov method, the system’s Melnikov integral is computed and the parametric threshold for chaotic motions is obtained. Using the Monte-Carlo and Runge-Kutta methods, the erosion of the safe basins is also discussed. The sudden change in the character of the stochastic safe basins when the bifurcation parameter of the system passes through a critical value may be defined as an alternative stochastic bifurcation. It is founded that random noise may destroy the integrity of the safe basins, bring forward the occurrence of the stochastic bifurcation, and make the parametric threshold for motions vary in a larger region, hence making the system become more unsafely and chaotic motions may occur more easily.
Energy Technology Data Exchange (ETDEWEB)
Shimizu, Kuniyasu, E-mail: kuniyasu.shimizu@it-chiba.ac.jp [Department of Electrical, Electronics and Computer Engineering, Chiba Institute of Technology, Narashino 275-0016 (Japan); Sekikawa, Munehisa [Department of Mechanical and Intelligent Engineering, Utsunomiya University, Utsunomiya 321-8585 (Japan); Inaba, Naohiko [Organization for the Strategic Coordination of Research and Intellectual Property, Meiji University, Kawasaki 214-8571 (Japan)
2015-02-15
Bifurcations of complex mixed-mode oscillations denoted as mixed-mode oscillation-incrementing bifurcations (MMOIBs) have frequently been observed in chemical experiments. In a previous study [K. Shimizu et al., Physica D 241, 1518 (2012)], we discovered an extremely simple dynamical circuit that exhibits MMOIBs. Our model was represented by a slow/fast Bonhoeffer-van der Pol circuit under weak periodic perturbation near a subcritical Andronov-Hopf bifurcation point. In this study, we experimentally and numerically verify that our dynamical circuit captures the essence of the underlying mechanism causing MMOIBs, and we observe MMOIBs and chaos with distinctive waveforms in real circuit experiments.
Energy Technology Data Exchange (ETDEWEB)
Horley, Paul P., E-mail: paul.horley@cimav.edu.mx [Centro de Investigación en Materiales Avanzados, S.C. (CIMAV), Chihuahua/Monterrey, 120 Avenida Miguel de Cervantes, 31109 Chihuahua (Mexico); Kushnir, Mykola Ya. [Yuri Fedkovych Chernivtsi National University, 2 Kotsyubynsky str., 58012 Chernivtsi (Ukraine); Morales-Meza, Mishel [Centro de Investigación en Materiales Avanzados, S.C. (CIMAV), Chihuahua/Monterrey, 120 Avenida Miguel de Cervantes, 31109 Chihuahua (Mexico); Sukhov, Alexander [Institut für Physik, Martin-Luther Universität Halle-Wittenberg, 06120 Halle (Saale) (Germany); Rusyn, Volodymyr [Yuri Fedkovych Chernivtsi National University, 2 Kotsyubynsky str., 58012 Chernivtsi (Ukraine)
2016-04-01
We report on complex magnetization dynamics in a forced spin valve oscillator subjected to a varying magnetic field and a constant spin-polarized current. The transition from periodic to chaotic magnetic motion was illustrated with bifurcation diagrams and Hausdorff dimension – the methods developed for dissipative self-organizing systems. It was shown that bifurcation cascades can be obtained either by tuning the injected spin-polarized current or by changing the magnitude of applied magnetic field. The order–chaos transition in magnetization dynamics can be also directly observed from the hysteresis curves. The resulting complex oscillations are useful for development of spin-valve devices operating in harmonic and chaotic modes.
Periodic solutions and bifurcations of delay-differential equations
International Nuclear Information System (INIS)
He Jihuan
2005-01-01
In this Letter a simple but effective iteration method is proposed to search for limit cycles or bifurcation curves of delay-differential equations. An example is given to illustrate its convenience and effectiveness
Yang, YongGe; Xu, Wei; Yang, Guidong
2018-04-01
To the best of authors' knowledge, little work was referred to the study of a noisy vibro-impact oscillator with a fractional derivative. Stochastic bifurcations of a vibro-impact oscillator with two kinds of fractional derivative elements driven by Gaussian white noise excitation are explored in this paper. We can obtain the analytical approximate solutions with the help of non-smooth transformation and stochastic averaging method. The numerical results from Monte Carlo simulation of the original system are regarded as the benchmark to verify the accuracy of the developed method. The results demonstrate that the proposed method has a satisfactory level of accuracy. We also discuss the stochastic bifurcation phenomena induced by the fractional coefficients and fractional derivative orders. The important and interesting result we can conclude in this paper is that the effect of the first fractional derivative order on the system is totally contrary to that of the second fractional derivative order.
Period-doubling bifurcation and chaos control in a discrete-time mosquito model
Directory of Open Access Journals (Sweden)
Qamar Din
2017-12-01
Full Text Available This article deals with the study of some qualitative properties of a discrete-time mosquito Model. It is shown that there exists period-doubling bifurcation for wide range of bifurcation parameter for the unique positive steady-state of given system. In order to control the bifurcation we introduced a feedback strategy. For further confirmation of complexity and chaotic behavior largest Lyapunov exponents are plotted.
Bifurcation analysis of the logistic map via two periodic impulsive forces
International Nuclear Information System (INIS)
Jiang Hai-Bo; Li Tao; Zeng Xiao-Liang; Zhang Li-Ping
2014-01-01
The complex dynamics of the logistic map via two periodic impulsive forces is investigated in this paper. The influences of the system parameter and the impulsive forces on the dynamics of the system are studied respectively. With the parameter varying, the system produces the phenomenon such as periodic solutions, chaotic solutions, and chaotic crisis. Furthermore, the system can evolve to chaos by a cascading of period-doubling bifurcations. The Poincaré map of the logistic map via two periodic impulsive forces is constructed and its bifurcation is analyzed. Finally, the Floquet theory is extended to explore the bifurcation mechanism for the periodic solutions of this non-smooth map. (general)
Discontinuous Spirals of Stable Periodic Oscillations
DEFF Research Database (Denmark)
Sack, Achim; Freire, Joana G.; Lindberg, Erik
2013-01-01
We report the experimental discovery of a remarkable organization of the set of self-generated periodic oscillations in the parameter space of a nonlinear electronic circuit. When control parameters are suitably tuned, the wave pattern complexity of the periodic oscillations is found to increase...
Bifurcations and degenerate periodic points in a three dimensional chaotic fluid flow
International Nuclear Information System (INIS)
Smith, L. D.; Rudman, M.; Lester, D. R.; Metcalfe, G.
2016-01-01
Analysis of the periodic points of a conservative periodic dynamical system uncovers the basic kinematic structure of the transport dynamics and identifies regions of local stability or chaos. While elliptic and hyperbolic points typically govern such behaviour in 3D systems, degenerate (parabolic) points also play an important role. These points represent a bifurcation in local stability and Lagrangian topology. In this study, we consider the ramifications of the two types of degenerate periodic points that occur in a model 3D fluid flow. (1) Period-tripling bifurcations occur when the local rotation angle associated with elliptic points is reversed, creating a reversal in the orientation of associated Lagrangian structures. Even though a single unstable point is created, the bifurcation in local stability has a large influence on local transport and the global arrangement of manifolds as the unstable degenerate point has three stable and three unstable directions, similar to hyperbolic points, and occurs at the intersection of three hyperbolic periodic lines. The presence of period-tripling bifurcation points indicates regions of both chaos and confinement, with the extent of each depending on the nature of the associated manifold intersections. (2) The second type of bifurcation occurs when periodic lines become tangent to local or global invariant surfaces. This bifurcation creates both saddle–centre bifurcations which can create both chaotic and stable regions, and period-doubling bifurcations which are a common route to chaos in 2D systems. We provide conditions for the occurrence of these tangent bifurcations in 3D conservative systems, as well as constraints on the possible types of tangent bifurcation that can occur based on topological considerations.
Hopf-pitchfork bifurcation and periodic phenomena in nonlinear financial system with delay
International Nuclear Information System (INIS)
Ding Yuting; Jiang Weihua; Wang Hongbin
2012-01-01
Highlights: ► We derive the unfolding of a financial system with Hopf-pitchfork bifurcation. ► We show the coexistence of a pair of stable small amplitudes periodic solutions. ► At the same time, also there is a pair of stable large amplitudes periodic solutions. ► Chaos can appear by period-doubling bifurcation far away from Hopf-pitchfork value. ► The study will be useful for interpreting economics phenomena in theory. - Abstract: In this paper, we identify the critical point for a Hopf-pitchfork bifurcation in a nonlinear financial system with delay, and derive the normal form up to third order with their unfolding in original system parameters near the bifurcation point by normal form method and center manifold theory. Furthermore, we analyze its local dynamical behaviors, and show the coexistence of a pair of stable periodic solutions. We also show that there coexist a pair of stable small-amplitude periodic solutions and a pair of stable large-amplitude periodic solutions for different initial values. Finally, we give the bifurcation diagram with numerical illustration, showing that the pair of stable small-amplitude periodic solutions can also exist in a large region of unfolding parameters, and the financial system with delay can exhibit chaos via period-doubling bifurcations as the unfolding parameter values are far away from the critical point of the Hopf-pitchfork bifurcation.
Oscillations of the fluid flow and the free surface in a cavity with a submerged bifurcated nozzle
International Nuclear Information System (INIS)
Kalter, R.; Tummers, M.J.; Kenjereš, S.; Righolt, B.W.; Kleijn, C.R.
2013-01-01
Highlights: • Self-sustained oscillations in a thin cavity with submerged nozzle were observed. • Three flow regimes are detected depending on nozzle depth and inlet velocity. • The three flow regimes have been summarized in a flow regime map. • PIV measurements are performed to link free surface behavior to the bulk-flow. • We report a close correlation between jet-behavior and free surface dynamics. -- Abstract: The free surface dynamics and sub-surface flow behavior in a thin (height and width much larger than thickness), liquid filled, rectangular cavity with a submerged bifurcated nozzle were investigated using free surface visualization and particle image velocimetry (PIV). Three regimes in the free surface behavior were identified, depending on nozzle depth and inlet velocity. For small nozzle depths, an irregular free surface is observed without clear periodicities. For intermediate nozzle depths and sufficiently high inlet velocities, natural mode oscillations consistent with gravity waves are present, while at large nozzle depths long term self-sustained asymmetric oscillations occur. For the latter case, time-resolved PIV measurements of the flow below the free surface indicated a strong oscillation of the direction with which each of the two jets issue from the nozzle. The frequency of the jet oscillation is identical to the free surface oscillation frequency. The two jets oscillate in anti-phase, causing the asymmetric free surface oscillation. The jets interact through a cross-flow in the gaps between the inlet channel and the front and back walls of the cavity
Sufficient conditions for a period incrementing big bang bifurcation in one-dimensional maps
International Nuclear Information System (INIS)
Avrutin, V; Granados, A; Schanz, M
2011-01-01
Typically, big bang bifurcation occurs for one (or higher)-dimensional piecewise-defined discontinuous systems whenever two border collision bifurcation curves collide transversely in the parameter space. At that point, two (feasible) fixed points collide with one boundary in state space and become virtual, and, in the one-dimensional case, the map becomes continuous. Depending on the properties of the map near the codimension-two bifurcation point, there exist different scenarios regarding how the infinite number of periodic orbits are born, mainly the so-called period adding and period incrementing. In our work we prove that, in order to undergo a big bang bifurcation of the period incrementing type, it is sufficient for a piecewise-defined one-dimensional map that the colliding fixed points are attractive and with associated eigenvalues of different signs
Sufficient conditions for a period incrementing big bang bifurcation in one-dimensional maps
Avrutin, V.; Granados, A.; Schanz, M.
2011-09-01
Typically, big bang bifurcation occurs for one (or higher)-dimensional piecewise-defined discontinuous systems whenever two border collision bifurcation curves collide transversely in the parameter space. At that point, two (feasible) fixed points collide with one boundary in state space and become virtual, and, in the one-dimensional case, the map becomes continuous. Depending on the properties of the map near the codimension-two bifurcation point, there exist different scenarios regarding how the infinite number of periodic orbits are born, mainly the so-called period adding and period incrementing. In our work we prove that, in order to undergo a big bang bifurcation of the period incrementing type, it is sufficient for a piecewise-defined one-dimensional map that the colliding fixed points are attractive and with associated eigenvalues of different signs.
Directory of Open Access Journals (Sweden)
Kirillov O.N.
2007-01-01
Full Text Available Paradoxical effect of small dissipative and gyroscopic forces on the stability of a linear non-conservative system, which manifests itself through the unpredictable at first sight behavior of the critical non-conservative load, is studied. By means of the analysis of bifurcation of multiple roots of the characteristic polynomial of the non-conservative system, the analytical description of this phenomenon is obtained. As mechanical examples two systems possessing friction induced oscillations are considered: a mass sliding over a conveyor belt and a model of a disc brake describing the onset of squeal during the braking of a vehicle.
Experimental bifurcation analysis of an impact oscillator - Tuning a non-invasive control scheme
DEFF Research Database (Denmark)
Bureau, Emil; Schilder, Frank; Santos, Ilmar
2013-01-01
We investigate a non-invasive, locally stabilizing control scheme necessary for an experimental bifurcation analysis. Our test-rig comprises a harmonically forced impact oscillator with hardening spring nonlinearity controlled by electromagnetic actuators, and serves as a prototype...... for electromagnetic bearings and other machinery with build-in actuators. We propose a sequence of experiments that allows one to choose optimal control-gains, filter parameters and settings for a continuation method without a priori study of a model. Depending on the algorithm for estimating the Jacobian required...
Directory of Open Access Journals (Sweden)
Ming Ma
2015-08-01
Full Text Available It has long been recognized that the diffusion of adsorbed molecules and clusters is the key controlling factor in most dynamical processes occurring on surfaces and in nanoscale-confined spaces. The ability to manipulate diffusion is essential for achieving efficient transport in nano- and microstructures and for many other applications. Through simulations and experiments, we found that under the influence of mechanical oscillations, the diffusion coefficient in nanoscale-confined regions can be greatly enhanced. This effect occurs due to bifurcations of particle trajectories caused by the reconstruction of the energy landscape during oscillations. We derive a parameter-free analytical model for the enhanced diffusion that is in excellent agreement with results of our numerical simulations. The oscillation-induced enhancement of diffusion may have interesting and promising applications in such areas as directed molecular transport, sorting of particles, and tribology. Here, our findings have been applied to studies of mechanical cleaning of surfaces from contamination. Through both experiments and simulations, we have shown that using an oscillating slider, one can significantly reduce the concentration of contaminants in a confined region, which is crucial for achieving superlow friction.
International Nuclear Information System (INIS)
Bondarenko, Vladimir E.; Cymbalyuk, Gennady S.; Patel, Girish; DeWeerth, Stephen P.; Calabrese, Ronald L.
2004-01-01
Oscillatory activity in the central nervous system is associated with various functions, like motor control, memory formation, binding, and attention. Quasiperiodic oscillations are rarely discussed in the neurophysiological literature yet they may play a role in the nervous system both during normal function and disease. Here we use a physical system and a model to explore scenarios for how quasiperiodic oscillations might arise in neuronal networks. An oscillatory system of two mutually inhibitory neuronal units is a ubiquitous network module found in nervous systems and is called a half-center oscillator. Previously we created a half-center oscillator of two identical oscillatory silicon (analog Very Large Scale Integration) neurons and developed a mathematical model describing its dynamics. In the mathematical model, we have shown that an in-phase limit cycle becomes unstable through a subcritical torus bifurcation. However, the existence of this torus bifurcation in experimental silicon two-neuron system was not rigorously demonstrated or investigated. Here we demonstrate the torus predicted by the model for the silicon implementation of a half-center oscillator using complex time series analysis, including bifurcation diagrams, mapping techniques, correlation functions, amplitude spectra, and correlation dimensions, and we investigate how the properties of the quasiperiodic oscillations depend on the strengths of coupling between the silicon neurons. The potential advantages and disadvantages of quasiperiodic oscillations (torus) for biological neural systems and artificial neural networks are discussed
Energy Technology Data Exchange (ETDEWEB)
Makarenko, A. V., E-mail: avm.science@mail.ru [Constructive Cybernetics Research Group (Russian Federation)
2016-10-15
A new class of bifurcations is defined in discrete dynamical systems, and methods for their diagnostics and the analysis of their properties are presented. The TQ-bifurcations considered are implemented in discrete mappings and are related to the qualitative rearrangement of the shape of trajectories in an extended space of states. Within the demonstration of the main capabilities of the toolkit, an analysis is carried out of a logistic mapping in a domain to the right of the period-doubling limit point. Five critical values of the parameter are found for which the geometric structure of the trajectories of the mapping experiences a qualitative rearrangement. In addition, an analysis is carried out of the so-called “trace map,” which arises in the problems of quantum-mechanical description of various properties of discrete crystalline and quasicrystalline lattices.
On period doubling bifurcations of cycles and the harmonic balance method
International Nuclear Information System (INIS)
Itovich, Griselda R.; Moiola, Jorge L.
2006-01-01
This works attempts to give quasi-analytical expressions for subharmonic solutions appearing in the vicinity of a Hopf bifurcation. Starting with well-known tools as the graphical Hopf method for recovering the periodic branch emerging from classical Hopf bifurcation, precise frequency and amplitude estimations of the limit cycle can be obtained. These results allow to attain approximations for period doubling orbits by means of harmonic balance techniques, whose accuracy is established by comparison of Floquet multipliers with continuation software packages. Setting up a few coefficients, the proposed methodology yields to approximate solutions that result from a second period doubling bifurcation of cycles and to extend the validity limits of the graphical Hopf method
International Nuclear Information System (INIS)
Liu, Yongbao; Wang, Qiang; Xu, Huidong
2017-01-01
The smooth bifurcation and non-smooth grazing bifurcation of periodic solution of three-degree-of-freedom vibro-impact systems with clearance are studied in this paper. Firstly, six-dimensional Poincaré maps are established through choosing suitable Poincaré section and solving periodic solutions of vibro-impact system. Then, as the analytic expressions of all eigenvalues of Jacobi matrix of six-dimensional map are unavailable, the numerical calculations to search for the critical bifurcation values point by point is a laborious job based on the classical critical criterion described by the properties of eigenvalues. To overcome the difficulty from the classical bifurcation criteria, the explicit critical criterion without using eigenvalues calculation of high-dimensional map is applied to determine bifurcation points of Co-dimension-one bifurcations and Co-dimension-two bifurcations, and then local dynamical behaviors of these bifurcations are further analyzed. Finally, the existence of the grazing periodic solution of the vibro-impact system and grazing bifurcation point are analyzed, the discontinuous grazing bifurcation behavior is studied based on the compound normal form map near the grazing point, the discontinuous jumping phenomenon and the co-existing multiple solutions near the grazing bifurcation point are revealed.
Bifurcation structure of a model of bursting pancreatic cells
DEFF Research Database (Denmark)
Mosekilde, Erik; Lading, B.; Yanchuk, S.
2001-01-01
One- and two-dimensional bifurcation studies of a prototypic model of bursting oscillations in pancreatic P-cells reveal a squid-formed area of chaotic dynamics in the parameter plane, with period-doubling bifurcations on one side of the arms and saddle-node bifurcations on the other. The transit......One- and two-dimensional bifurcation studies of a prototypic model of bursting oscillations in pancreatic P-cells reveal a squid-formed area of chaotic dynamics in the parameter plane, with period-doubling bifurcations on one side of the arms and saddle-node bifurcations on the other....... The transition from this structure to the so-called period-adding structure is found to involve a subcritical period-doubling bifurcation and the emergence of type-III intermittency. The period-adding transition itself is not smooth but consists of a saddle-node bifurcation in which (n + 1)-spike bursting...
Solar Dynamo Driven by Periodic Flow Oscillation
Mayr, Hans G.; Hartle, Richard E.; Einaudi, Franco (Technical Monitor)
2001-01-01
We have proposed that the periodicity of the solar magnetic cycle is determined by wave mean flow interactions analogous to those driving the Quasi Biennial Oscillation in the Earth's atmosphere. Upward propagating gravity waves would produce oscillating flows near the top of the radiation zone that in turn would drive a kinematic dynamo to generate the 22-year solar magnetic cycle. The dynamo we propose is built on a given time independent magnetic field B, which allows us to estimate the time dependent, oscillating components of the magnetic field, (Delta)B. The toroidal magnetic field (Delta)B(sub phi) is directly driven by zonal flow and is relatively large in the source region, (Delta)(sub phi)/B(sub Theta) much greater than 1. Consistent with observations, this field peaks at low latitudes and has opposite polarities in both hemispheres. The oscillating poloidal magnetic field component, (Delta)B(sub Theta), is driven by the meridional circulation, which is difficult to assess without a numerical model that properly accounts for the solar atmosphere dynamics. Scale-analysis suggests that (Delta)B(sub Theta) is small compared to B(sub Theta) in the dynamo region. Relative to B(sub Theta), however, the oscillating magnetic field perturbations are expected to be transported more rapidly upwards in the convection zone to the solar surface. As a result, (Delta)B(sub Theta) (and (Delta)B(sub phi)) should grow relative to B(sub Theta), so that the magnetic fields reverse at the surface as observed. Since the meridional and zonai flow oscillations are out of phase, the poloidal magnetic field peaks during times when the toroidal field reverses direction, which is observed. With the proposed wave driven flow oscillation, the magnitude of the oscillating poloidal magnetic field increases with the mean rotation rate of the fluid. This is consistent with the Bode-Blackett empirical scaling law, which reveals that in massive astrophysical bodies the magnetic moment tends
International Nuclear Information System (INIS)
Gerold, Bjoern; Prentice, Paul; Rachmilevitch, Itay
2013-01-01
The acoustic emissions from single cavitation clouds at an early stage of development in 0.521 MHz focused ultrasound of varying intensity, are detected and directly correlated to high-speed microscopic observations, recorded at 1 × 10 6 frames per second. At lower intensities, a stable regime of cloud response is identified whereby bubble-ensembles exhibit oscillations at half the driving frequency, which is also detected in the acoustic emission spectra. Higher intensities generate clouds that develop more rapidly, with increased nonlinearity evidenced by a bifurcation in the frequency of ensemble response, and in the acoustic emissions. A single bubble oscillation model is subject to equivalent ultrasound conditions and fitted to features in the hydrophone and high-speed spectral data, allowing an effective quiescent radius to be inferred for the clouds that evolve at each intensity. The approach indicates that the acoustic emissions originate from the ensemble dynamics and that the cloud acts as a single bubble of equivalent radius in terms of the scattered field. Jetting from component cavities on the periphery of clouds is regularly observed at higher intensities. The results may be of relevance for monitoring and controlling cavitation in therapeutic applications of focused ultrasound, where the phenomenon has the potential to mediate drug delivery from vasculature. (paper)
Limit cycles bifurcating from the periodic annulus of cubic homogeneous polynomial centers
Directory of Open Access Journals (Sweden)
Jaume Llibre
2015-10-01
Full Text Available We obtain an explicit polynomial whose simple positive real roots provide the limit cycles which bifurcate from the periodic orbits of any cubic homogeneous polynomial center when it is perturbed inside the class of all polynomial differential systems of degree n.
Amplitude calculation near a period-doubling bifurcation: An example
DEFF Research Database (Denmark)
Wiesenfeld, K.; Pedersen, Niels Falsig
1987-01-01
For the rf-driven Josephson junction, the dynamical behavior is studied near a period-doubling transition. The center-manifold theorem simplifies the problem and enables us to study only a first-order system, the parameters of which are expressed in terms of the Josephson-junction parameters....
Ngonghala, Calistus N; Teboh-Ewungkem, Miranda I; Ngwa, Gideon A
2015-06-01
We derive and study a deterministic compartmental model for malaria transmission with varying human and mosquito populations. Our model considers disease-related deaths, asymptomatic immune humans who are also infectious, as well as mosquito demography, reproduction and feeding habits. Analysis of the model reveals the existence of a backward bifurcation and persistent limit cycles whose period and size is determined by two threshold parameters: the vectorial basic reproduction number Rm, and the disease basic reproduction number R0, whose size can be reduced by reducing Rm. We conclude that malaria dynamics are indeed oscillatory when the methodology of explicitly incorporating the mosquito's demography, feeding and reproductive patterns is considered in modeling the mosquito population dynamics. A sensitivity analysis reveals important control parameters that can affect the magnitudes of Rm and R0, threshold quantities to be taken into consideration when designing control strategies. Both Rm and the intrinsic period of oscillation are shown to be highly sensitive to the mosquito's birth constant λm and the mosquito's feeding success probability pw. Control of λm can be achieved by spraying, eliminating breeding sites or moving them away from human habitats, while pw can be controlled via the use of mosquito repellant and insecticide-treated bed-nets. The disease threshold parameter R0 is shown to be highly sensitive to pw, and the intrinsic period of oscillation is also sensitive to the rate at which reproducing mosquitoes return to breeding sites. A global sensitivity and uncertainty analysis reveals that the ability of the mosquito to reproduce and uncertainties in the estimations of the rates at which exposed humans become infectious and infectious humans recover from malaria are critical in generating uncertainties in the disease classes.
Chaplygin sleigh with periodically oscillating internal mass
Bizyaev, Ivan A.; Borisov, Alexey V.; Kuznetsov, Sergey P.
2017-09-01
We consider the movement of Chaplygin sleigh on a plane that is a solid body with imposed nonholonomic constraint, which excludes the possibility of motions transversal to the constraint element (“knife-edge”), and complement the model with an attached mass, periodically oscillating relatively to the main platform of the sleigh. Numerical simulations indicate the occurrence of either unrestricted acceleration of the sleigh, or motions with bounded velocities and momenta, depending on parameters. We note the presence of phenomena characteristic to nonholonomic systems with complex dynamics; in particular, attractors occur responsible for chaotic motions. In addition, quasiperiodic regimes take place similar to those observed in conservative nonlinear dynamics.
Genesis and bifurcations of unstable periodic orbits in a jet flow
International Nuclear Information System (INIS)
Uleysky, M Yu; Budyansky, M V; Prants, S V
2008-01-01
We study the origin and bifurcations of typical classes of unstable periodic orbits in a jet flow that was introduced before as a kinematic model of chaotic advection, transport and mixing of passive scalars in meandering oceanic and atmospheric currents. A method to detect and locate the unstable periodic orbits and classify them by the origin and bifurcations is developed. We consider in detail period-1 and period-4 orbits playing an important role in chaotic advection. We introduce five classes of period-4 orbits: western and eastern ballistic ones, whose origin is associated with ballistic resonances of the fourth-order, rotational ones, associated with rotational resonances of the second and fourth orders and rotational-ballistic ones associated with a rotational-ballistic resonance. It is a new kind of unstable periodic orbits that may appear in a chaotic flow with jets and/or circulation cells. Varying the perturbation amplitude, we track out the origin and bifurcations of the orbits for each class
Sessoms, D. A.; Amon, A.; Courbin, L.; Panizza, P.
2010-10-01
The binary path selection of droplets reaching a T junction is regulated by time-delayed feedback and nonlinear couplings. Such mechanisms result in complex dynamics of droplet partitioning: numerous discrete bifurcations between periodic regimes are observed. We introduce a model based on an approximation that makes this problem tractable. This allows us to derive analytical formulae that predict the occurrence of the bifurcations between consecutive regimes, establish selection rules for the period of a regime, and describe the evolutions of the period and complexity of droplet pattern in a cycle with the key parameters of the system. We discuss the validity and limitations of our model which describes semiquantitatively both numerical simulations and microfluidic experiments.
Bifurcations and Periodic Solutions for an Algae-Fish Semicontinuous System
Directory of Open Access Journals (Sweden)
Chuanjun Dai
2013-01-01
Full Text Available We propose an algae-fish semicontinuous system for the Zeya Reservoir to study the control of algae, including biological and chemical controls. The bifurcation and periodic solutions of the system were studied using a Poincaré map and a geometric method. The existence of order-1 periodic solution of the system is discussed. Based on previous analysis, we investigated the change in the location of the order-1 periodic solution with variable parameters and we described the transcritical bifurcation of the system. Finally, we provided a series of numerical results to illustrate the feasibility of the theoretical results. These results may help to facilitate a better understanding of algal control in the Zeya Reservoir.
Replicate periodic windows in the parameter space of driven oscillators
Energy Technology Data Exchange (ETDEWEB)
Medeiros, E.S., E-mail: esm@if.usp.br [Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo (Brazil); Souza, S.L.T. de [Universidade Federal de Sao Joao del-Rei, Campus Alto Paraopeba, Minas Gerais (Brazil); Medrano-T, R.O. [Departamento de Ciencias Exatas e da Terra, Universidade Federal de Sao Paulo, Diadema, Sao Paulo (Brazil); Caldas, I.L. [Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo (Brazil)
2011-11-15
Highlights: > We apply a weak harmonic perturbation to control chaos in two driven oscillators. > We find replicate periodic windows in the driven oscillator parameter space. > We find that the periodic window replication is associated with the chaos control. - Abstract: In the bi-dimensional parameter space of driven oscillators, shrimp-shaped periodic windows are immersed in chaotic regions. For two of these oscillators, namely, Duffing and Josephson junction, we show that a weak harmonic perturbation replicates these periodic windows giving rise to parameter regions correspondent to periodic orbits. The new windows are composed of parameters whose periodic orbits have the same periodicity and pattern of stable and unstable periodic orbits already existent for the unperturbed oscillator. Moreover, these unstable periodic orbits are embedded in chaotic attractors in phase space regions where the new stable orbits are identified. Thus, the observed periodic window replication is an effective oscillator control process, once chaotic orbits are replaced by regular ones.
International Nuclear Information System (INIS)
Zhang Guangjun; Xu Jianxue; Wang Jue; Yue Zhifeng; Zou Hailin
2009-01-01
In this paper stochastic resonance induced by the novel random transitions of two-dimensional weak damping bistable Duffing oscillator is analyzed by moment method. This kind of novel transition refers to the one among three potential well on two sides of bifurcation point of original system at the presence of internal noise. Several conclusions are drawn. First, the semi-analytical result of stochastic resonance induced by the novel random transitions of two-dimensional weak damping bistable Duffing oscillator can be obtained, and the semi-analytical result is qualitatively compatible with the one of Monte Carlo simulation. Second, a bifurcation of double-branch fixed point curves occurs in the moment equations with noise intensity as their bifurcation parameter. Third, the bifurcation of moment equations corresponds to stochastic resonance of original system. Finally, the mechanism of stochastic resonance is presented from another viewpoint through analyzing the energy transfer induced by the bifurcation of moment equation.
Periodic and chaotic oscillations in a tumor and immune system interaction model with three delays
International Nuclear Information System (INIS)
Bi, Ping; Ruan, Shigui; Zhang, Xinan
2014-01-01
In this paper, a tumor and immune system interaction model consisted of two differential equations with three time delays is considered in which the delays describe the proliferation of tumor cells, the process of effector cells growth stimulated by tumor cells, and the differentiation of immune effector cells, respectively. Conditions for the asymptotic stability of equilibria and existence of Hopf bifurcations are obtained by analyzing the roots of a second degree exponential polynomial characteristic equation with delay dependent coefficients. It is shown that the positive equilibrium is asymptotically stable if all three delays are less than their corresponding critical values and Hopf bifurcations occur if any one of these delays passes through its critical value. Numerical simulations are carried out to illustrate the rich dynamical behavior of the model with different delay values including the existence of regular and irregular long periodic oscillations
Periodic motions and grazing in a harmonically forced, piecewise, linear oscillator with impacts
International Nuclear Information System (INIS)
Luo, Albert C.J.; Chen Lidi
2005-01-01
In this paper, an idealized, piecewise linear system is presented to model the vibration of gear transmission systems. Periodic motions in a generalized, piecewise linear oscillator with perfectly plastic impacts are predicted analytically. The analytical predictions of periodic motion are based on the mapping structures, and the generic mappings based on the discontinuous boundaries are developed. This method for the analytical prediction of the periodic motions in non-smooth dynamic systems can give all possible periodic motions based on the adequate mapping structures. The stability and bifurcation conditions for specified periodic motions are obtained. The periodic motions and grazing motion are demonstrated. This model is applicable to prediction of periodic motion in nonlinear dynamics of gear transmission systems
Harikrishnan, K. P.
2018-02-01
We consider the simplest model in the family of discrete predator-prey system and introduce for the first time an environmental factor in the evolution of the system by periodically modulating the natural death rate of the predator. We show that with the introduction of environmental modulation, the bifurcation structure becomes much more complex with bubble structure and inverse period doubling bifurcation. The model also displays the peculiar phenomenon of coexistence of multiple limit cycles in the domain of attraction for a given parameter value that combine and finally gets transformed into a single strange attractor as the control parameter is increased. To identify the chaotic regime in the parameter plane of the model, we apply the recently proposed scheme based on the correlation dimension analysis. We show that the environmental modulation is more favourable for the stable coexistence of the predator and the prey as the regions of fixed point and limit cycle in the parameter plane increase at the expense of chaotic domain.
Mixed-Mode Oscillations Due to a Singular Hopf Bifurcation in a Forest Pest Model
DEFF Research Database (Denmark)
Brøns, Morten; Desroches, Mathieu; Krupa, Martin
2015-01-01
In a forest pest model, young trees are distinguished from old trees. The pest feeds on old trees. The pest grows on a fast scale, the young trees on an intermediate scale, and the old trees on a slow scale. A combination of a singular Hopf bifurcation and a “weak return” mechanism, characterized...
Amplitude death and spatiotemporal bifurcations in nonlocally delay-coupled oscillators
International Nuclear Information System (INIS)
Guo, Yuxiao; Niu, Ben
2015-01-01
Amplitude death and spatiotemporal oscillations are remarkable patterns in coupled systems. We consider a ring of n identical oscillators with distance-dependent couplings and time delay. The amplitude death region is the intersection of three stable regions. Employing the method of multiple scales and normal form theory, the stability and criticality of spatiotemporal oscillations are determined. Around the amplitude death boundary there exist one branch of synchronized oscillations, n − 3 branches of co-existing phase-locked oscillations, n branches of mirror-reflecting oscillations, n branches of standing-wave oscillations, one branch of quasiperiodic oscillations and two branches of co-existing synchronized oscillations. It is proved that amplitude death is robust to small inhomogeneity of couplings, and the stability of synchronized or phase-locked oscillations inherits that of the individual decoupled oscillator. For the arbitrary form of coupling functions, some general results are also obtained for the thermodynamic limit. Finally, two examples are given to support the main results. (paper)
Short periodic oscillations of the dwarf nova VW Hydri
International Nuclear Information System (INIS)
Haefner, R.; Schoembs, R.
1977-01-01
A coherent oscillation of approximately 88 s period and 0.m005 amplitude was detected during the decline stage at the end of the long eruption of VW Hyi in December 1975. The period changed erratically between 86 and 90 s during eight nights. There are indications that the amplitude depends on the phase of the orbital revolution. The new period favours models in which such oscillations are caused by the orbital motion of inhomogeneities in the disc. (orig.) [de
Spatial interaction creates period-doubling bifurcation and chaos of urbanization
International Nuclear Information System (INIS)
Chen Yanguang
2009-01-01
This paper provides a new way of looking at complicated dynamics of simple mathematical models. The complicated behavior of simple equations is one of the headstreams of chaos theory. However, a recent study based on dynamical equations of urbanization shows that there are still some undiscovered secrets behind the simple mathematical models such as logistic equation. The rural-urban interaction model can also display varied kinds of complicated dynamics, including period-doubling bifurcation and chaos. The two-dimension map of urbanization presents the same dynamics as that from the one-dimension logistic map. In theory, the logistic equation can be derived from the two-population interaction model. This seems to suggest that the complicated behavior of simple models results from interaction rather than pure intrinsic randomicity. In light of this idea, the classical predator-prey interaction model can be revised to explain the complex dynamics of logistic equation in physical and social sciences.
Periodic synchronization and chimera in conformist and contrarian oscillators
Hong, Hyunsuk
2014-06-01
We consider a system of phase oscillators that couple with both attractive and repulsive interaction under a pinning force and explore collective behavior of the system. The oscillators can be divided into two subpopulations of "conformist" oscillators with attractive interaction and "contrarian" ones with repulsive interaction. We find that the interplay between the pinning force and the opposite relationship of the conformist and contrarian oscillators induce peculiar dynamic states: periodic synchronization, breathing chimera, and fully pinned state depending on the fraction of the conformists. Using the Watanabe-Strogatz transformation, we reduce the dynamics into a low-dimensional one and find that the above dynamic states are generated from the reduced dynamics.
Ferruzzo Correa, Diego P.; Bueno, Átila M.; Castilho Piqueira, José R.
2017-04-01
In this paper we investigate stability conditions for small-amplitude periodic solutions emerging near symmetry-preserving Hopf bifurcations in a time-delayed fully-connected N-node PLL network. The study of this type of systems which includes the time delay between connections has attracted much attention among researchers mainly because the delayed coupling between nodes emerges almost naturally in mathematical modeling in many areas of science such as neurobiology, population dynamics, physiology and engineering. In a previous work it has been shown that symmetry breaking and symmetry preserving Hopf bifurcations can emerge in the parameter space. We analyze the stability along branches of periodic solutions near fully-synchronized Hopf bifurcations in the fixed-point space, based on the reduction of the infinite-dimensional space onto a two-dimensional center manifold in normal form. Numerical results are also presented in order to confirm our analytical results.
Bifurcation structure of a model of bursting pancreatic cells
DEFF Research Database (Denmark)
Mosekilde, Erik; Lading, B.; Yanchuk, S.
2001-01-01
. The transition from this structure to the so-called period-adding structure is found to involve a subcritical period-doubling bifurcation and the emergence of type-III intermittency. The period-adding transition itself is not smooth but consists of a saddle-node bifurcation in which (n + 1)-spike bursting...... behavior is born, slightly overlapping with a subcritical period-doubling bifurcation in which n-spike bursting behavior loses its stability.......One- and two-dimensional bifurcation studies of a prototypic model of bursting oscillations in pancreatic P-cells reveal a squid-formed area of chaotic dynamics in the parameter plane, with period-doubling bifurcations on one side of the arms and saddle-node bifurcations on the other...
On the short periods oscillation in relativistic stars
International Nuclear Information System (INIS)
Aquilano, R.; Morales, S.; Navone, H.; Sevilla, D.; Zorzi, A.
2009-01-01
We expand the study of neutron and strange matter stars with general relativistic formalism. We analyze the correlation with the observational data short periods oscillations in these stars, and we intend to discriminate between them.
The period adding and incrementing bifurcations: from rotation theory to applications
DEFF Research Database (Denmark)
Granados, Albert; Alseda, Lluis; Krupa, Maciej
2017-01-01
This survey article is concerned with the study of bifurcations of piecewise-smooth maps. We review the literature in circle maps and quasi-contractions and provide paths through this literature to prove sufficient conditions for the occurrence of two types of bifurcation scenarios involving rich...
Periodic Solutions for Highly Nonlinear Oscillation Systems
DEFF Research Database (Denmark)
Ghadimi, M; Barari, Amin; Kaliji, H.D
2012-01-01
In this paper, Frequency-Amplitude Formulation is used to analyze the periodic behavior of tapered beam as well as two complex nonlinear systems. Many engineering structures, such as offshore foundations, oil platform supports, tower structures and moving arms, are modeled as tapered beams...
Dynamical bifurcation in a system of coupled oscillators with slowly varying parameters
Directory of Open Access Journals (Sweden)
Igor Parasyuk
2016-08-01
Full Text Available This paper deals with a fast-slow system representing n nonlinearly coupled oscillators with slowly varying parameters. We find conditions which guarantee that all omega-limit sets near the slow surface of the system are equilibria and invariant tori of all dimensions not exceeding n, the tori of dimensions less then n being hyperbolic. We show that a typical trajectory demonstrates the following transient process: while its slow component is far from the stationary points of the slow vector field, the fast component exhibits damping oscillations; afterwards, the former component enters and stays in a small neighborhood of some stationary point, and the oscillation amplitude of the latter begins to increase; eventually the trajectory is attracted by an n-dimesional invariant torus and a multi-frequency oscillatory regime is established.
Induction of Hopf bifurcation and oscillation death by delays in coupled networks
International Nuclear Information System (INIS)
Cheng, C.-Y.
2009-01-01
This work explores a system of two coupled networks that each has four nodes. Delayed effects of short-cuts in each network and the coupling between the two groups are considered. When the short-cut delay is fixed, the arising and death of oscillations are caused by the variational coupling delay.
Can oscillating physics explain an apparently periodic universe?
International Nuclear Information System (INIS)
Hill, C.T.; Steinhardt, P.J.; Turner, M.S.; Chicago Univ., IL; Fermi National Accelerator Lab., Batavia, IL
1990-01-01
Recently, Broadhurst et al. have reported an apparent periodicity in a north-south pencil-beam red-shift survey of galaxies. We consider whether the periodicity may be an illusion caused by the oscillations of physical constants. Should the periodicity be disproven by subsequent observations, the same analysis can be used to derive new, stringent limits on the variations of physical constants. (orig.)
Nonlinear effects on Turing patterns: Time oscillations and chaos
Aragó n, J. L.; Barrio, R. A.; Woolley, T. E.; Baker, R. E.; Maini, P. K.
2012-01-01
consequence, the patterns oscillate in time. When varying a single parameter, a series of bifurcations leads to period doubling, quasiperiodic, and chaotic oscillations without modifying the underlying Turing pattern. A Ruelle-Takens-Newhouse route to chaos
Directory of Open Access Journals (Sweden)
Randhir Singh Baghel
2012-02-01
Full Text Available In this article, we propose a three dimensional mathematical model of phytoplankton dynamics with the help of reaction-diffusion equations that studies the bifurcation and pattern formation mechanism. We provide an analytical explanation for understanding phytoplankton dynamics with three population classes: susceptible, incubated, and infected. This model has a Holling type II response function for the population transformation from susceptible to incubated class in an aquatic ecosystem. Our main goal is to provide a qualitative analysis of Hopf bifurcation mechanisms, taking death rate of infected phytoplankton as bifurcation parameter, and to study further spatial patterns formation due to spatial diffusion. Here analytical findings are supported by the results of numerical experiments. It is observed that the coexistence of all classes of population depends on the rate of diffusion. Also we obtained the time evaluation pattern formation of the spatial system.
Image Segmentation Based on Period Difference of the Oscillation
Institute of Scientific and Technical Information of China (English)
王直杰; 张珏; 范宏; 柯克峰
2004-01-01
A new method for image segmentation based on pulse neural network is proposed. Every neuron in the network represents one pixel in the image and the network is locally connected.Each group of the neurons that correspond to each object synchronizes while different gronps of the neurons oscillate at different period. Applying this period difference,different objects are divided. In addition to simulation, an analysis of the mechanism of the method is presented in this paper.
Computation of periods of acoustical oscillations of the sun
International Nuclear Information System (INIS)
Vorontsov, S.V.; Zharkov, V.N.
1977-01-01
It is stated that regular pulsations of the Sun were first reported in 1975-76 by several investigators (see Nature 259:87 and 92 (1976)), and that these oscillations were difficult to identify. It was decided to compute the periods of some acoustical modes using experience gained in calculations of free oscillations of Jupiter and Saturn, employing some complete solar models for the interior, the convective zone and the solar atmosphere. The equations employed and the methods of computations are described, and the results are given. (U.K.)
Hopf bifurcation analysis of Chen circuit with direct time delay feedback
International Nuclear Information System (INIS)
Hai-Peng, Ren; Wen-Chao, Li; Ding, Liu
2010-01-01
Direct time delay feedback can make non-chaotic Chen circuit chaotic. The chaotic Chen circuit with direct time delay feedback possesses rich and complex dynamical behaviours. To reach a deep and clear understanding of the dynamics of such circuits described by delay differential equations, Hopf bifurcation in the circuit is analysed using the Hopf bifurcation theory and the central manifold theorem in this paper. Bifurcation points and bifurcation directions are derived in detail, which prove to be consistent with the previous bifurcation diagram. Numerical simulations and experimental results are given to verify the theoretical analysis. Hopf bifurcation analysis can explain and predict the periodical orbit (oscillation) in Chen circuit with direct time delay feedback. Bifurcation boundaries are derived using the Hopf bifurcation analysis, which will be helpful for determining the parameters in the stabilisation of the originally chaotic circuit
Periodic oscillation and exponential stability of delayed CNNs
Cao, Jinde
2000-05-01
Both the global exponential stability and the periodic oscillation of a class of delayed cellular neural networks (DCNNs) is further studied in this Letter. By applying some new analysis techniques and constructing suitable Lyapunov functionals, some simple and new sufficient conditions are given ensuring global exponential stability and the existence of periodic oscillatory solution of DCNNs. These conditions can be applied to design globally exponentially stable DCNNs and periodic oscillatory DCNNs and easily checked in practice by simple algebraic methods. These play an important role in the design and applications of DCNNs.
Bifurcation and instability problems in vortex wakes
DEFF Research Database (Denmark)
Aref, Hassan; Brøns, Morten; Stremler, Mark A.
2007-01-01
A number of instability and bifurcation problems related to the dynamics of vortex wake flows are addressed using various analytical tools and approaches. We discuss the bifurcations of the streamline pattern behind a bluff body as a vortex wake is produced, a theory of the universal Strouhal......-Reynolds number relation for vortex wakes, the bifurcation diagram for "exotic" wake patterns behind an oscillating cylinder first determined experimentally by Williamson & Roshko, and the bifurcations in topology of the streamlines pattern in point vortex streets. The Hamiltonian dynamics of point vortices...... in a periodic strip is considered. The classical results of von Kármán concerning the structure of the vortex street follow from the two-vortices-in-a-strip problem, while the stability results follow largely from a four-vortices-in-a-strip analysis. The three-vortices-in-a-strip problem is argued...
Whitchurch, Brandon; Kevrekidis, Panayotis G.; Koukouloyannis, Vassilis
2018-01-01
In this work we study the dynamical behavior of two interacting vortex pairs, each one of them consisting of two point vortices with opposite circulation in the two-dimensional plane. The vortices are considered as effective particles and their interaction can be described in classical mechanics terms. We first construct a Poincaré section, for a typical value of the energy, in order to acquire a picture of the structure of the phase space of the system. We divide the phase space in different regions which correspond to qualitatively distinct motions and we demonstrate its different temporal evolution in the "real" vortex space. Our main emphasis is on the leapfrogging periodic orbit, around which we identify a region that we term the "leapfrogging envelope" which involves mostly regular motions, such as higher order periodic and quasiperiodic solutions. We also identify the chaotic region of the phase plane surrounding the leapfrogging envelope as well as the so-called walkabout and braiding motions. Varying the energy as our control parameter, we construct a bifurcation tree of the main leapfrogging solution and its instabilities, as well as the instabilities of its daughter branches. We identify the symmetry-breaking instability of the leapfrogging solution (in line with earlier works), and also obtain the corresponding asymmetric branches of periodic solutions. We then characterize their own instabilities (including period doubling ones) and bifurcations in an effort to provide a more systematic perspective towards the types of motions available to this dynamical system.
Nonlinear stability control and λ-bifurcation
International Nuclear Information System (INIS)
Erneux, T.; Reiss, E.L.; Magnan, J.F.; Jayakumar, P.K.
1987-01-01
Passive techniques for nonlinear stability control are presented for a model of fluidelastic instability. They employ the phenomena of λ-bifurcation and a generalization of it. λ-bifurcation occurs when a branch of flutter solutions bifurcates supercritically from a basic solution and terminates with an infinite period orbit at a branch of divergence solutions which bifurcates subcritically from the basic solution. The shape of the bifurcation diagram then resembles the greek letter λ. When the system parameters are in the range where flutter occurs by λ-bifurcation, then as the flow velocity increase the flutter amplitude also increases, but the frequencies of the oscillations decrease to zero. This diminishes the damaging effects of structural fatigue by flutter, and permits the flow speed to exceed the critical flutter speed. If generalized λ-bifurcation occurs, then there is a jump transition from the flutter states to a divergence state with a substantially smaller amplitude, when the flow speed is sufficiently larger than the critical flutter speed
Evolution of the clock from yeast to man by period-doubling folds in the cellular oscillator.
Klevecz, R R; Li, C M
2007-01-01
Analysis of genome-wide oscillations in transcription reveals that the cell is an oscillator and an attractor and that the maintenance of a stable phenotype requires that maximums in expression in clusters of transcripts must be poised at antipodal phases around the steady state-this is the dynamic architecture of phenotype. Plots of the path through concentration phase space taken by all of the transcripts of Saccharomyces cerevisiae yield a simple three-dimensional surface. How this surface might change as period lengthens or as a cell differentiates is at the center of current work. We have shown that changes in gene expression in response to mutation or perturbation by drugs occur through a folding or unfolding of the surface described by this circle of transcripts and we suggest that the path from this 40-minute oscillation to the cell cycle and circadian rhythms takes place through a series of period-two or period-three bifurcations. These foldings in the surface of the putative attractor result in an increasingly dense set of nested trajectories in the concentrations of message and protein. Evolutionary advantage might accrue to an organism that could change period by changes in just one or a few genes as day length increased from 4 hours in the prebiotic Earth, through 8 hours during the expansion of photoautotrophs, to the present 24 hours.
International Nuclear Information System (INIS)
Aulova, T V; Kravtsov, Nikolai V; Lariontsev, E G; Chekina, S N
2011-01-01
The synchronisation of periodic self-modulation oscillations in a ring Nd:YAG chip laser under an external periodic signal modulating the pump power has been experimentally investigated. A new quasi-periodic regime of synchronisation of self-modulation oscillations is found. The characteristic features of the behaviour of spectral and temporal structures of synchronised quasi-periodic oscillations with a change in the external signal frequency are studied. (control of laser radiation parameters)
International Nuclear Information System (INIS)
Cerrada, Lucia; San Martin, Jesus
2011-01-01
In this Letter, it is shown that from a two region partition of the phase space of a one-dimensional dynamical system, a p-region partition can be obtained for the CRL...LR...R orbits. That is, permutations associated with symbolic sequences are obtained. As a consequence, the trajectory in phase space is directly deduced from permutation. From this permutation other permutations associated with period-doubling and saddle-node bifurcation cascades are derived, as well as other composite permutations. - Research highlights: → Symbolic sequences are the usual topological approach to dynamical systems. → Permutations bear more physical information than symbolic sequences. → Period-doubling cascade permutations associated with original sequences are obtained. → Saddle-node cascade permutations associated with original sequences are obtained. → Composite permutations are derived.
Bifurcation and chaos in a Tessiet type food chain chemostat with pulsed input and washout
International Nuclear Information System (INIS)
Wang Fengyan; Hao Chunping; Chen Lansun
2007-01-01
In this paper, we introduce and study a model of a Tessiet type food chain chemostat with pulsed input and washout. We investigate the subsystem with substrate and prey and study the stability of the periodic solutions, which are the boundary periodic solutions of the system. The stability analysis of the boundary periodic solution yields an invasion threshold. By use of standard techniques of bifurcation theory, we prove that above this threshold there are periodic oscillations in substrate, prey and predator. Simple cycles may give way to chaos in a cascade of period-doubling bifurcations. Furthermore, by comparing bifurcation diagrams with different bifurcation parameters, we can see that the impulsive system shows two kinds of bifurcations, whose are period doubling and period halving
Holmes, Philip J.
1981-06-01
We study the instabilities known to aeronautical engineers as flutter and divergence. Mathematically, these states correspond to bifurcations to limit cycles and multiple equilibrium points in a differential equation. Making use of the center manifold and normal form theorems, we concentrate on the situation in which flutter and divergence become coupled, and show that there are essentially two ways in which this is likely to occur. In the first case the system can be reduced to an essential model which takes the form of a single degree of freedom nonlinear oscillator. This system, which may be analyzed by conventional phase-plane techniques, captures all the qualitative features of the full system. We discuss the reduction and show how the nonlinear terms may be simplified and put into normal form. Invariant manifold theory and the normal form theorem play a major role in this work and this paper serves as an introduction to their application in mechanics. Repeating the approach in the second case, we show that the essential model is now three dimensional and that far more complex behavior is possible, including nonperiodic and ‘chaotic’ motions. Throughout, we take a two degree of freedom system as an example, but the general methods are applicable to multi- and even infinite degree of freedom problems.
Bifurcations of propellant burning rate at oscillatory pressure
Energy Technology Data Exchange (ETDEWEB)
Novozhilov, Boris V. [N. N. Semenov Institute of Chemical Physics, Russian Academy of Science, 4 Kosygina St., Moscow 119991 (Russian Federation)
2006-06-15
A new phenomenon, the disparity between pressure and propellant burning rate frequencies, has revealed in numerical studies of propellant burning rate response to oscillatory pressure. As is clear from the linear approximation, under small pressure amplitudes, h, pressure and propellant burning rate oscillations occur with equal period T (T-solution). In the paper, however, it is shown that at a certain critical value of the parameter h the system in hand undergoes a bifurcation so that the T-solution converts to oscillations with period 2T (2T-solution). When the bifurcation parameter h increases, the subsequent behavior of the system becomes complicated. It is obtained a sequence of period doubling to 4T-solution and 8T-solution. Beyond a certain value of the bifurcation parameter h an apparently fully chaotic solution is found. These effects undoubtedly should be taken into account in studies of oscillatory processes in combustion chambers. (Abstract Copyright [2006], Wiley Periodicals, Inc.)
Li, Li; Xu, Jian
Time delay is inevitable in unidirectionally coupled drive-free vibratory gyroscope system. The effect of time delay on the gyroscope system is studied in this paper. To this end, amplitude death and Hopf bifurcation induced by small time delay are first investigated by analyzing the related characteristic equation. Then, the direction of Hopf bifurcations and stability of Hopf-bifurcating periodic oscillations are determined by calculating the normal form on the center manifold. Next, spatiotemporal patterns of these Hopf-bifurcating periodic oscillations are analyzed by using the symmetric bifurcation theory of delay differential equations. Finally, it is found that numerical simulations agree with the associated analytic results. These phenomena could be induced although time delay is very small. Therefore, it is shown that time delay is an important factor which influences the sensitivity and accuracy of the gyroscope system and cannot be neglected during the design and manufacture.
Rapid oscillations in cataclysmic variables. VI. Periodicities in erupting dwarf novae
International Nuclear Information System (INIS)
Patterson, J.
1981-01-01
We report an extensive study of the coherent oscillations observed in high-speed photometry of dwarf novae during eruption. The oscillations are in all cases singly periodic and sinusoidal to the limits of measurement. The detection of oscillations in 14 separate eruptions of AH Her and SY Cnc enables a general study of period variations. The stars trace out characteristic loops (''banana diagrams'') in the period-intensity plane. New detections are also reported for SS Cyg, EM Cyg, and HT Cas
Asymmetry in Signal Oscillations Contributes to Efficiency of Periodic Systems.
Bae, Seul-A; Acevedo, Alison; Androulakis, Ioannis P
2016-01-01
Oscillations are an important feature of cellular signaling that result from complex combinations of positive- and negative-feedback loops. The encoding and decoding mechanisms of oscillations based on amplitude and frequency have been extensively discussed in the literature in the context of intercellular and intracellular signaling. However, the fundamental questions of whether and how oscillatory signals offer any competitive advantages-and, if so, what-have not been fully answered. We investigated established oscillatory mechanisms and designed a study to analyze the oscillatory characteristics of signaling molecules and system output in an effort to answer these questions. Two classic oscillators, Goodwin and PER, were selected as the model systems, and corresponding no-feedback models were created for each oscillator to discover the advantage of oscillating signals. Through simulating the original oscillators and the matching no-feedback models, we show that oscillating systems have the capability to achieve better resource-to-output efficiency, and we identify oscillatory characteristics that lead to improved efficiency.
Period-doubling cascades and strange attractors in the triple-well Φ6-Van der Pol oscillator
International Nuclear Information System (INIS)
Yu Jun; Zhang Rongbo; Pan Weizhen; Schimansky-Geier, L
2008-01-01
Duffing-Van der Pol equation with the fifth nonlinear-restoring force is investigated. The bifurcation structure and chaotic motion under the periodic perturbation are obtained by numerical simulations. Numerical simulations, including bifurcation diagrams, Lyapunov exponents, phase portraits and Poincare maps, exhibit some new complex dynamical behaviors of the system. Different routes to chaos, such as period doubling and quasi-periodic routes, and various kinds of strange attractors are also demonstrated
Lu, Jia; Zhang, Xiaoxing; Xiong, Hao
The chaotic van der Pol oscillator is a powerful tool for detecting defects in electric systems by using online partial discharge (PD) monitoring. This paper focuses on realizing weak PD signal detection in the strong periodic narrowband interference by using high sensitivity to the periodic narrowband interference signals and immunity to white noise and PD signals of chaotic systems. A new approach to removing the periodic narrowband interference by using a van der Pol chaotic oscillator is described by analyzing the motion characteristic of the chaotic oscillator on the basis of the van der Pol equation. Furthermore, the Floquet index for measuring the amplitude of periodic narrowband signals is redefined. The denoising signal processed by the chaotic van der Pol oscillators is further processed by wavelet analysis. Finally, the denoising results verify that the periodic narrowband and white noise interference can be removed efficiently by combining the theory of the chaotic van der Pol oscillator and wavelet analysis.
Investigation of Quasi-periodic Solar Oscillations in Sunspots Based on SOHO/MDI Magnetograms
Kallunki, J.; Riehokainen, A.
2012-10-01
In this work we study quasi-periodic solar oscillations in sunspots, based on the variation of the amplitude of the magnetic field strength and the variation of the sunspot area. We investigate long-period oscillations between three minutes and ten hours. The magnetic field synoptic maps were obtained from the SOHO/MDI. Wavelet (Morlet), global wavelet spectrum (GWS) and fast Fourier transform (FFT) methods are used in the periodicity analysis at the 95 % significance level. Additionally, the quiet Sun area (QSA) signal and an instrumental effect are discussed. We find several oscillation periods in the sunspots above the 95 % significance level: 3 - 5, 10 - 23, 220 - 240, 340 and 470 minutes, and we also find common oscillation periods (10 - 23 minutes) between the sunspot area variation and that of the magnetic field strength. We discuss possible mechanisms for the obtained results, based on the existing models for sunspot oscillations.
Mobility induces global synchronization of oscillators in periodic extended systems
International Nuclear Information System (INIS)
Peruani, Fernando; Nicola, Ernesto M; Morelli, Luis G
2010-01-01
We study the synchronization of locally coupled noisy phase oscillators that move diffusively in a one-dimensional ring. Together with the disordered and the globally synchronized states, the system also exhibits wave-like states displaying local order. We use a statistical description valid for a large number of oscillators to show that for any finite system there is a critical mobility above which all wave-like solutions become unstable. Through Langevin simulations, we show that the transition to global synchronization is mediated by a shift in the relative size of attractor basins associated with wave-like states. Mobility disrupts these states and paves the way for the system to attain global synchronization.
Relative Lyapunov Center Bifurcations
DEFF Research Database (Denmark)
Wulff, Claudia; Schilder, Frank
2014-01-01
Relative equilibria (REs) and relative periodic orbits (RPOs) are ubiquitous in symmetric Hamiltonian systems and occur, for example, in celestial mechanics, molecular dynamics, and rigid body motion. REs are equilibria, and RPOs are periodic orbits of the symmetry reduced system. Relative Lyapunov...... center bifurcations are bifurcations of RPOs from REs corresponding to Lyapunov center bifurcations of the symmetry reduced dynamics. In this paper we first prove a relative Lyapunov center theorem by combining recent results on the persistence of RPOs in Hamiltonian systems with a symmetric Lyapunov...... center theorem of Montaldi, Roberts, and Stewart. We then develop numerical methods for the detection of relative Lyapunov center bifurcations along branches of RPOs and for their computation. We apply our methods to Lagrangian REs of the N-body problem....
Quasi-Periodicity and Border-Collision Bifurcations in a DC-DC Converter with Pulsewidth Modulation
DEFF Research Database (Denmark)
Zhusubalaliyev, Zh. T.; Soukhoterin, E.A.; Mosekilde, Erik
2003-01-01
border-collision bifurcations (BCB) on a two-dimensional torus. The arrangement of the resonance domains within the parameter plane is related to the Farey series, and their internal structure is described. It is shown that transitions to chaos mainly occur through finite sequences of BCB. Some other...
International Nuclear Information System (INIS)
Papaloizou, J.; Pringle, J.E.
1978-01-01
The usual hypothesis, that the short-period coherent oscillations seen in cataclysmic variables are attributable to g modes in a slowly rotating white dwarf, is considered. It is shown that this hypothesis is untenable for three main reasons: (i) the observed periods are too short for reasonable white dwarf models, (ii) the observed variability of the oscillations is too rapid and (iii) the expected rotation of the white dwarf, due to accretion, invalidates the slow rotation assumption on which standard g-mode theory is based. The low-frequency spectrum of a rotating pulsating star is investigated taking the effects of rotation fully into account. In this case there are two sets of low-frequency modes, the g modes, and modes similar to Rossby waves in the Earth's atmosphere and oceans, which are designated r modes. Typical periods for such modes are 1/m times the rotation period of the white dwarfs outer layers (m is the aximuthal wavenumber). It is concluded that non-radial oscillations of rotating white dwarfs can account for the properties of the oscillations seen in dwarf novae. Application of these results to other systems is also discussed. (author)
Sarkar, Jayanta; Puska, Antti; Hassel, Juha; Hakonen, Pertti
2014-03-01
Bloch oscillating transistor (BOT) is mesoscopic current amplier based on a combination of a Josephson junction or a squid connected with a large resistor and a NIS junction. We have studied the dynamics of BOT near the bifurcation threshold. This is an important feature for an amplifier as this can be utilized to improve its performance characteristics. We have measured the I - V characteristics of the BOT with different base currents (IB) over a wide range of Josephson coupling energies (EJ) . The current gain (β) is found to be increasing with increasing IB and eventually diverging. We have found a record large β = 50 in our experiment. In order to determine the common mode rejection ratio (CMRR) of a differential pair BOT we have used two BOTs fabricated on the same chip. The common mode port is connected to the bases of the two BOTs and fed with varying voltages; simultaneously emitter currents of the two BOTs are recorded. In our experiment we found a 20dB of CMRR.
Excitation of high numbers harmonics by flows of oscillators in a periodic potential
International Nuclear Information System (INIS)
Buts, V.A.; Marekha, V.I.; Tolstoluzhsky, A.P.
2005-01-01
It is shown that the maximum of radiation spectrum of nonrelativistic oscillators, which move into a periodically inhomogeneous potential, can be in the region of high numbers harmonics. Spectrum of such oscillators radiation becomes similar to the radiation spectrum of relativistic oscillators. The equations, describing the non-linear self-consistent theory of excitations, of high numbers harmonics by ensemble of oscillators are formulated and its numerical analysis is conducted. The numerical analysis has confirmed the capability of radiation of high numbers of harmonics. Such peculiarity of radiation allows t expect of creation of nonrelativistic FEL
International Nuclear Information System (INIS)
Olmstead, W.E.; Davis, S.H.; Rosenblat, S.; Kath, W.L.
1986-01-01
A model equation containing a memory integral is posed. The extent of the memory, the relaxation time lambda, controls the bifurcation behavior as the control parameter R is increased. Small (large) lambda gives steady (periodic) bifurcation. There is a double eigenvalue at lambda = lambda 1 , separating purely steady (lambda 1 ) from combined steady/T-periodic (lambda > lambda 1 ) states with T → infinity as lambda → lambda + 1 . Analysis leads to the co-existence of stable steady/periodic states and as R is increased, the periodic states give way to the steady states. Numerical solutions show that this behavior persists away from lambda = lambda 1
Bifurcation analysis of nephron pressure and flow regulation
DEFF Research Database (Denmark)
Barfred, Mikael; Mosekilde, Erik; Holstein-Rathlou, N.-H.
1996-01-01
One- and two-dimensional continuation techniques are applied to study the bifurcation structure of a model of renal flow and pressure control. Integrating the main physiological mechanisms by which the individual nephron regulates the incoming blood flow, the model describes the interaction between...... the tubuloglomerular feedback and the response of the afferent arteriole. It is shown how a Hopf bifurcation leads the system to perform self-sustained oscillations if the feedback gain becomes sufficiently strong, and how a further increase of this parameter produces a folded structure of overlapping period...
Bifurcation and chaotic behavior in the Euler method for a Kaplan-Yorke prototype delay model
International Nuclear Information System (INIS)
Peng Mingshu
2004-01-01
A discrete model with a simple cubic nonlinearity term is treated in the study the rich dynamics of a prototype delayed dynamical system under Euler discretization. The effect of breaking the symmetry of the system is to create a wide complex operating conditions which would not otherwise be seen. These include multiple steady states, complex periodic oscillations, chaos by period doubling bifurcations
Periodic Forcing of a 555-IC Based Electronic Oscillator in the Strong Coupling Limit
Santillán, Moisés
We designed and developed a master-slave electronic oscillatory system (based on the 555-timer IC working in the astable mode), and investigated its dynamic behavior regarding synchronization. For that purpose, we measured the rotation numbers corresponding to the phase-locking rhythms achieved in a large set of values of the normalized forcing frequency (NFF) and of the coupling strength between the master and the slave oscillators. In particular, we were interested in the system behavior in the strong-coupling limit, because such problem has not been extensively studied from an experimental perspective. Our results indicate that, in such a limit, a degenerate codimension-2 bifurcation point at NFF = 2 exists, in which all the phase-locking regions converge. These findings were corroborated by means of a mathematical model developed to that end, as well as by ad hoc further experiments.
A bifurcation giving birth to order in an impulsively driven complex system
Energy Technology Data Exchange (ETDEWEB)
Seshadri, Akshay, E-mail: akshayseshadri@gmail.com; Sujith, R. I., E-mail: sujith@iitm.ac.in [Indian Institute of Technology Madras, Chennai (India)
2016-08-15
Nonlinear oscillations lie at the heart of numerous complex systems. Impulsive forcing arises naturally in many scenarios, and we endeavour to study nonlinear oscillators subject to such forcing. We model these kicked oscillatory systems as a piecewise smooth dynamical system, whereby their dynamics can be investigated. We investigate the problem of pattern formation in a turbulent combustion system and apply this formalism with the aim of explaining the observed dynamics. We identify that the transition of this system from low amplitude chaotic oscillations to large amplitude periodic oscillations is the result of a discontinuity induced bifurcation. Further, we provide an explanation for the occurrence of intermittent oscillations in the system.
Solar wind oscillations with a 1.3 year period
Richardson, John D.; Paularena, Karolen I.; Belcher, John W.; Lazarus, Alan J.
1994-01-01
The Interplanetary Monitoring Platform 8 (IMP-8) and Voyager 2 spacecraft have recently detected a very strong modulation in the solar wind speed with an approximately 1.3 year period. Combined with evidence from long-term auroral and magnetometer studies, this suggests that fundamental changes in the Sun occur on a roughly 1.3 year time scale.
Effect of various periodic forces on Duffing oscillator
Indian Academy of Sciences (India)
ω respectively. However, the Fourier series of all the forces except the force sin ωt considered in our study have various frequencies. The frequencies present in the forces and in the periodic solution confined to the left well alone corresponding to the amplitude f = 0.2 are studied by constructing the Fourier series. 352.
Bakala, P.; Goluchová, K.; Török, G.; Šrámková, E.; Abramowicz, M. A.; Vincent, F. H.; Mazur, G. P.
2015-09-01
Context. High-frequency (millisecond) quasi-periodic oscillations (HF QPOs) are observed in the X-ray power-density spectra of several microquasars and low-mass X-ray binaries. Two distinct QPO peaks, so-called twin peak QPOs, are often detected simultaneously exhibiting their frequency ratio close or equal to 3:2. A widely discussed class of proposed QPOs models is based on oscillations of accretion toroidal structures orbiting in the close vicinity of black holes or neutron stars. Aims: Following the analytic theory and previous studies of observable spectral signatures, we aim to model the twin peak QPOs as a spectral imprint of specific dual oscillation regime defined by a combination of the lowest radial and vertical oscillation mode of slender tori. We consider the model of an optically thick slender accretion torus with constant specific angular momentum. We examined power spectra and fluorescent Kα iron line profiles for two different simulation setups with the mode frequency relations corresponding to the epicyclic resonance HF QPOs model and modified relativistic precession QPOs model. Methods: We used relativistic ray-tracing implemented in the parallel simulation code LSDplus. In the background of the Kerr spacetime geometry, we analyzed the influence of the distant observer inclination and the spin of the central compact object. Relativistic optical projection of the oscillating slender torus is illustrated by images in false colours related to the frequency shift. Results: We show that performed simulations yield power spectra with the pair of dominant peaks that correspond to the frequencies of radial and vertical oscillation modes and with the peak frequency ratio equal to the proper value 3:2 on a wide range of inclinations and spin values. We also discuss exceptional cases of a very low and very high inclination, as well as unstable high spin relativistic precession-like configurations that predict a constant frequency ratio equal to 1:2. We
International Nuclear Information System (INIS)
Zhang Jiao; Wang Yanhui; Wang Dezhen; Zhuang Juan
2014-01-01
As a spatially extended dissipated system, atmospheric-pressure dielectric barrier discharges (DBDs) could in principle possess complex nonlinear behaviors. In order to improve the stability and uniformity of atmospheric-pressure dielectric barrier discharges, studies on temporal behaviors and radial structure of discharges with strong nonlinear behaviors under different controlling parameters are much desirable. In this paper, a two-dimensional fluid model is developed to simulate the radial discharge structure of period-doubling bifurcation, chaos, and inverse period-doubling bifurcation in an atmospheric-pressure DBD. The results show that the period-2n (n = 1, 2…) and chaotic discharges exhibit nonuniform discharge structure. In period-2n or chaos, not only the shape of current pulses doesn't remains exactly the same from one cycle to another, but also the radial structures, such as discharge spatial evolution process and the strongest breakdown region, are different in each neighboring discharge event. Current-voltage characteristics of the discharge system are studied for further understanding of the radial structure. (low temperature plasma)
Stability and dynamics of a controlled van der Pol-Duffing oscillator
International Nuclear Information System (INIS)
Ji, J.C.; Hansen, C.H.
2006-01-01
The trivial equilibrium of a van der Pol-Duffing oscillator under a linear-plus-nonlinear feedback control may change its stability either via a single or via a double Hopf bifurcation if the time delay involved in the feedback reaches certain values. It is found that the trivial equilibrium may lose its stability via a subcritical or supercritical Hopf bifurcation and regain its stability via a reverse subcritical or supercritical Hopf bifurcation as the time delay increases. A stable limit cycle appears after a supercritical Hopf bifurcation occurs and disappears through a reverse supercritical Hopf bifurcation. The interaction of the weakly periodic excitation and the stable bifurcating solution is investigated for the forced system under primary resonance conditions. It is shown that the forced periodic response may lose its stability via a Neimark-Sacker bifurcation. Analytical results are validated by a comparison with those of direct numerical integration
Analytical approximations for the amplitude and period of a relaxation oscillator
Directory of Open Access Journals (Sweden)
Golkhou Vahid
2009-01-01
Full Text Available Abstract Background Analysis and design of complex systems benefit from mathematically tractable models, which are often derived by approximating a nonlinear system with an effective equivalent linear system. Biological oscillators with coupled positive and negative feedback loops, termed hysteresis or relaxation oscillators, are an important class of nonlinear systems and have been the subject of comprehensive computational studies. Analytical approximations have identified criteria for sustained oscillations, but have not linked the observed period and phase to compact formulas involving underlying molecular parameters. Results We present, to our knowledge, the first analytical expressions for the period and amplitude of a classic model for the animal circadian clock oscillator. These compact expressions are in good agreement with numerical solutions of corresponding continuous ODEs and for stochastic simulations executed at literature parameter values. The formulas are shown to be useful by permitting quick comparisons relative to a negative-feedback represillator oscillator for noise (10× less sensitive to protein decay rates, efficiency (2× more efficient, and dynamic range (30 to 60 decibel increase. The dynamic range is enhanced at its lower end by a new concentration scale defined by the crossing point of the activator and repressor, rather than from a steady-state expression level. Conclusion Analytical expressions for oscillator dynamics provide a physical understanding for the observations from numerical simulations and suggest additional properties not readily apparent or as yet unexplored. The methods described here may be applied to other nonlinear oscillator designs and biological circuits.
A 20-day period standing oscillation in the northern winter stratosphere
Directory of Open Access Journals (Sweden)
K. Hocke
2013-04-01
Full Text Available Observations of the ozone profile by a ground-based microwave radiometer in Switzerland indicate a dominant 20-day oscillation in stratospheric ozone, possibly related to oscillations of the polar vortex edge during winter. For further understanding of the nature of the 20-day oscillation, the ozone data set of ERA Interim meteorological reanalysis is analyzed at the latitude belt of 47.5° N and in the time from 1979 to 2010. Spectral analysis of ozone time series at 7 hPa indicates that the 20-day oscillation is maximal at two locations: 7.5° E, 47.5° N and 60° E, 47.5° N. Composites of the stream function are derived for different phases of the 20-day oscillation of stratospheric ozone at 7 hPa in the Northern Hemisphere. The streamline at Ψ = −2 × 107 m2 s−1 is in the vicinity of the polar vortex edge. The other streamline at Ψ = 4 × 107 m2 s1 surrounds the Aleutian anticyclone and goes to the subtropics. The composites show 20-day period standing oscillations at the polar vortex edge and in the subtropics above Northern Africa, India, and China. The 20-day period standing oscillation above Aral Sea and India is correlated to the strength of the Aleutian anticyclone.
The periodicities in the infrared excess of G29-38 - An oscillating brown dwarf?
International Nuclear Information System (INIS)
Marley, M.S.; Lunine, J.I.; Hubbard, W.B.
1990-01-01
The oscillatory behavior of brown dwarfs has been investigated. The observed periodicities in the infrared excess of the white dwarf Giclas 29-38 are consistent with low-degree, intermediate radial order p-mode oscillations of a brown dwarf companion to the white dwarf. These oscillation modes have the correct frequencies, act on observable layers of the atmosphere, and may be excited to sufficient amplitudes to explain the observations. 14 refs
Directory of Open Access Journals (Sweden)
Hongli Liu
2009-01-01
Full Text Available We derive a new criterion for checking the global stability of periodic oscillation of bidirectional associative memory (BAM neural networks with periodic coefficients and distributed delay, and find that the criterion relies on the Lipschitz constants of the signal transmission functions, weights of the neural network, and delay kernels. The proposed model transforms the original interacting network into matrix analysis problem which is easy to check, thereby significantly reducing the computational complexity and making analysis of periodic oscillation for even large-scale networks.
Synchronization of Time-Continuous Chaotic Oscillators
DEFF Research Database (Denmark)
Yanchuk, S.; Maistrenko, Yuri; Mosekilde, Erik
2003-01-01
Considering a system of two coupled identical chaotic oscillators, the paper first establishes the conditions of transverse stability for the fully synchronized chaotic state. Periodic orbit threshold theory is applied to determine the bifurcations through which low-periodic orbits embedded...
Periodic auroral forms and geomagnetic field oscillations in the 1400 MLT region
International Nuclear Information System (INIS)
Potemra, T.A.; Vo, H.; Venkatesan, D.; Cogger, L.L.; Erlandson, R.E.; Zanetti, L.J.; Bythrow, P.F.; Anderson, B.J.
1990-01-01
The UV images obtained with the Viking satellite often show bright features which resemble beads or pearls aligned in the east-west direction between noon and 1800 MLT. Viking acquired a series of 25 UV images during a 28-min period on July 29, 1986, which showed a distinct series of periodic bright features in this region. Magnetic field and hot plasma measurements obtained by Viking confirm that the UV emissions are colocated with the field line projection of an upward-flowing region 1 Birkeland current and precipitating energetic (∼200 eV) electrons. The magnetic field and electric field measurements show transverse oscillations with a nearly constant period of about 3.5 min from 67 degree invariant latitude equatorward up to the location of the large-scale Birkeland current system near 76 degree invariant latitude. The electric field oscillations lead the magnetic field oscillations by about a quarter-period. The authors interpret the observed oscillations as standing Alfven waves driven at a frequency near the local resonance frequency by a large-scale wave in the boundary layer. They propose that the energy flux of the precipitating low-energy electrons in this afternoon region is modulated by this boundary wave and produces the periodic UV emission features. The results of this study support the view that large-scale oscillations of magnetospheric boundaries, possibly associated with the Kelvin-Helmholtz instability, can modulate currents, particles, and auroral forms
Energy Technology Data Exchange (ETDEWEB)
Takahashi, Takuya; Shibata, Kazunari [Kwasan and Hida Observatories, Kyoto University, Yamashina, Kyoto 607-8471 (Japan); Qiu, Jiong, E-mail: takahasi@kusastro.kyoto-u.ac.jp [Department of Physics, Montana State University, Bozeman, MT 59717-3840 (United States)
2017-10-20
We propose a mechanism for quasi-periodic oscillations of both coronal mass ejections (CMEs) and flare loops as related to magnetic reconnection in eruptive solar flares. We perform two-dimensional numerical MHD simulations of magnetic flux rope eruption, with three different values of the global Lundquist number. In the low Lundquist number run, no oscillatory behavior is found. In the moderate Lundquist number run, on the other hand, quasi-periodic oscillations are excited both at the bottom of the flux rope and at the flare loop top. In the high Lundquist number run, quasi-periodic oscillations are also excited; in the meanwhile, the dynamics become turbulent owing to the formation of multiple plasmoids in the reconnection current sheet. In high and moderate Lundquist number runs, thin reconnection jets collide with the flux rope bottom or flare loop top and dig them deeply. Steep oblique shocks are formed as termination shocks where reconnection jets are bent (rather than decelerated) in the horizontal direction, resulting in supersonic backflows. The structure becomes unstable, and quasi-periodic oscillations of supersonic backflows appear at locally confined high-beta regions at both the flux rope bottom and flare loop top. We compare the observational characteristics of quasi-periodic oscillations in erupting flux ropes, post-CME current sheets, flare ribbons, and light curves with corresponding dynamical structures found in our simulation.
Bifurcation analysis of a delayed mathematical model for tumor growth
International Nuclear Information System (INIS)
Khajanchi, Subhas
2015-01-01
In this study, we present a modified mathematical model of tumor growth by introducing discrete time delay in interaction terms. The model describes the interaction between tumor cells, healthy tissue cells (host cells) and immune effector cells. The goal of this study is to obtain a better compatibility with reality for which we introduced the discrete time delay in the interaction between tumor cells and host cells. We investigate the local stability of the non-negative equilibria and the existence of Hopf-bifurcation by considering the discrete time delay as a bifurcation parameter. We estimate the length of delay to preserve the stability of bifurcating periodic solutions, which gives an idea about the mode of action for controlling oscillations in the tumor growth. Numerical simulations of the model confirm the analytical findings
1991-01-01
Dynamical Bifurcation Theory is concerned with the phenomena that occur in one parameter families of dynamical systems (usually ordinary differential equations), when the parameter is a slowly varying function of time. During the last decade these phenomena were observed and studied by many mathematicians, both pure and applied, from eastern and western countries, using classical and nonstandard analysis. It is the purpose of this book to give an account of these developments. The first paper, by C. Lobry, is an introduction: the reader will find here an explanation of the problems and some easy examples; this paper also explains the role of each of the other paper within the volume and their relationship to one another. CONTENTS: C. Lobry: Dynamic Bifurcations.- T. Erneux, E.L. Reiss, L.J. Holden, M. Georgiou: Slow Passage through Bifurcation and Limit Points. Asymptotic Theory and Applications.- M. Canalis-Durand: Formal Expansion of van der Pol Equation Canard Solutions are Gevrey.- V. Gautheron, E. Isambe...
Short-period oscillations in photoemission from thin films of Cr(100)
Vyalikh, Denis V.; Zahn, Peter; Richter, Manuel; Dedkov, Yu. S.; Molodtsov, S. L.
2005-07-01
Angle-resolved photoemission (PE) study of thin films of Cr grown on Fe(100) reveals thickness-dependent short-period oscillations of the PE intensity close to the Fermi energy at k‖˜0 . The oscillations are assigned to quantum-well states (QWS) caused by the nesting between the Fermi-surface sheets around the Γ and the X points in the Brillouin zone of antiferromagnetic Cr. The experimental data are confirmed by density-functional calculations applying a screened Korringa-Kohn-Rostoker Green’s function method. The period of the experimentally observed QWS oscillations amounts to about 2.6 monolayers and is larger than the fundamental 2-monolayer period of antiferromagnetic coupling in Cr.
DEFF Research Database (Denmark)
Elmegård, Michael; Krauskopf, B.; Osinga, H.M.
2014-01-01
bifurca tions disappear when the transition of the switching is sufficiently and increasingly localized as the impact becomes harder. The bifurcation structure of the impact oscillator response is investigated via the one- and twoparameter continuation of periodic orbits in the driving frequency and....../or forcing amplitude. The results are in good agreement with experimental measurements....
Equivariant bifurcation in a coupled complex-valued neural network rings
International Nuclear Information System (INIS)
Zhang, Chunrui; Sui, Zhenzhang; Li, Hongpeng
2017-01-01
Highlights: • Complex value Hopfield-type network with Z4 × Z2 symmetry is discussed. • The spatio-temporal patterns of bifurcating periodic oscillations are obtained. • The oscillations can be in phase or anti-phase depending on the parameters and delay. - Abstract: Network with interacting loops and time delays are common in physiological systems. In the past few years, the dynamic behaviors of coupled interacting loops neural networks have been widely studied due to their extensive applications in classification of pattern recognition, signal processing, image processing, engineering optimization and animal locomotion, and other areas, see the references therein. In a large amount of applications, complex signals often occur and the complex-valued recurrent neural networks are preferable. In this paper, we study a complex value Hopfield-type network that consists of a pair of one-way rings each with four neurons and two-way coupling between each ring. We discuss the spatio-temporal patterns of bifurcating periodic oscillations by using the symmetric bifurcation theory of delay differential equations combined with representation theory of Lie groups. The existence of multiple branches of bifurcating periodic solution is obtained. We also found that the spatio-temporal patterns of bifurcating periodic oscillations alternate according to the change of the propagation time delay in the coupling, i.e., different ranges of delays correspond to different patterns of neural network oscillators. The oscillations of corresponding neurons in the two loops can be in phase or anti-phase depending on the parameters and delay. Some numerical simulations support our analysis results.
Intermittent and sustained periodic windows in networked chaotic Rössler oscillators
International Nuclear Information System (INIS)
He, Zhiwei; Sun, Yong; Zhan, Meng
2013-01-01
Route to chaos (or periodicity) in dynamical systems is one of fundamental problems. Here, dynamical behaviors of coupled chaotic Rössler oscillators on complex networks are investigated and two different types of periodic windows with the variation of coupling strength are found. Under a moderate coupling, the periodic window is intermittent, and the attractors within the window extremely sensitively depend on the initial conditions, coupling parameter, and topology of the network. Therefore, after adding or removing one edge of network, the periodic attractor can be destroyed and substituted by a chaotic one, or vice versa. In contrast, under an extremely weak coupling, another type of periodic window appears, which insensitively depends on the initial conditions, coupling parameter, and network. It is sustained and unchanged for different types of network structure. It is also found that the phase differences of the oscillators are almost discrete and randomly distributed except that directly linked oscillators more likely have different phases. These dynamical behaviors have also been generally observed in other networked chaotic oscillators
Graf, T.; McConnell, G.; Ferguson, A.I.; Bente, E.A.J.M.; Burns, D.; Dawson, M.D.
1999-01-01
We report on a rugged all-solid-state laser source of near-IR radiation in the range of 1461–1601 nm based on a high-power Nd:YVO4 laser that is mode locked by a semiconductor saturable Bragg reflector as the pump source of a synchronously pumped optical parametric oscillator with a periodically
Robust periodic steady state analysis of autonomous oscillators based on generalized eigenvalues
Mirzavand, R.; Maten, ter E.J.W.; Beelen, T.G.J.; Schilders, W.H.A.; Abdipour, A.
2011-01-01
In this paper, we present a new gauge technique for the Newton Raphson method to solve the periodic steady state (PSS) analysis of free-running oscillators in the time domain. To find the frequency a new equation is added to the system of equations. Our equation combines a generalized eigenvector
Robust periodic steady state analysis of autonomous oscillators based on generalized eigenvalues
Mirzavand, R.; Maten, ter E.J.W.; Beelen, T.G.J.; Schilders, W.H.A.; Abdipour, A.; Michielsen, B.; Poirier, J.R.
2012-01-01
In this paper, we present a new gauge technique for the Newton Raphson method to solve the periodic steady state (PSS) analysis of free-running oscillators in the time domain. To find the frequency a new equation is added to the system of equations. Our equation combines a generalized eigenvector
Provan, G.; Cowley, S. W. H.; Bunce, E. J.; Hunt, G. J.; Dougherty, M. K.
2017-12-01
We investigate planetary period oscillations (PPOs) in Saturn's magnetosphere using Cassini magnetic field data during the high cadence ( 7 days) F-ring and proximal orbits. Previous results have shown that there are two PPO systems, one in each hemisphere. Both PPO periods show seasonal dependence, and since mid-2014 the Northern PPO period has been 10.8 h and the Southern PPO period 10.7 h. The beat period of the two oscillations is 45 days. Previous results demonstrated that in the Northern (Southern) polar region only pure Northern (Southern) oscillations can be observed, whilst in the equatorial region both oscillations are present and constructively and destructively interfere over the beat-cycle of the two oscillations. The PPOs are believed to be driven by twin-cell convection patterns in the polar ionosphere/thermosphere regions, with two systems of field-aligned currents transmitting the PPO flows to the magnetospheric plasma.The F-ring and proximal orbits uniquely observe the PPOs over 6 orbits during each PPO beat cycle. This high-cadence data demonstrates that over a beat cycle both the periods and amplitudes of the PPO observed within the each polar region are modulated by the PPO system from the opposite hemisphere. When the two oscillations are in phase (anti-phase) the `drag' of one system on the other acts to decrease (increase) the amplitude of the oscillations and the two PPO periods diverge (converge). We present a theoretical model showing that this coupling is due to the PPO flows from one hemisphere not just being communicated to the magnetosphere as previously assumed, but also to the opposite hemisphere. The result is inter-hemispheric coupling of the PPO flow systems within the ionosphere/thermosphere system, so that the northern PPO system drives a northern twin-cell convection pattern in the southern hemisphere, and vice versa, thus leading to the observed polar modulations of the PPOs.We will also present PPO phase models determined
Period doubling of azimuthal oscillations on a non-neutral magnetized electron column
International Nuclear Information System (INIS)
Boswell, R.W.
1985-01-01
The low-frequency azimuthal oscillations on a non-neutral magnetized electron column of very low density are investigated. A perturbation analysis of the slow mode of the rigid rotator equilibrium is developed to illustrate the nature of large-amplitude fundamental-mode oscillations. The results of this theoretical analysis show two important characteristics: firstly, as the perturbation amplitude is increased the wave form ceases to be purely sinusoidal and shows period doubling. Secondly, above a certain threshold, all harmonics of the wave grow and the wave breaks. The results of the former are compared with a simple electron beam experiment and are found to be in good qualitative agreement. (author)
Du, Lei; Fan, Chu-Hui; Zhang, Han-Xiao; Wu, Jin-Hui
2017-11-20
We study the synchronization behaviors of two indirectly coupled mechanical oscillators of different frequencies in a doublecavity optomechanical system. It is found that quantum synchronization is roughly vanishing though classical synchronization seems rather good when each cavity mode is driven by an external field in the absence of temporal modulations. By periodically modulating cavity detunings or driving amplitudes, however, it is possible to observe greatly enhanced quantum synchronization accompanied with nearly perfect classical synchronization. The level of quantum synchronization observed here is, in particular, much higher than that for two directly coupled mechanical oscillators. Note also that the modulation on cavity detunings is more appealing than that on driving amplitudes when the robustness of quantum synchronization is examined against the bath's mean temperature or the oscillators' frequency difference.
Existence of Stick-Slip Periodic Solutions in a Dry Friction Oscillator
International Nuclear Information System (INIS)
Li Qun-Hong; Chen Yu-Ming; Qin Zhi-Ying
2011-01-01
The stick-slip behavior in friction oscillators is very complicated due to the non-smoothness of the dry friction, which is the basic form of motion of dynamical systems with friction. In this paper, the stick-slip periodic solution in a single-degree-of-freedom oscillator with dry friction is investigated in detail. Under the assumption of kinetic friction being the Coulomb friction, the existence of the stick-slip periodic solution is considered to give out an analytic criterion in a class of friction systems. A two-parameter unfolding diagram is also described. Moreover, the time and states of motion on the boundary of the stick and slip motions are semi-analytically obtained in a single stick-slip period. (general)
Bifurcation analysis of Rössler system with multiple delayed feedback
Directory of Open Access Journals (Sweden)
Meihong Xu
2010-10-01
Full Text Available In this paper, regarding the delay as parameter, we investigate the effect of delay on the dynamics of a Rössler system with multiple delayed feedback proposed by Ghosh and Chowdhury. At first we consider the stability of equilibrium and the existence of Hopf bifurcations. Then an explicit algorithm for determining the direction and the stability of the bifurcating periodic solutions is derived by using the normal form theory and center manifold argument. Finally, we give a numerical simulation example which indicates that chaotic oscillation is converted into a stable steady state or a stable periodic orbit when the delay passes through certain critical values.
Part 2: Dynamics of magnetic oscillator
International Nuclear Information System (INIS)
Anon.
1987-01-01
This is an experimental study of a forced symmetric oscillator containing a saturable inductor with magnetic hysteresis. It displays a Hopf bifurcation to quasiperiodicity, entrainment horns, and chaos. The bifurcations and hysteresis occurring near points of resonance (particularly ''strong resonance'') are studied in detail and it is shown how the observed behavior can be understood using Arnold's theory. Much of the behavior relating to the entrainment horns is explored: period doubling and symmetry breaking bifurcations; homoclinic bifurcations; and crises and other bifurcations taking place at the horn boundaries. Important features of the behavior related to symmetry properties of the oscillator are studied and explained through the concept of a half-cycle map. The system is shown to exhibit a Hopf bifurcation from a phase-locked state to periodic ''islands,'' similar to those found in Hamiltonian systems. An initialization technique is used to observe the manifolds of saddle orbits and other hidden structure. An unusual differential equation model is developed which is irreversible and generates a noninvertible Poincare map of the plane. Noninvertibility of this planar map has important effects on the behavior observed. The Poincare map may also be approximated through experimental measurements, resulting in a planar map with parameter dependence. This model gives good correspondence with the system in a region of the parameter space. 31 refs., 36 figs., 1 tab
Patsis, P. A.; Harsoula, M.
2018-05-01
Context. We present and discuss the orbital content of a rather unusual rotating barred galaxy model, in which the three-dimensional (3D) family, bifurcating from x1 at the 2:1 vertical resonance with the known "frown-smile" side-on morphology, is unstable. Aims: Our goal is to study the differences that occur in the phase space structure at the vertical 2:1 resonance region in this case, with respect to the known, well studied, standard case, in which the families with the frown-smile profiles are stable and support an X-shaped morphology. Methods: The potential used in the study originates in a frozen snapshot of an N-body simulation in which a fast bar has evolved. We follow the evolution of the vertical stability of the central family of periodic orbits as a function of the energy (Jacobi constant) and we investigate the phase space content by means of spaces of section. Results: The two bifurcating families at the vertical 2:1 resonance region of the new model change their stability with respect to that of most studied analytic potentials. The structure in the side-on view that is directly supported by the trapping of quasi-periodic orbits around 3D stable periodic orbits has now an infinity symbol (i.e. ∞-type) profile. However, the available sticky orbits can reinforce other types of side-on morphologies as well. Conclusions: In the new model, the dynamical mechanism of trapping quasi-periodic orbits around the 3D stable periodic orbits that build the peanut, supports the ∞-type profile. The same mechanism in the standard case supports the X shape with the frown-smile orbits. Nevertheless, in both cases (i.e. in the new and in the standard model) a combination of 3D quasi-periodic orbits around the stable x1 family with sticky orbits can support a profile reminiscent of the shape of the orbits of the 3D unstable family existing in each model.
Ren, Fengli; Cao, Jinde
2007-03-01
In this paper, several sufficient conditions are obtained ensuring existence, global attractivity and global asymptotic stability of the periodic solution for the higher-order bidirectional associative memory neural networks with periodic coefficients and delays by using the continuation theorem of Mawhin's coincidence degree theory, the Lyapunov functional and the non-singular M-matrix. Two examples are exploited to illustrate the effectiveness of the proposed criteria. These results are more effective than the ones in the literature for some neural networks, and can be applied to the design of globally attractive or globally asymptotically stable networks and thus have important significance in both theory and applications.
4. 7s nearly periodic oscillations superimposed on the solar microwave great burst of 28 March 1976
Energy Technology Data Exchange (ETDEWEB)
Kaufmann, P; Piazza, L R; Raffaelli, J C [Universidade Mackenzie, Sao Paulo (Brazil). Centro de Radio-Astronomia e Astrofisica
1977-09-01
An unusual fast oscillation was found superimposed on the solar great burst on 28 March 1976, as measured at 7 GHz. The period of the oscillation was 4.7 +- 0.9 s, defined over the entire duration of the event. The amplitude of the oscillation was proportional to the flux density in the range 50periodic time structure.
Visser, Sid; Meijer, Hil G.E.; van Putten, Michel J.A.M.; van Gils, Stephan A.
2012-01-01
A lumped model of neural activity in neocortex is studied to identify regions of multi-stability of both steady states and periodic solutions. Presence of both steady states and periodic solutions is considered to correspond with epileptogenesis. The model, which consists of two delay differential
Resonance spiking by periodic loss in the double-sided liquid cooling disk oscillator
Nie, Rongzhi; She, Jiangbo; Li, Dongdong; Li, Fuli; Peng, Bo
2017-03-01
A double-sided liquid cooling Nd:YAG disk oscillator working at a pump repetition rate of 20 Hz is demonstrated. The output energy of 376 mJ is realized, corresponding to the optical-optical efficiency of 12.8% and the slope efficiency of 14%. The pump pulse width is 300 µs and the laser pulse width is 260 µs. Instead of being a damped signal, the output of laser comprises undamped spikes. A periodic intra-cavity loss was found by numerical analysis, which has a frequency component near the eigen frequency of the relaxation oscillation. Resonance effect will induce amplified spikes even though the loss fluctuates in a small range. The Shark-Hartmann sensor was used to investigate the wavefront aberration induced by turbulent flow and temperature gradient. According to the wavefront and fluid mechanics analysis, it is considered that the periodic intra-cavity loss can be attributed to turbulent flow and temperature gradient.
Symmetry, Hopf bifurcation, and the emergence of cluster solutions in time delayed neural networks.
Wang, Zhen; Campbell, Sue Ann
2017-11-01
We consider the networks of N identical oscillators with time delayed, global circulant coupling, modeled by a system of delay differential equations with Z N symmetry. We first study the existence of Hopf bifurcations induced by the coupling time delay and then use symmetric Hopf bifurcation theory to determine how these bifurcations lead to different patterns of symmetric cluster oscillations. We apply our results to a case study: a network of FitzHugh-Nagumo neurons with diffusive coupling. For this model, we derive the asymptotic stability, global asymptotic stability, absolute instability, and stability switches of the equilibrium point in the plane of coupling time delay (τ) and excitability parameter (a). We investigate the patterns of cluster oscillations induced by the time delay and determine the direction and stability of the bifurcating periodic orbits by employing the multiple timescales method and normal form theory. We find that in the region where stability switching occurs, the dynamics of the system can be switched from the equilibrium point to any symmetric cluster oscillation, and back to equilibrium point as the time delay is increased.
Towards classification of the bifurcation structure of a spherical cavitation bubble.
Behnia, Sohrab; Sojahrood, Amin Jafari; Soltanpoor, Wiria; Sarkhosh, Leila
2009-12-01
We focus on a single cavitation bubble driven by ultrasound, a system which is a specimen of forced nonlinear oscillators and is characterized by its extreme sensitivity to the initial conditions. The driven radial oscillations of the bubble are considered to be implicated by the principles of chaos physics and owing to specific ranges of control parameters, can be periodic or chaotic. Despite the growing number of investigations on its dynamics, there is not yet an inclusive yardstick to sort the dynamical behavior of the bubble into classes; also, the response oscillations are so complex that long term prediction on the behavior becomes difficult to accomplish. In this study, the nonlinear dynamics of a bubble oscillator was treated numerically and the simulations were proceeded with bifurcation diagrams. The calculated bifurcation diagrams were compared in an attempt to classify the bubble dynamic characteristics when varying the control parameters. The comparison reveals distinctive bifurcation patterns as a consequence of driving the systems with unequal ratios of R(0)lambda (where R(0) is the bubble initial radius and lambda is the wavelength of the driving ultrasonic wave). Results indicated that systems having the equal ratio of R(0)lambda, share remarkable similarities in their bifurcating behavior and can be classified under a unit category.
Symmetry, Hopf bifurcation, and the emergence of cluster solutions in time delayed neural networks
Wang, Zhen; Campbell, Sue Ann
2017-11-01
We consider the networks of N identical oscillators with time delayed, global circulant coupling, modeled by a system of delay differential equations with ZN symmetry. We first study the existence of Hopf bifurcations induced by the coupling time delay and then use symmetric Hopf bifurcation theory to determine how these bifurcations lead to different patterns of symmetric cluster oscillations. We apply our results to a case study: a network of FitzHugh-Nagumo neurons with diffusive coupling. For this model, we derive the asymptotic stability, global asymptotic stability, absolute instability, and stability switches of the equilibrium point in the plane of coupling time delay (τ) and excitability parameter (a). We investigate the patterns of cluster oscillations induced by the time delay and determine the direction and stability of the bifurcating periodic orbits by employing the multiple timescales method and normal form theory. We find that in the region where stability switching occurs, the dynamics of the system can be switched from the equilibrium point to any symmetric cluster oscillation, and back to equilibrium point as the time delay is increased.
Resonant Homoclinic Flips Bifurcation in Principal Eigendirections
Directory of Open Access Journals (Sweden)
Tiansi Zhang
2013-01-01
Full Text Available A codimension-4 homoclinic bifurcation with one orbit flip and one inclination flip at principal eigenvalue direction resonance is considered. By introducing a local active coordinate system in some small neighborhood of homoclinic orbit, we get the Poincaré return map and the bifurcation equation. A detailed investigation produces the number and the existence of 1-homoclinic orbit, 1-periodic orbit, and double 1-periodic orbits. We also locate their bifurcation surfaces in certain regions.
Hopf bifurcation in an Internet congestion control model
International Nuclear Information System (INIS)
Li Chunguang; Chen Guanrong; Liao Xiaofeng; Yu Juebang
2004-01-01
We consider an Internet model with a single link accessed by a single source, which responds to congestion signals from the network, and study bifurcation of such a system. By choosing the gain parameter as a bifurcation parameter, we prove that Hopf bifurcation occurs. The stability of bifurcating periodic solutions and the direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Finally, a numerical example is given to verify the theoretical analysis
Aharonov-Bohm oscillations with fractional period in a multichannel Wigner crystal ring
International Nuclear Information System (INIS)
Krive, I.V.; Krokhin, A.A.
1997-01-01
We study the persistent current in a quasi 1D ring with strongly correlated electrons forming a multichannel Wigner crystal (WC). The influence of the Coulomb interaction manifests itself only in the presence of external scatterers that pin the WC. Two regimes of weak and strong pinning are considered. For strong pinning we predict the Aharonov-Bohm oscillations with fractional period. Fractionalization is due to the interchannel coupling in the process of quantum tunneling of the WC. The fractional period depends on the filling of the channels and may serve as an indicator of non-Fermi-liquid behaviour of interacting electrons in quasi 1D rings. (author). 20 refs
Song, Yongli; Zhang, Tonghua; Tadé, Moses O.
2009-12-01
The dynamical behavior of a delayed neural network with bi-directional coupling is investigated by taking the delay as the bifurcating parameter. Some parameter regions are given for conditional/absolute stability and Hopf bifurcations by using the theory of functional differential equations. As the propagation time delay in the coupling varies, stability switches for the trivial solution are found. Conditions ensuring the stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. We also discuss the spatio-temporal patterns of bifurcating periodic oscillations by using the symmetric bifurcation theory of delay differential equations combined with representation theory of Lie groups. In particular, we obtain that the spatio-temporal patterns of bifurcating periodic oscillations will alternate according to the change of the propagation time delay in the coupling, i.e., different ranges of delays correspond to different patterns of neural activities. Numerical simulations are given to illustrate the obtained results and show the existence of bursts in some interval of the time for large enough delay.
Quasi-16-day period oscillations observed in middle atmospheric ozone and temperature in Antarctica
Energy Technology Data Exchange (ETDEWEB)
Demissie, T.D.; Hibbins, R.E.; Espy, P.J. [Norwegian Univ. of Science and Technology (NTNU), Trondheim (Norway); Birkeland Centre for Space Science, Bergen (Norway); Kleinknecht, N.H.; Straub, C. [Norwegian Univ. of Science and Technology (NTNU), Trondheim (Norway)
2013-09-01
Nightly averaged mesospheric temperature derived from the hydroxyl nightglow at Rothera station (67 34' S, 68 08' W) and nightly midnight measurements of ozone mixing ratio obtained from Troll station (72 01' S, 2 32' E) in Antarctica have been used to investigate the presence and vertical profile of the quasi-16-day planetary wave in the stratosphere and mesosphere during the Antarctic winter of 2009. The variations caused by planetary waves on the ozone mixing ratio and temperature are discussed, and spectral and cross-correlation analyses are performed to extract the wave amplitudes and to examine the vertical structure of the wave from 34 to 80 km. The results show that while planetary-wave signatures with periods 3-12 days are strong below the stratopause, the oscillations associated with the 16-day wave are the strongest and present in both the mesosphere and stratosphere. The period of the wave is found to increase below 42 km due to the Doppler shifting by the strong eastward zonal wind. The 16-day oscillation in the temperature is found to be correlated and phase coherent with the corresponding oscillation observed in O{sub 3} volume mixing ratio at all levels, and the wave is found to have vertical phase fronts consistent with a normal mode structure. (orig.)
International Nuclear Information System (INIS)
Fox, Ronald F.; Vela-Arevalo, Luz V.
2002-01-01
The problem of multiphoton processes for intense, long-wavelength irradiation of atomic and molecular electrons is presented. The recently developed method of quasiadiabatic time evolution is used to obtain a nonperturbative analysis. When applied to the standard vector potential coupling, an exact auxiliary equation is obtained that is in the electric dipole coupling form. This is achieved through application of the Goeppert-Mayer gauge. While the analysis to this point is general and aimed at microwave irradiation of Rydberg atoms, a Floquet analysis of the auxiliary equation is presented for the special case of the periodically driven harmonic oscillator. Closed form expressions for a complete set of Floquet states are obtained. These are used to demonstrate that for the oscillator case there are no multiphoton resonances
Bifurcation and Chaos in a Pulse Width modulation controlled Buck Converter
DEFF Research Database (Denmark)
Kocewiak, Lukasz; Bak, Claus Leth; Munk-Nielsen, Stig
2007-01-01
by a system of piecewise-smooth nonautonomous differential equations. The research are focused on chaotic oscillations analysis and analytical search for bifurcations dependent on parameter. The most frequent route to chaos by the period doubling is observed in the second order DC-DC buck converter. Other...... bifurcations as a complex behaviour in power electronic system evidence are also described. In order to verify theoretical study the experimental DC-DC buck converter was build. The results obtained from three sources were presented and compared. A very good agreement between theory and experiment was observed....
International Nuclear Information System (INIS)
Shukla, Anant Kant; Ramamohan, T R; Srinivas, S
2014-01-01
In this paper we propose a technique to obtain limit cycles and quasi-periodic solutions of forced nonlinear oscillators. We apply this technique to the forced Van der Pol oscillator and the forced Van der Pol Duffing oscillator and obtain for the first time their limit cycles (periodic) and quasi-periodic solutions analytically. We introduce a modification of the homotopy analysis method to obtain these solutions. We minimize the square residual error to obtain accurate approximations to these solutions. The obtained analytical solutions are convergent and agree well with numerical solutions even at large times. Time trajectories of the solution, its first derivative and phase plots are presented to confirm the validity of the proposed approach. We also provide rough criteria for the determination of parameter regimes which lead to limit cycle or quasi-periodic behaviour. (papers)
Uncertainty Quantification and Bifurcation Analysis of an Airfoil with Multiple Nonlinearities
Directory of Open Access Journals (Sweden)
Haitao Liao
2013-01-01
Full Text Available In order to calculate the limit cycle oscillations and bifurcations of nonlinear aeroelastic system, the problem of finding periodic solutions with maximum vibration amplitude is transformed into a nonlinear optimization problem. An algebraic system of equations obtained by the harmonic balance method and the stability condition derived from the Floquet theory are used to construct the general nonlinear equality and inequality constraints. The resulting constrained maximization problem is then solved by using the MultiStart algorithm. Finally, the proposed approach is validated, and the effects of structural parameter uncertainty on the limit cycle oscillations and bifurcations of an airfoil with multiple nonlinearities are studied. Numerical examples show that the coexistence of multiple nonlinearities may lead to low amplitude limit cycle oscillation.
Oscillations of a Beam on a Non-Linear Elastic Foundation under Periodic Loads
Directory of Open Access Journals (Sweden)
Donald Mark Santee
2006-01-01
Full Text Available The complexity of the response of a beam resting on a nonlinear elastic foundation makes the design of this structural element rather challenging. Particularly because, apparently, there is no algebraic relation for its load bearing capacity as a function of the problem parameters. Such an algebraic relation would be desirable for design purposes. Our aim is to obtain this relation explicitly. Initially, a mathematical model of a flexible beam resting on a non-linear elastic foundation is presented, and its non-linear vibrations and instabilities are investigated using several numerical methods. At a second stage, a parametric study is carried out, using analytical and semi-analytical perturbation methods. So, the influence of the various physical and geometrical parameters of the mathematical model on the non-linear response of the beam is evaluated, in particular, the relation between the natural frequency and the vibration amplitude and the first period doubling and saddle-node bifurcations. These two instability phenomena are the two basic mechanisms associated with the loss of stability of the beam. Finally Melnikov's method is used to determine an algebraic expression for the boundary that separates a safe from an unsafe region in the force parameters space. It is shown that this can be used as a basis for a reliable engineering design criterion.
Energy Technology Data Exchange (ETDEWEB)
Funakoshi, Satoshi; Sato, Tomoyoshi; Miyazaki, Takeshi, E-mail: funakosi@miyazaki.mce.uec.ac.jp, E-mail: miyazaki@mce.uec.ac.jp [Department of Mechanical Engineering and Intelligent Systems, University of Electro-Communications, 1-5-1, Chofugaoka, Chofu, Tokyo 182-8585 (Japan)
2012-06-01
We investigate the statistical mechanics of quasi-geostrophic point vortices of mixed sign (bi-disperse system) numerically and theoretically. Direct numerical simulations under periodic boundary conditions are performed using a fast special-purpose computer for molecular dynamics (GRAPE-DR). Clustering of point vortices of like sign is observed and two-dimensional (2D) equilibrium states are formed. It is shown that they are the solutions of the 2D mean-field equation, i.e. the sinh-Poisson equation. The sinh-Poisson equation is generalized to study the 3D nature of the equilibrium states, and a new mean-field equation with the 3D Laplace operator is derived based on the maximum entropy theory. 3D solutions are obtained at very low energy level. These solution branches, however, cannot be traced up to the higher energy level at which the direct numerical simulations are performed, and transitions to 2D solution branches take place when the energy is increased. (paper)
Emission of SNF-oscillations by the plasma - periodic decelerating structure system
International Nuclear Information System (INIS)
Antonov, A.N.; Gestrina, G.N.; Kovpik, O.F.; Kornilov, E.A.; Moiseev, S.S.
1983-01-01
Emission of SHF-oscillations by a magnetoactive plasma inside a decelerating structure (annular waveguide), which is excited by an electron beam, has been studied. The electron beam is formed by a diode electron gun. Pulse duration was 400 μs, beam energy = 10 keV, current - up to 5 A. The beam 1.8 cm in diameter is injected into a glass interaction chamber. The chamber diameter is 20 cm, the length is 1 m. The interaction chamber and electron gun chamber were placed in a homogeneous magnetic field with intensity up to 2.5x10 5 axm -1 . The periodic deceleration structure was located in the interaction chamber coaxially with the electron beam. The structure total length was 40 cm. The working gas, argon, was fed into the structure through a needle injector. It is shown that the three-dimensional waves appearing in the plasma can be transformed by the structure to those emited without plasma density gradients and magnetic field. Conditions of effective separation of the energy of SHF-oscillations from the system: plasm-beam-narrow-slit decelerating structure are found. The above system can be used for amplification and generation of monochromatic oscillations in the millimeter waves range. Results of experimental studies are compared with theoretical calculations
Pulsations of the Free Oscillations of the Earth in an Hourly Period Range
Sobolev, G. A.; Zakrzhevskaya, N. A.; Akatova, K. N.
2018-05-01
The records from 161 identical broadband seismic stations located in different regions of the world after the strong earthquakes off Sumatra Island on December 26, 2004 with magnitude M = 9.1, in Chile on February 27, 2010 with M = 8.8, and the Tohoku earthquake in Japan on March 11, 2011 with M = 9.0 are studied. Oscillations with a period of 11 h are analyzed. They are observed as pulsations in the free radial oscillations of the Earth lasting more than one week. The stations located a few hundred kilometers apart from each other demonstrate identical records. As the distance between the stations becomes larger, the structure of the records becomes different. At interstation distances of about 3800 km, the records at the stations have opposite phases, and at distances of 7600 km, the phases coincide. This is reflected in the spatial structure of the areas of the positive and negative phases of the oscillations on the Earth's surface. This structure recurs at the same time instant after the three considered earthquakes, which indicates that this effect is independent of the properties of the sources. The spatial positions of the areas of positive and negative phases are also not correlated to the geological conditions in the vicinity of the stations which are located both in the subduction zone and within the platform. The structure of the pulsations and their spatial distribution differ from the variations of the Earth's tides.
Periodic oscillations in linear continuous media coupled with nonlinear discrete systems
International Nuclear Information System (INIS)
Lupini, R.
1998-01-01
A general derivation of partial differential equations with boundary conditions in the form of ordinary differential equations is obtained using the principle of stationary action for a Lagrangian function composed of continuous plus discrete parts in interaction across the boundaries of a 1-dimensional medium. This approach leads directly to the theorem of energy conservation. For linear continuous medium, homogeneous Dirichlet condition at one boundary, and nonlinear oscillator at the other boundary, the entire differential problem reduces to a nonlinear differential-difference equation of neutral type and of the second order. The lag parameter is τ = l/c, where c is the phase speed, l the length of the continuum. The Author investigate the problem of the occurrence of periodic solutions of period integer multiple of the lag (super harmonic solutions) in the case of zero inertia of the boundary system. The problem for such oscillations is shown to reduce to systems of ordinary differential equations with matching conditions in a phase space of lower dimensionality: Phase-plane techniques are used to determine solutions of period 4τ, 8τ and 6τ
Dry soil diurnal quasi-periodic oscillations in soil 222Rn concentrations
International Nuclear Information System (INIS)
Tommasone Pascale, F.; De Francesco, S.; Carbone, P.; Cuoco, E.; Tedesco, D.
2014-01-01
222 Rn concentrations have been monitored during the dry season in August 2009 and August 2010, in a reworked alluvial-pyroclastic soil of the Pietramelara Plain, in Southern Italy, with the aim of determining the role of atmospheric factors in producing the quasi-periodic oscillations in soil 222 Rn concentrations reported in the literature. In this study we present the results of a detailed analysis and matching of soil 222 Rn concentrations, meteorological and solar parameters where the observed oscillations feature a characteristic behavior with second order build-up and depletion limbs, separated by a daily maximum and minimum. All these features are clearly shown to be tied to sunrise and sunset timings and environmental radiative flux regimes. Furthermore, a significant, and previously unreported, second order correlation (r 2 = 0.73) between daily maximum hourly global radiation and the daily range of soil 222 Rn concentrations has been detected, allowing estimates of the amplitude of these oscillations to be made from estimated or measured solar radiation data. The correlation has been found to be valid even in the presence of persistent patchy daytime cloudiness. In this case a daytime prolongation of the night-time build up stage and an attenuation or even suppression of daytime depletion is observed (a previously unreported effect). Neither soil cracking, nor precipitation, both suggested in some studies as causative factors for these oscillations, during the dry season appear to be necessary in explaining their occurrence. We also report the results of an artificial shading experiment, conducted in August 2009, that further support this conclusion. As soil 222 Rn concentrations during the dry season show a characteristic daily cycle, radon monitoring in soils under these conditions necessarily has to be gauged to the timings of the daily maximum and minimum, as well as to the eventual occurrence of cloudiness and to its related effects, in order to
An easy trick to a periodic solution of relativistic harmonic oscillator
Directory of Open Access Journals (Sweden)
Jafar Biazar
2014-04-01
Full Text Available In this paper, the relativistic harmonic oscillator equation which is a nonlinear ordinary differential equation is investigated by Homotopy perturbation method. Selection of a linear operator, which is a part of the main operator, is one of the main steps in HPM. If the aim is to obtain a periodic solution, this choice does not work here. To overcome this lack, a linear operator is imposed, and Fourier series of sines will be used in solving the linear equations arise in the HPM. Comparison of the results, with those of resulted by Differential Transformation and Harmonic Balance Method, shows an excellent agreement.
Missey, M; Dominic, V; Powers, P; Schepler, K L
2000-02-15
We used elliptical beams to demonstrate aperture scaling effects in nanosecond single-grating and multigrating periodically poled lithium niobate (PPLN) monolithic optical parametric oscillators and generators. Increasing the cavity Fresnel number in single-grating crystals broadened both the beam divergence and the spectral bandwidth. Both effects are explained in terms of the phase-matching geometry. These effects are suppressed when a multigrating PPLN crystal is used because the individual gratings provide small effective subapertures. A flood-pumped multigrating optical parametric generator displayed a low output beam divergence and contained 19 pairs of signal and idler frequencies.
Quasi-periodic oscillations and noise in low-mass X-ray binaries
International Nuclear Information System (INIS)
Van der Klis, M.
1989-01-01
The phenomenology of quasi-periodic oscillations (QPOs) and noise in low-mass X-ray binaries (LMXBs) is discussed. Signal analysis aspects of QPO and noise are addressed along with the relationship between LMXBs and millisecond radio pulsars. The history and prehistory of QPOs and noise in LMXBs are examined. Universal noise components and normal and flaring branch QPOs in Z sources are described and the phenomenology of Z sources is discussed. Bright LMXBs known as atoll sources are considered, as are nonpersistently bright LMXBs accreting pulsars and black hole candidates. 162 refs
Bifurcations of Tumor-Immune Competition Systems with Delay
Directory of Open Access Journals (Sweden)
Ping Bi
2014-01-01
Full Text Available A tumor-immune competition model with delay is considered, which consists of two-dimensional nonlinear differential equation. The conditions for the linear stability of the equilibria are obtained by analyzing the distribution of eigenvalues. General formulas for the direction, period, and stability of the bifurcated periodic solutions are given for codimension one and codimension two bifurcations, including Hopf bifurcation, steady-state bifurcation, and B-T bifurcation. Numerical examples and simulations are given to illustrate the bifurcations analysis and obtained results.
Bifurcation and chaos in neural excitable system
International Nuclear Information System (INIS)
Jing Zhujun; Yang Jianping; Feng Wei
2006-01-01
In this paper, we investigate the dynamical behaviors of neural excitable system without periodic external current (proposed by Chialvo [Generic excitable dynamics on a two-dimensional map. Chaos, Solitons and Fractals 1995;5(3-4):461-79] and with periodic external current as system's parameters vary. The existence and stability of three fixed points, bifurcation of fixed points, the conditions of existences of fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using bifurcation theory and center manifold theorem. The chaotic existence in the sense of Marotto's definition of chaos is proved. We then give the numerical simulated results (using bifurcation diagrams, computations of Maximum Lyapunov exponent and phase portraits), which not only show the consistence with the analytic results but also display new and interesting dynamical behaviors, including the complete period-doubling and inverse period-doubling bifurcation, symmetry period-doubling bifurcations of period-3 orbit, simultaneous occurrence of two different routes (invariant cycle and period-doubling bifurcations) to chaos for a given bifurcation parameter, sudden disappearance of chaos at one critical point, a great abundance of period windows (period 2 to 10, 12, 19, 20 orbits, and so on) in transient chaotic regions with interior crises, strange chaotic attractors and strange non-chaotic attractor. In particular, the parameter k plays a important role in the system, which can leave the chaotic behavior or the quasi-periodic behavior to period-1 orbit as k varies, and it can be considered as an control strategy of chaos by adjusting the parameter k. Combining the existing results in [Generic excitable dynamics on a two-dimensional map. Chaos, Solitons and Fractals 1995;5(3-4):461-79] with the new results reported in this paper, a more complete description of the system is now obtained
Detection of very long period solar free oscillations in ambient seismic array noise
Caton, R.; Pavlis, G. L.; Thomson, D. J.; Vernon, F.
2017-12-01
For nearly two decades long-period seismologists have been aware that the Earth's free oscillations are in a constant state of excitement, even in the absence of large earthquakes. This phenomenon is now called the "Earth's hum," and much research has been done to determine what generates this hum. Here we examine a hypothesis first put forward by Thomson et al. in 2007 that a portion of the hum's energy comes from the sun. They hypothesized that solar free oscillations couple into the solid Earth, likely through electromagnetic processes, and produce signals that are observable in the frequency domain. If this is true, then at least some measurement of helioseismic oscillations may be possible using relatively cheap, ground-based instruments rather than spacecraft. In this project we attempt to improve upon previous studies by producing spectra from seismic arrays, rather than a single station. We use data from two arrays: The Homestake Mine 3D array in Lead, SD, and the Pinyon Flats array, which has seismometers in boreholes drilled into bedrock. Both have exceptionally low noise levels at ultra long periods and show easily visible earth tides on horizontal component data filtered to below the microseism band. In the Homestake data, below 500 μHz we have found evidence of what we suggest may be closely spaced solar g-mode lines. Such modes are produced by a density inversion at the top of the solar core. There is no sign of these modes in the Pinyon Flats data, but we find this is likely due to the signal-to-noise ratio of those data, which is significantly lower than Homestake. Significance tests of bands below 500 μHz indicate with probability levels as high as 40σ that these lines are not the result of random processes. Critical examination of our processing steps for sources of bias indicate that the observed line structure is not a processing artifact.
Mapping of the quasi-periodic oscillations at the flank magnetopause into the ionosphere
Directory of Open Access Journals (Sweden)
E. R. Dougal
2013-11-01
Full Text Available We have estimated the ionospheric location, area, and travel time of quasi-periodic oscillations originating from the magnetospheric flanks. This was accomplished by utilizing global and local MHD models and Tsyganenko semi-empirical magnetic field model on multiple published and four new cases believed to be caused by the Kelvin–Helmholtz Instability. Finally, we used auroral, magnetometer, and radar instruments to observe the ionospheric signatures. The ionospheric magnetic latitude determined using global MHD and Tsyganenko models ranged from 58.3–80.2 degrees in the Northern Hemisphere and −59.6 degrees to −83.4 degrees in the Southern Hemisphere. The ionospheric magnetic local time ranged between 5.0–13.8 h in the Northern Hemisphere and 1.3–11.9 h in the Southern Hemisphere. Typical Alfvén wave travel time from spacecraft location to the closest ionosphere ranged between 0.6–3.6 min. The projected ionospheric size calculated at an altitude of 100 km ranged from 47–606 km, the same order of magnitude as previously determined ionospheric signature sizes. Stationary and traveling convection vortices were observed in SuperDARN radar data in both hemispheres. The vortices were between 1000–1800 km in size. Some events were located within the ionospheric footprint ranges. Pc5 magnetic oscillations were observed in SuperMAG magnetometer data in both hemispheres. The oscillations had periods between 4–10 min with amplitudes of 3–25 nT. They were located within the ionospheric footprint ranges. Some ground magnetometer data power spectral density peaked at frequencies within one tenth of a mHz of the peaks found in the corresponding Cluster data. These magnetometer observations were consistent with previously published results.
On the totality of periodic motions in the meridian plane of a magnetic dipole
International Nuclear Information System (INIS)
Markellos, V.V.; Halioulias, A.A.
1977-01-01
The structure of the periodic solutions of the Stoermer problem, representing the magnetic field of the Earth, is examined by considering the equatorial oscillations of the charged particle and their 'vertical' bifurcations with meridian periodic oscillations. An infinity of new families of simple-periodic oscillations are found to exist in the vicinity of the 'thalweg' and four such new families are actually established by numerical integration. (Auth.)
Disruption of Saturn's quasi-periodic equatorial oscillation by the great northern storm
Fletcher, Leigh N.; Guerlet, Sandrine; Orton, Glenn S.; Cosentino, Richard G.; Fouchet, Thierry; Irwin, Patrick G. J.; Li, Liming; Flasar, F. Michael; Gorius, Nicolas; Morales-Juberías, Raúl
2017-11-01
The equatorial middle atmospheres of the Earth1, Jupiter2 and Saturn3,4 all exhibit a remarkably similar phenomenon—a vertical, cyclic pattern of alternating temperatures and zonal (east-west) wind regimes that propagate slowly downwards with a well-defined multi-year period. Earth's quasi-biennial oscillation (QBO) (observed in the lower stratospheric winds with an average period of 28 months) is one of the most regular, repeatable cycles exhibited by our climate system1,5,6, and yet recent work has shown that this regularity can be disrupted by events occurring far away from the equatorial region, an example of a phenomenon known as atmospheric teleconnection7,8. Here, we reveal that Saturn's equatorial quasi-periodic oscillation (QPO) (with an 15-year period3,9) can also be dramatically perturbed. An intense springtime storm erupted at Saturn's northern mid-latitudes in December 201010-12, spawning a gigantic hot vortex in the stratosphere at 40° N that persisted for three years13. Far from the storm, the Cassini temperature measurements showed a dramatic 10 K cooling in the 0.5-5 mbar range across the entire equatorial region, disrupting the regular QPO pattern and significantly altering the middle-atmospheric wind structure, suggesting an injection of westward momentum into the equatorial wind system from waves generated by the northern storm. Hence, as on Earth, meteorological activity at mid-latitudes can have a profound effect on the regular atmospheric cycles in Saturn's tropics, demonstrating that waves can provide horizontal teleconnections between the phenomena shaping the middle atmospheres of giant planets.
eAMI: A Qualitative Quantification of Periodic Breathing Based on Amplitude of Oscillations
Fernandez Tellez, Helio; Pattyn, Nathalie; Mairesse, Olivier; Dolenc-Groselj, Leja; Eiken, Ola; Mekjavic, Igor B.; Migeotte, P. F.; Macdonald-Nethercott, Eoin; Meeusen, Romain; Neyt, Xavier
2015-01-01
Study Objectives: Periodic breathing is sleep disordered breathing characterized by instability in the respiratory pattern that exhibits an oscillatory behavior. Periodic breathing is associated with increased mortality, and it is observed in a variety of situations, such as acute hypoxia, chronic heart failure, and damage to respiratory centers. The standard quantification for the diagnosis of sleep related breathing disorders is the apnea-hypopnea index (AHI), which measures the proportion of apneic/hypopneic events during polysomnography. Determining the AHI is labor-intensive and requires the simultaneous recording of airflow and oxygen saturation. In this paper, we propose an automated, simple, and novel methodology for the detection and qualification of periodic breathing: the estimated amplitude modulation index (eAMI). Patients or Participants: Antarctic cohort (3,800 meters): 13 normal individuals. Clinical cohort: 39 different patients suffering from diverse sleep-related pathologies. Measurements and Results: When tested in a population with high levels of periodic breathing (Antarctic cohort), eAMI was closely correlated with AHI (r = 0.95, P Dolenc-Groselj L, Eiken O, Mekjavic IB, Migeotte PF, Macdonald-Nethercott E, Meeusen R, Neyt X. eAMI: a qualitative quantification of periodic breathing based on amplitude of oscillations. SLEEP 2015;38(3):381–389. PMID:25581914
Existence of periodic orbits in nonlinear oscillators of Emden–Fowler form
Energy Technology Data Exchange (ETDEWEB)
Mancas, Stefan C., E-mail: mancass@erau.edu [Department of Mathematics, Embry–Riddle Aeronautical University, Daytona Beach, FL 32114-3900 (United States); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICyT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Camino a la presa San José 2055, Col. Lomas 4a Sección, 78216 San Luis Potosí, SLP (Mexico)
2016-01-28
The nonlinear pseudo-oscillator recently tackled by Gadella and Lara is mapped to an Emden–Fowler (EF) equation that is written as an autonomous two-dimensional ODE system for which we provide the phase-space analysis and the parametric solution. Through an invariant transformation we find periodic solutions to a certain class of EF equations that pass an integrability condition. We show that this condition is necessary to have periodic solutions and via the ODE analysis we also find the sufficient condition for periodic orbits. EF equations that do not pass integrability conditions can be made integrable via an invariant transformation which also allows us to construct periodic solutions to them. Two other nonlinear equations, a zero-frequency Ermakov equation and a positive power Emden–Fowler equation, are discussed in the same context. - Highlights: • An invariant transformation is used to find periodic solution of EF equations. • Phase plane study of the EF autonomous two-dimensional ODE system is performed. • Three examples are presented from the standpoint of the phase plane analysis.
Altamirano, D.; Linares, M.; Patruno, A.; Degenaar, N.; Wijnands, R.; Klein-Wolt, M.; van der Klis, M.; Markwardt, C.; Swank, J.
2010-01-01
We present a detailed study of the X-ray energy and power spectral properties of the neutron star transient IGR J17191−2821. We discovered four instances of pairs of simultaneous kilohertz quasi-periodic oscillations (kHz QPOs). The frequency difference between these kHz QPOs is between 315 and 362
International Nuclear Information System (INIS)
Chedjou, Jean Chamberlain; Kyamakya, Kyandoghere
2010-01-01
It is well known that a machine vision-based analysis of a dynamic scene, for example in the context of advanced driver assistance systems (ADAS), does require real-time processing capabilities. Therefore, the system used must be capable of performing both robust and ultrafast analyses. Machine vision in ADAS must fulfil the above requirements when dealing with a dynamically changing visual context (i.e. driving in darkness or in a foggy environment, etc). Among the various challenges related to the analysis of a dynamic scene, this paper focuses on contrast enhancement, which is a well-known basic operation to improve the visual quality of an image (dynamic or static) suffering from poor illumination. The key objective is to develop a systematic and fundamental concept for image contrast enhancement that should be robust despite a dynamic environment and that should fulfil the real-time constraints by ensuring an ultrafast analysis. It is demonstrated that the new approach developed in this paper is capable of fulfilling the expected requirements. The proposed approach combines the good features of the 'coupled oscillators'-based signal processing paradigm with the good features of the 'cellular neural network (CNN)'-based one. The first paradigm in this combination is the 'master system' and consists of a set of coupled nonlinear ordinary differential equations (ODEs) that are (a) the so-called 'van der Pol oscillator' and (b) the so-called 'Duffing oscillator'. It is then implemented or realized on top of a 'slave system' platform consisting of a CNN-processors platform. An offline bifurcation analysis is used to find out, a priori, the windows of parameter settings in which the coupled oscillator system exhibits the best and most appropriate behaviours of interest for an optimal resulting image processing quality. In the frame of the extensive bifurcation analysis carried out, analytical formulae have been derived, which are capable of determining the various
International Nuclear Information System (INIS)
Hao, Lijie; Yang, Zhuoqin; Lei, Jinzhi
2015-01-01
Highlights: • A delay differentiation equation model for CREB regulation is developed. • Increasing the time delay can generate various bifurcations. • Increasing the time delay can induce chaos by two routes. - Abstract: The ability to form long-term memories is an important function for the nervous system, and the formation process is dynamically regulated through various transcription factors, including CREB proteins. In this paper, we investigate the dynamics of a delay differential equation model for CREB protein activities, which involves two positive and two negative feedbacks in the regulatory network. We discuss the dynamical mechanisms underlying the induction of long-term memory, in which bistability is essential for the formation of long-term memory, while long time delay can destabilize the high level steady state to inhibit the long-term memory formation. The model displays rich dynamical response to stimuli, including monostability, bistability, and oscillations, and can transit between different states by varying the negative feedback strength. Introduction of a time delay to the model can generate various bifurcations such as Hopf bifurcation, fold limit cycle bifurcation, Neimark–Sacker bifurcation of cycles, and period-doubling bifurcation, etc. Increasing the time delay can induce chaos by two routes: quasi-periodic route and period-doubling cascade.
Hopf bifurcation and chaos in a third-order phase-locked loop
Piqueira, José Roberto C.
2017-01-01
Phase-locked loops (PLLs) are devices able to recover time signals in several engineering applications. The literature regarding their dynamical behavior is vast, specifically considering that the process of synchronization between the input signal, coming from a remote source, and the PLL local oscillation is robust. For high-frequency applications it is usual to increase the PLL order by increasing the order of the internal filter, for guarantying good transient responses; however local parameter variations imply structural instability, thus provoking a Hopf bifurcation and a route to chaos for the phase error. Here, one usual architecture for a third-order PLL is studied and a range of permitted parameters is derived, providing a rule of thumb for designers. Out of this range, a Hopf bifurcation appears and, by increasing parameters, the periodic solution originated by the Hopf bifurcation degenerates into a chaotic attractor, therefore, preventing synchronization.
Renson, Ludovic; Barton, David A. W.; Neild, Simon A.
Control-based continuation (CBC) is a means of applying numerical continuation directly to a physical experiment for bifurcation analysis without the use of a mathematical model. CBC enables the detection and tracking of bifurcations directly, without the need for a post-processing stage as is often the case for more traditional experimental approaches. In this paper, we use CBC to directly locate limit-point bifurcations of a periodically forced oscillator and track them as forcing parameters are varied. Backbone curves, which capture the overall frequency-amplitude dependence of the system’s forced response, are also traced out directly. The proposed method is demonstrated on a single-degree-of-freedom mechanical system with a nonlinear stiffness characteristic. Results are presented for two configurations of the nonlinearity — one where it exhibits a hardening stiffness characteristic and one where it exhibits softening-hardening.
Kološ, Martin; Tursunov, Arman; Stuchlík, Zdeněk
2017-12-01
The study of quasi-periodic oscillations (QPOs) of X-ray flux observed in the stellar-mass black hole binaries can provide a powerful tool for testing of the phenomena occurring in the strong gravity regime. Magnetized versions of the standard geodesic models of QPOs can explain the observationally fixed data from the three microquasars. We perform a successful fitting of the HF QPOs observed for three microquasars, GRS 1915+105, XTE 1550-564 and GRO 1655-40, containing black holes, for magnetized versions of both epicyclic resonance and relativistic precession models and discuss the corresponding constraints of parameters of the model, which are the mass and spin of the black hole and the parameter related to the external magnetic field. The estimated magnetic field intensity strongly depends on the type of objects giving the observed HF QPOs. It can be as small as 10^{-5} G if electron oscillatory motion is relevant, but it can be by many orders higher for protons or ions (0.02-1 G), or even higher for charged dust or such exotic objects as lighting balls, etc. On the other hand, if we know by any means the magnetic field intensity, our model implies strong limit on the character of the oscillating matter, namely its specific charge.
Energy Technology Data Exchange (ETDEWEB)
Kolos, Martin; Tursunov, Arman; Stuchlik, Zdenek [Silesian University in Opava, Institute of Physics and Research Centre of Theoretical Physics and Astrophysics, Faculty of Philosophy and Science, Opava (Czech Republic)
2017-12-15
The study of quasi-periodic oscillations (QPOs) of X-ray flux observed in the stellar-mass black hole binaries can provide a powerful tool for testing of the phenomena occurring in the strong gravity regime. Magnetized versions of the standard geodesic models of QPOs can explain the observationally fixed data from the three microquasars. We perform a successful fitting of the HF QPOs observed for three microquasars, GRS 1915+105, XTE 1550-564 and GRO 1655-40, containing black holes, for magnetized versions of both epicyclic resonance and relativistic precession models and discuss the corresponding constraints of parameters of the model, which are the mass and spin of the black hole and the parameter related to the external magnetic field. The estimated magnetic field intensity strongly depends on the type of objects giving the observed HF QPOs. It can be as small as 10{sup -5} G if electron oscillatory motion is relevant, but it can be by many orders higher for protons or ions (0.02-1 G), or even higher for charged dust or such exotic objects as lighting balls, etc. On the other hand, if we know by any means the magnetic field intensity, our model implies strong limit on the character of the oscillating matter, namely its specific charge. (orig.)
Bifurcation analysis of a delay reaction-diffusion malware propagation model with feedback control
Zhu, Linhe; Zhao, Hongyong; Wang, Xiaoming
2015-05-01
With the rapid development of network information technology, information networks security has become a very critical issue in our work and daily life. This paper attempts to develop a delay reaction-diffusion model with a state feedback controller to describe the process of malware propagation in mobile wireless sensor networks (MWSNs). By analyzing the stability and Hopf bifurcation, we show that the state feedback method can successfully be used to control unstable steady states or periodic oscillations. Moreover, formulas for determining the properties of the bifurcating periodic oscillations are derived by applying the normal form method and center manifold theorem. Finally, we conduct extensive simulations on large-scale MWSNs to evaluate the proposed model. Numerical evidences show that the linear term of the controller is enough to delay the onset of the Hopf bifurcation and the properties of the bifurcation can be regulated to achieve some desirable behaviors by choosing the appropriate higher terms of the controller. Furthermore, we obtain that the spatial-temporal dynamic characteristics of malware propagation are closely related to the rate constant for nodes leaving the infective class for recovered class and the mobile behavior of nodes.
Quantum dot spin-V(E)CSELs: polarization switching and periodic oscillations
Li, Nianqiang; Alexandropoulos, Dimitris; Susanto, Hadi; Henning, Ian; Adams, Michael
2017-09-01
Spin-polarized vertical (external) cavity surface-emitting lasers [Spin-V(E)CSELs] using quantum dot (QD) material for the active region, can display polarization switching between the right- and left-circularly polarized fields via control of the pump polarization. In particular, our previous experimental results have shown that the output polarization ellipticity of the spin-V(E)CSEL emission can exhibit either the same handedness as that of the pump polarization or the opposite, depending on the experimental operating conditions. In this contribution, we use a modified version of the spin-flip model in conjunction with combined time-independent stability analysis and direct time integration. With two representative sets of parameters our simulation results show good agreement with experimental observations. In addition periodic oscillations provide further insight into the dynamic properties of spin-V(E)CSELs.
Atsumi, Yu; Nakao, Hiroya
2012-05-01
A system of phase oscillators with repulsive global coupling and periodic external forcing undergoing asynchronous rotation is considered. The synchronization rate of the system can exhibit persistent fluctuations depending on parameters and initial phase distributions, and the amplitude of the fluctuations scales with the system size for uniformly random initial phase distributions. Using the Watanabe-Strogatz transformation that reduces the original system to low-dimensional macroscopic equations, we show that the fluctuations are collective dynamics of the system corresponding to low-dimensional trajectories of the reduced equations. It is argued that the amplitude of the fluctuations is determined by the inhomogeneity of the initial phase distribution, resulting in system-size scaling for the random case.
Queiroz-Claret, C; Valon, C; Queiroz, O
1988-01-01
An unconventional hypothesis to the molecular basis of enzyme rhythms is that the intrinsic physical instability of the protein molecules which, in an aqueous medium, tend to move continuously from one conformational state to another could lead, in the population of enzyme molecules, to sizeable long-period oscillations in affinity for substrate and sensitivity to ligands and regulatory effects. To investigate this hypothesis, malate dehydrogenase was extracted and purified from leaves of the plant Kalanchoe blossfeldiana. The enzyme solutions were maintained under constant conditions and sampled at regular intervals for up to 40 or 70 h for measurements of activity as a function of substrate concentration, Km for oxaloacetic acid and sensitivity to the action of 2,3-butanedione, a modifier of active site arginyl residues. The results show that continuous slow oscillations in the catalytic capacity of the enzyme occur in all the extracts checked, together with fluctuations in Km. Apparent circadian periodicities were observed in accordance with previous data established during long run (100 h) experiments. The saturation curves for substrate showed multiple kinetic functions, with various pronounced intermediary plateaus and "bumps" depending on the time of sampling. Variation in the response to the effect of butanedione indicated fluctuation in the accessibility to the active site. Taken together, the results suggest that, under constant conditions, the enzyme in solution shifts continuously and reversibly between different configurations. This was confirmed by parallel studies on the proton-NMR spectrum of water aggregates in the enzyme solution and proton exchange rates.(ABSTRACT TRUNCATED AT 250 WORDS)
QUASI-PERIODIC OSCILLATIONS AND BROADBAND VARIABILITY IN SHORT MAGNETAR BURSTS
Energy Technology Data Exchange (ETDEWEB)
Huppenkothen, Daniela; Watts, Anna L.; Uttley, Phil; Van der Horst, Alexander J.; Van der Klis, Michiel [Astronomical Institute ' ' Anton Pannekoek' ' , University of Amsterdam, Postbus 94249, 1090-GE Amsterdam (Netherlands); Kouveliotou, Chryssa [Office of Science and Technology, ZP12, NASA Marshall Space Flight Center, Huntsville, AL 35812 (United States); Goegues, Ersin [Sabanc Latin-Small-Letter-Dotless-I University, Orhanl Latin-Small-Letter-Dotless-I -Tuzla, Istanbul 34956 (Turkey); Granot, Jonathan [The Open University of Israel, 1 University Road, P.O. Box 808, Ra' anana 43537 (Israel); Vaughan, Simon [X-Ray and Observational Astronomy Group, University of Leicester, Leicester LE1 7RH (United Kingdom); Finger, Mark H., E-mail: D.Huppenkothen@uva.nl [Universities Space Research Association, Huntsville, AL 35805 (United States)
2013-05-01
The discovery of quasi-periodic oscillations (QPOs) in magnetar giant flares has opened up prospects for neutron star asteroseismology. However, with only three giant flares ever recorded, and only two with data of sufficient quality to search for QPOs, such analysis is seriously data limited. We set out a procedure for doing QPO searches in the far more numerous, short, less energetic magnetar bursts. The short, transient nature of these bursts requires the implementation of sophisticated statistical techniques to make reliable inferences. Using Bayesian statistics, we model the periodogram as a combination of red noise at low frequencies and white noise at high frequencies, which we show is a conservative approach to the problem. We use empirical models to make inferences about the potential signature of periodic and QPOs at these frequencies. We compare our method with previously used techniques and find that although it is on the whole more conservative, it is also more reliable in ruling out false positives. We illustrate our Bayesian method by applying it to a sample of 27 bursts from the magnetar SGR J0501+4516 observed by the Fermi Gamma-ray Burst Monitor, and we find no evidence for the presence of QPOs in any of the bursts in the unbinned spectra, but do find a candidate detection in the binned spectra of one burst. However, whether this signal is due to a genuine quasi-periodic process, or can be attributed to unmodeled effects in the noise is at this point a matter of interpretation.
A Search for Quasi-periodic Oscillations in the Blazar 1ES 1959+650
Energy Technology Data Exchange (ETDEWEB)
Li, Xiao-Pan; Luo, Yu-Hui; Yang, Hai-Yan; Cai, Yan; Yang, Hai-Tao [Department of Physics, Zhaotong University, Zhaotong, 657000 (China); Yang, Cheng, E-mail: lxpzrc@163.com [College of Photoelectron and Communication Engineering, Yunnan Open University, Kunming, 650223 (China)
2017-09-20
We have searched quasi-periodic oscillations (QPOs) in the 15 GHz light curve of the BL Lac object 1ES 1959+650 monitored by the Owens Valley Radio Observatory 40 m telescope during the period from 2008 January to 2016 February, using the Lomb–Scargle Periodogram, power spectral density (PSD), discrete autocorrelation function, and phase dispersion minimization (PDM) techniques. The red noise background has been established via the PSD method, and no QPO can be derived at the 3 σ confidence level accounting for the impact of the red noise variability. We conclude that the light curve of 1ES 1959+650 can be explained by a stochastic red noise process that contributes greatly to the total observed variability amplitude, dominates the power spectrum, causes spurious bumps and wiggles in the autocorrelation function and can result in the variance of the folded light curve decreasing toward lower temporal frequencies when few-cycle, sinusoid-like patterns are present. Moreover, many early supposed periodicity claims for blazar light curves need to be reevaluated assuming red noise.
Homoclinic bifurcation in Chua's circuit
Indian Academy of Sciences (India)
spiking and bursting behaviors of neurons. Recent experiments ... a limit cycle increases in a wiggle with alternate sequences of stable and unstable orbits via ... further changes in parameter, the system shows period-adding bifurcation when .... [21–23] transition from limit cycle to single scroll chaos via PD and then to alter-.
International Nuclear Information System (INIS)
Woafo, P.
1999-12-01
This paper deals with the dynamics of a model describing systems consisting of the classical Van der Pol oscillator coupled gyroscopically to a linear oscillator. Both the forced and autonomous cases are considered. Harmonic response is investigated along with its stability boundaries. Condition for quenching phenomena in the autonomous case is derived. Neimark bifurcation is observed and it is found that our model shows period doubling and period-m sudden transitions to chaos. Synchronization of two and more systems in their chaotic regime is presented. (author)
Weak wide-band signal detection method based on small-scale periodic state of Duffing oscillator
Hou, Jian; Yan, Xiao-peng; Li, Ping; Hao, Xin-hong
2018-03-01
The conventional Duffing oscillator weak signal detection method, which is based on a strong reference signal, has inherent deficiencies. To address these issues, the characteristics of the Duffing oscillatorʼs phase trajectory in a small-scale periodic state are analyzed by introducing the theory of stopping oscillation system. Based on this approach, a novel Duffing oscillator weak wide-band signal detection method is proposed. In this novel method, the reference signal is discarded, and the to-be-detected signal is directly used as a driving force. By calculating the cosine function of a phase space angle, a single Duffing oscillator can be used for weak wide-band signal detection instead of an array of uncoupled Duffing oscillators. Simulation results indicate that, compared with the conventional Duffing oscillator detection method, this approach performs better in frequency detection intervals, and reduces the signal-to-noise ratio detection threshold, while improving the real-time performance of the system. Project supported by the National Natural Science Foundation of China (Grant No. 61673066).
ON THE HIGH-FREQUENCY QUASI-PERIODIC OSCILLATIONS FROM BLACK HOLES
International Nuclear Information System (INIS)
Erkut, M. Hakan
2011-01-01
We apply the global mode analysis, which has been recently developed for the modeling of kHz quasi-periodic oscillations (QPOs) from neutron stars, to the inner region of an accretion disk around a rotating black hole. Within a pseudo-Newtonian approach that keeps the ratio of the radial epicyclic frequency κ to the orbital frequency Ω the same as the corresponding ratio for a Kerr black hole, we determine the innermost disk region where the hydrodynamic modes grow in amplitude. We find that the radiation flux emerging from the inner disk has the highest values within the same region. Using the flux-weighted averages of the frequency bands over this region we identify the growing modes with highest frequency branches Ω + κ and Ω to be the plausible candidates for the high-frequency QPO pairs observed in black hole systems. The observed frequency ratio around 1.5 can therefore be understood naturally in terms of the global free oscillations in the innermost region of a viscous accretion disk around a black hole without invoking a particular resonance to produce black hole QPOs. Although the frequency ratio (Ω + κ)/(Ω) is found to be not sensitive to the black hole's spin which is good for explaining the high-frequency QPOs, it may work as a limited diagnostic of the spin parameter to distinguish black holes with very large spin from the slowly rotating ones. Within our model we estimate the frequency ratio of a high-frequency QPO pair to be greater than 1.5 if the black hole is a slow rotator. For fast rotating black holes, we expect the same ratio to be less than 1.5.
A codimension two bifurcation in a railway bogie system
DEFF Research Database (Denmark)
Zhang, Tingting; True, Hans; Dai, Huanyun
2017-01-01
In this paper, a comprehensive analysis is presented to investigate a codimension two bifurcation that exists in a nonlinear railway bogie dynamic system combining theoretical analysis with numerical investigation. By using the running velocity V and the primary longitudinal stiffness (Formula...... coexist in a range of the bifurcation parameters which can lead to jumps in the lateral oscillation amplitude of the railway bogie system. Furthermore, reduce the values of the bifurcation parameters gradually. Firstly, the supercritical Hopf bifurcation turns into a subcritical one with multiple limit...
Juckett, David A.
2001-09-01
A more complete understanding of the periodic dynamics of the Sun requires continued exploration of non-11-year oscillations in addition to the benchmark 11-year sunspot cycle. In this regard, several solar, geomagnetic, and cosmic ray time series were examined to identify common spectral components and their relative phase relationships. Several non-11-year oscillations were identified within the near-decadal range with periods of ~8, 10, 12, 15, 18, 22, and 29 years. To test whether these frequency components were simply low-level noise or were related to a common source, the phases were extracted for each component in each series. The phases were nearly identical across the solar and geomagnetic series, while the corresponding components in four cosmic ray surrogate series exhibited inverted phases, similar to the known phase relationship with the 11-year sunspot cycle. Cluster analysis revealed that this pattern was unlikely to occur by chance. It was concluded that many non-11-year oscillations truly exist in the solar dynamical environment and that these contribute to the complex variations observed in geomagnetic and cosmic ray time series. Using the different energy sensitivities of the four cosmic ray surrogate series, a preliminary indication of the relative intensities of the various solar-induced oscillations was observed. It provides evidence that many of the non-11-year oscillations result from weak interplanetary magnetic field/solar wind oscillations that originate from corresponding variations in the open-field regions of the Sun.
Multiple-wavelength Variability and Quasi-periodic Oscillation of PMN J0948+0022
Energy Technology Data Exchange (ETDEWEB)
Zhang, Jin [Key Laboratory of Space Astronomy and Technology, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012 (China); Zhang, Hai-Ming; Zhu, Yong-Kai; Lu, Rui-Jing; Liang, En-Wei [Guangxi Key Laboratory for Relativistic Astrophysics, Department of Physics, Guangxi University, Nanning 530004 (China); Yi, Ting-Feng [Department of Physics, Yunnan Normal University, Kunming 650500 (China); Yao, Su, E-mail: jinzhang@bao.ac.cn [Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871 (China)
2017-11-01
We present a comprehensive analysis of multiple-wavelength observational data of the first GeV-selected narrow-line Seyfert 1 galaxy PMN J0948+0022. We derive its light curves in the γ -ray and X-ray bands from the data observed with Fermi /LAT and Swift /XRT, and generate the optical and radio light curves by collecting the data from the literature. These light curves show significant flux variations. With the LAT data we show that this source is analogous to typical flat spectrum radio quasars in the L {sub γ} –Γ {sub γ} plane, where L {sub γ} and Γ {sub γ} are the luminosity and spectral index in the LAT energy band. The γ -ray flux is correlated with the V-band flux with a lag of ∼44 days, and a moderate quasi-periodic oscillation (QPO) with a periodicity of ∼490 days observed in the LAT light curve. A similar QPO signature is also found in the V-band light curve. The γ -ray flux is not correlated with the radio flux in 15 GHz, and no similar QPO signature is found at a confidence level of 95%. Possible mechanisms of the QPO are discussed. We propose that gravitational-wave observations in the future may clarify the current plausible models for the QPO.
Bifurcation scenarios for bubbling transition.
Zimin, Aleksey V; Hunt, Brian R; Ott, Edward
2003-01-01
Dynamical systems with chaos on an invariant submanifold can exhibit a type of behavior called bubbling, whereby a small random or fixed perturbation to the system induces intermittent bursting. The bifurcation to bubbling occurs when a periodic orbit embedded in the chaotic attractor in the invariant manifold becomes unstable to perturbations transverse to the invariant manifold. Generically the periodic orbit can become transversely unstable through a pitchfork, transcritical, period-doubling, or Hopf bifurcation. In this paper a unified treatment of the four types of bubbling bifurcation is presented. Conditions are obtained determining whether the transition to bubbling is soft or hard; that is, whether the maximum burst amplitude varies continuously or discontinuously with variation of the parameter through its critical value. For soft bubbling transitions, the scaling of the maximum burst amplitude with the parameter is derived. For both hard and soft transitions the scaling of the average interburst time with the bifurcation parameter is deduced. Both random (noise) and fixed (mismatch) perturbations are considered. Results of numerical experiments testing our theoretical predictions are presented.
International Nuclear Information System (INIS)
Kumar, Pankaj; Cho, Kyung-Suk; Nakariakov, Valery M.
2015-01-01
We report decaying quasi-periodic intensity oscillations in the X-ray (6–12 keV) and extreme-ultraviolet (EUV) channels (131, 94, 1600, 304 Å) observed by the Fermi Gamma-ray Burst Monitor and Solar Dynamics Observatory/Atmospheric Imaging Assembly (AIA), respectively, during a C-class flare. The estimated periods of oscillation and decay time in the X-ray channel (6–12 keV) were about 202 and 154 s, respectively. A similar oscillation period was detected at the footpoint of the arcade loops in the AIA 1600 and 304 Å channels. Simultaneously, AIA hot channels (94 and 131 Å) reveal propagating EUV disturbances bouncing back and forth between the footpoints of the arcade loops. The period of the oscillation and decay time were about 409 and 1121 s, respectively. The characteristic phase speed of the wave is about 560 km s −1 for about 115 Mm of loop length, which is roughly consistent with the sound speed at the temperature about 10–16 MK (480–608 km s −1 ). These EUV oscillations are consistent with the Solar and Heliospheric Observatory/Solar Ultraviolet Measurement of Emitted Radiation Doppler-shift oscillations interpreted as the global standing slow magnetoacoustic wave excited by a flare. The flare occurred at one of the footpoints of the arcade loops, where the magnetic topology was a 3D fan-spine with a null-point. Repetitive reconnection at this footpoint could have caused the periodic acceleration of non-thermal electrons that propagated to the opposite footpoint along the arcade and that are precipitating there, causing the observed 202 s periodicity. Other possible interpretations, e.g., the second harmonics of the slow mode, are also discussed
Energy Technology Data Exchange (ETDEWEB)
Kumar, Pankaj; Cho, Kyung-Suk [Korea Astronomy and Space Science Institute (KASI), Daejeon, 305-348 (Korea, Republic of); Nakariakov, Valery M., E-mail: pankaj@kasi.re.kr [Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick, CV4 7AL (United Kingdom)
2015-05-01
We report decaying quasi-periodic intensity oscillations in the X-ray (6–12 keV) and extreme-ultraviolet (EUV) channels (131, 94, 1600, 304 Å) observed by the Fermi Gamma-ray Burst Monitor and Solar Dynamics Observatory/Atmospheric Imaging Assembly (AIA), respectively, during a C-class flare. The estimated periods of oscillation and decay time in the X-ray channel (6–12 keV) were about 202 and 154 s, respectively. A similar oscillation period was detected at the footpoint of the arcade loops in the AIA 1600 and 304 Å channels. Simultaneously, AIA hot channels (94 and 131 Å) reveal propagating EUV disturbances bouncing back and forth between the footpoints of the arcade loops. The period of the oscillation and decay time were about 409 and 1121 s, respectively. The characteristic phase speed of the wave is about 560 km s{sup −1} for about 115 Mm of loop length, which is roughly consistent with the sound speed at the temperature about 10–16 MK (480–608 km s{sup −1}). These EUV oscillations are consistent with the Solar and Heliospheric Observatory/Solar Ultraviolet Measurement of Emitted Radiation Doppler-shift oscillations interpreted as the global standing slow magnetoacoustic wave excited by a flare. The flare occurred at one of the footpoints of the arcade loops, where the magnetic topology was a 3D fan-spine with a null-point. Repetitive reconnection at this footpoint could have caused the periodic acceleration of non-thermal electrons that propagated to the opposite footpoint along the arcade and that are precipitating there, causing the observed 202 s periodicity. Other possible interpretations, e.g., the second harmonics of the slow mode, are also discussed.
Bifurcations of a class of singular biological economic models
International Nuclear Information System (INIS)
Zhang Xue; Zhang Qingling; Zhang Yue
2009-01-01
This paper studies systematically a prey-predator singular biological economic model with time delay. It shows that this model exhibits two bifurcation phenomena when the economic profit is zero. One is transcritical bifurcation which changes the stability of the system, and the other is singular induced bifurcation which indicates that zero economic profit brings impulse, i.e., rapid expansion of the population in biological explanation. On the other hand, if the economic profit is positive, at a critical value of bifurcation parameter, the system undergoes a Hopf bifurcation, i.e., the increase of delay destabilizes the system and bifurcates into small amplitude periodic solution. Finally, by using Matlab software, numerical simulations illustrate the effectiveness of the results obtained here. In addition, we study numerically that the system undergoes a saddle-node bifurcation when the bifurcation parameter goes through critical value of positive economic profit.
Bifurcation of the spin-wave equations
International Nuclear Information System (INIS)
Cascon, A.; Koiller, J.; Rezende, S.M.
1990-01-01
We study the bifurcations of the spin-wave equations that describe the parametric pumping of collective modes in magnetic media. Mechanisms describing the following dynamical phenomena are proposed: (i) sequential excitation of modes via zero eigenvalue bifurcations; (ii) Hopf bifurcations followed (or not) by Feingenbaum cascades of period doubling; (iii) local and global homoclinic phenomena. Two new organizing center for routes to chaos are identified; in the classification given by Guckenheimer and Holmes [GH], one is a codimension-two local bifurcation, with one pair of imaginary eigenvalues and a zero eigenvalue, to which many dynamical consequences are known; secondly, global homoclinic bifurcations associated to splitting of separatrices, in the limit where the system can be considered a Hamiltonian subjected to weak dissipation and forcing. We outline what further numerical and algebraic work is necessary for the detailed study following this program. (author)
Lipovsky, B.; Dunham, E. M.
2013-12-01
Long-period seismicity due to the excitation of hydraulic fracture normal modes is thought to occur in many geological systems, including volcanoes, glaciers and ice sheets, and hydrocarbon reservoirs. To better quantify the physical dimensions of fluid-filled cracks and properties of the fluid within them, we study wave motion along a thin hydraulic fracture waveguide. We present a linearized analysis that accounts for quasi-dynamic elasticity of the fracture wall, as well as fluid drag, inertia, and compressibility. We consider symmetric perturbations and neglect the effects of stratification and gravity. In the long-wavelength or thin-fracture limit, dispersive guided waves known as crack waves propagate with phase velocity cw=√(G*|k|w/ρ), where G* = G/(1-υ) for shear modulus G and Poisson ratio υ, w is the crack half-width, k is the wavenumber, and ρ is the fluid density. Restoring forces from elastic wall deformation drive wave motions. In the opposite, short-wavelength limit, guided waves are simply sound waves within the fluid and little seismic excitation occurs due to minimal fluid-solid coupling. We focus on long-wavelength crack waves, which, in the form of standing wave modes in finite-length cracks, are thought to be a common mechanism for long-period seismicity. The dispersive nature of crack waves implies several basic scaling relations that might be useful when interpreting statistics of long-period events. Seismic observations may constrain a characteristic frequency f0 and seismic moment M0~GδwR2, where δw is the change in crack width and R is the crack dimension. Resonant modes of a fluid-filled crack have associated frequencies f~cw/R. Linear elasticity provides a link between pressure changes δp in the crack and the induced opening δw: δp~G δw/R. Combining these, and assuming that pressure changes have no variation with crack dimension, leads to the scaling law relating seismic moment and oscillation frequency, M0~(Gwδp/ρ)f0
Quasi-periodic oscillations from post-shock accretion column of polars
Bera, Prasanta; Bhattacharya, Dipankar
2018-02-01
A set of strongly magnetized accreting white dwarfs (polars) shows quasi-periodic oscillations (QPOs) with frequency about a Hz in their optical luminosity. These Hz-frequency QPOs are thought to be generated by intensity variations of the emitted radiation originating at the post-shock accretion column. Thermal instability in the post-shock region, triggered by efficient cooling process at the base, is believed to be the primary reason behind the temporal variability. Here, we study the structure and the dynamical properties of the post-shock accretion column including the effects of bremsstrahlung and cyclotron radiation. We find that the presence of significant cyclotron emission in optical band reduces the overall variability of the post-shock region. In the case of a larger post-shock region above the stellar surface, the effects of stratification due to stellar gravity become important. An accretion column, influenced by the strong gravity, has a smaller variability as the strength of the thermal instability at the base of the column is reduced. On the other hand, the cool, dense plasma, accumulated just above the stellar surface, may enhance the post-shock variability due to the propagation of magnetic perturbations. These characteristics of the post-shock region are consistent with the observed properties of V834 Cen and in general with cataclysmic variable sources that exhibit QPO frequency of about a Hz.
On one-parametric formula relating the frequencies of twin-peak quasi-periodic oscillations
Török, Gabriel; Goluchová, Kateřina; Šrámková, Eva; Horák, Jiří; Bakala, Pavel; Urbanec, Martin
2018-01-01
Twin-peak quasi-periodic oscillations (QPOs) are observed in several low-mass X-ray binary systems containing neutron stars. Timing the analysis of X-ray fluxes of more than dozen of such systems reveals remarkable correlations between the frequencies of two characteristic peaks present in the power density spectra. The individual correlations clearly differ, but they roughly follow a common individual pattern. High values of measured QPO frequencies and strong modulation of the X-ray flux both suggest that the observed correlations are connected to orbital motion in the innermost part of an accretion disc. Several attempts to model these correlations with simple geodesic orbital models or phenomenological relations have failed in the past. We find and explore a surprisingly simple analytic relation that reproduces individual correlations for a group of several sources through a single parameter. When an additional free parameter is considered within our relation, it well reproduces the data of a large group of 14 sources. The very existence and form of this simple relation support the hypothesis of the orbital origin of QPOs and provide the key for further development of QPO models. We discuss a possible physical interpretation of our relation's parameters and their links to concrete QPO models.
Strong gravity effects of rotating black holes: quasi-periodic oscillations
International Nuclear Information System (INIS)
Aliev, Alikram N; Esmer, Göksel Daylan; Talazan, Pamir
2013-01-01
We explore strong gravity effects of the geodesic motion in the spacetime of rotating black holes in general relativity and braneworld gravity. We focus on the description of the motion in terms of three fundamental frequencies: the orbital frequency, the radial and vertical epicyclic frequencies. For a Kerr black hole, we perform a detailed numerical analysis of these frequencies at the innermost stable circular orbits and beyond them as well as at the characteristic stable orbits, at which the radial epicyclic frequency attains its highest value. We find that the values of the epicyclic frequencies for a class of stable orbits exhibit good qualitative agreement with the observed frequencies of the twin peaks quasi-periodic oscillations (QPOs) in some black hole binaries. We also find that at the characteristic stable circular orbits, where the radial (or the vertical) epicyclic frequency has maxima, the vertical and radial epicyclic frequencies exhibit an approximate 2:1 ratio even in the case of near-extreme rotation of the black hole. Next, we perform a similar analysis of the fundamental frequencies for a rotating braneworld black hole and argue that the existence of such a black hole with a negative tidal charge, whose angular momentum exceeds the Kerr bound in general relativity, does not confront with the observations of high-frequency QPOs. (paper)
Quasi-periodic oscillations and the global modes of relativistic, MHD accretion discs
Dewberry, Janosz W.; Latter, Henrik N.; Ogilvie, Gordon I.
2018-05-01
The high-frequency quasi-periodic oscillations that punctuate the light curves of X-ray binary systems present a window on to the intrinsic properties of stellar-mass black holes and hence a testbed for general relativity. One explanation for these features is that relativistic distortion of the accretion disc's differential rotation creates a trapping region in which inertial waves (r-modes) might grow to observable amplitudes. Local analyses, however, predict that large-scale magnetic fields push this trapping region to the inner disc edge, where conditions may be unfavourable for r-mode growth. We revisit this problem from a pseudo-Newtonian but fully global perspective, deriving linearized equations describing a relativistic, magnetized accretion flow, and calculating normal modes with and without vertical density stratification. In an unstratified model we confirm that vertical magnetic fields drive r-modes towards the inner edge, though the effect depends on the choice of vertical wavenumber. In a global model we better quantify this susceptibility, and its dependence on the disc's vertical structure and thickness. Our calculations suggest that in thin discs, r-modes may remain independent of the inner disc edge for vertical magnetic fields with plasma betas as low as β ≈ 100-300. We posit that the appearance of r-modes in observations may be more determined by a competition between excitation and damping mechanisms near the ISCO than by the modification of the trapping region by magnetic fields.
Lin, Lyu-Chih; Liu, Ssu-Hsin; Lin, Fan-Yi
2017-10-16
We study the stability of period-one (P1) oscillations experimentally generated by semiconductor lasers subject to optical injection (OI) and by those subject to optical feedback (OF). With unique advantages of broad frequency tuning range and large sideband rejection ratio, P1 oscillations can be useful in applications such as photonic microwave generation, radio-over-fiber communication, and laser Doppler velocimeter. The stability of the P1 oscillations is critical for these applications, which can be affected by spontaneous emission and fluctuations in both temperature and injection current. Although linewidths of P1 oscillations generated by various schemes have been reported, the mechanisms and roles which each of the OI and the OF play have however not been investigated in detail. To characterize the stability of the P1 oscillations generated by the OI and the OF schemes, we measure the linewidths and linewidth reduction ratios (LRRs) of the P1 oscillations. The OF scheme has a narrowest linewidth of 0.21 ± 0.03 MHz compared to 4.7 ± 0.6 MHz in the OI scheme. In the OF scheme, a much larger region of LRRs higher than 90% is also found. The superior stability of the OF scheme is benefited by the fact that the P1 oscillations in the OF scheme are originated from the undamped relaxation oscillation of a single laser and can be phase-locked to one of its external cavity modes, whereas those in the OI scheme come from two independent lasers which bear no phase relation. Moreover, excess P1 linewidth broadening in the OI scheme caused by fluctuation in injection parameters associated with frequency jitter and relative intensity noise (RIN) is also minimized in the OF scheme.
Directory of Open Access Journals (Sweden)
Anatoly V. Klyuchevskii
2013-11-01
Full Text Available The current lithospheric geodynamics and tectonophysics in the Baikal rift are discussed in terms of a nonlinear oscillator with dissipation. The nonlinear oscillator model is applicable to the area because stress change shows up as quasi-periodic inharmonic oscillations at rifting attractor structures (RAS. The model is consistent with the space-time patterns of regional seismicity in which coupled large earthquakes, proximal in time but distant in space, may be a response to bifurcations in nonlinear resonance hysteresis in a system of three oscillators corresponding to the rifting attractors. The space-time distribution of coupled MLH > 5.5 events has been stable for the period of instrumental seismicity, with the largest events occurring in pairs, one shortly after another, on two ends of the rift system and with couples of smaller events in the central part of the rift. The event couples appear as peaks of earthquake ‘migration’ rate with an approximately decadal periodicity. Thus the energy accumulated at RAS is released in coupled large events by the mechanism of nonlinear oscillators with dissipation. The new knowledge, with special focus on space-time rifting attractors and bifurcations in a system of nonlinear resonance hysteresis, may be of theoretical and practical value for earthquake prediction issues. Extrapolation of the results into the nearest future indicates the probability of such a bifurcation in the region, i.e., there is growing risk of a pending M ≈ 7 coupled event to happen within a few years.
Bifurcation analysis and stability design for aircraft longitudinal motion with high angle of attack
Directory of Open Access Journals (Sweden)
Xin Qi
2015-02-01
Full Text Available Bifurcation analysis and stability design for aircraft longitudinal motion are investigated when the nonlinearity in flight dynamics takes place severely at high angle of attack regime. To predict the special nonlinear flight phenomena, bifurcation theory and continuation method are employed to systematically analyze the nonlinear motions. With the refinement of the flight dynamics for F-8 Crusader longitudinal motion, a framework is derived to identify the stationary bifurcation and dynamic bifurcation for high-dimensional system. Case study shows that the F-8 longitudinal motion undergoes saddle node bifurcation, Hopf bifurcation, Zero-Hopf bifurcation and branch point bifurcation under certain conditions. Moreover, the Hopf bifurcation renders series of multiple frequency pitch oscillation phenomena, which deteriorate the flight control stability severely. To relieve the adverse effects of these phenomena, a stabilization control based on gain scheduling and polynomial fitting for F-8 longitudinal motion is presented to enlarge the flight envelope. Simulation results validate the effectiveness of the proposed scheme.
Bifurcations of heterodimensional cycles with two saddle points
Energy Technology Data Exchange (ETDEWEB)
Geng Fengjie [School of Information Technology, China University of Geosciences (Beijing), Beijing 100083 (China)], E-mail: gengfengjie_hbu@163.com; Zhu Deming [Department of Mathematics, East China Normal University, Shanghai 200062 (China)], E-mail: dmzhu@math.ecnu.edu.cn; Xu Yancong [Department of Mathematics, East China Normal University, Shanghai 200062 (China)], E-mail: yancongx@163.com
2009-03-15
The bifurcations of 2-point heterodimensional cycles are investigated in this paper. Under some generic conditions, we establish the existence of one homoclinic loop, one periodic orbit, two periodic orbits, one 2-fold periodic orbit, and the coexistence of one periodic orbit and heteroclinic loop. Some bifurcation patterns different to the case of non-heterodimensional heteroclinic cycles are revealed.
Bifurcations of heterodimensional cycles with two saddle points
International Nuclear Information System (INIS)
Geng Fengjie; Zhu Deming; Xu Yancong
2009-01-01
The bifurcations of 2-point heterodimensional cycles are investigated in this paper. Under some generic conditions, we establish the existence of one homoclinic loop, one periodic orbit, two periodic orbits, one 2-fold periodic orbit, and the coexistence of one periodic orbit and heteroclinic loop. Some bifurcation patterns different to the case of non-heterodimensional heteroclinic cycles are revealed.
International Nuclear Information System (INIS)
Akopyan, A A; Oganesyan, D L
1998-01-01
It is shown that the wave equation can be solved by the method of unidirectional waves for a pulse with a duration of several oscillation periods in a medium with a quadratic nonlinearity, such as a group-3m crystal. The wave equation reduces to a system of two equations for waves with different polarisations. (laser applications and other topics in quantum electronics)
Shu, Hongying; Wang, Lin; Watmough, James
2014-01-01
Sustained and transient oscillations are frequently observed in clinical data for immune responses in viral infections such as human immunodeficiency virus, hepatitis B virus, and hepatitis C virus. To account for these oscillations, we incorporate the time lag needed for the expansion of immune cells into an immunosuppressive infection model. It is shown that the delayed antiviral immune response can induce sustained periodic oscillations, transient oscillations and even sustained aperiodic oscillations (chaos). Both local and global Hopf bifurcation theorems are applied to show the existence of periodic solutions, which are illustrated by bifurcation diagrams and numerical simulations. Two types of bistability are shown to be possible: (i) a stable equilibrium can coexist with another stable equilibrium, and (ii) a stable equilibrium can coexist with a stable periodic solution.
Unfolding the Riddling Bifurcation
DEFF Research Database (Denmark)
Maistrenko, Yu.; Popovych, O.; Mosekilde, Erik
1999-01-01
We present analytical conditions for the riddling bifurcation in a system of two symmetrically coupled, identical, smooth one-dimensional maps to be soft or hard and describe a generic scenario for the transformations of the basin of attraction following a soft riddling bifurcation.......We present analytical conditions for the riddling bifurcation in a system of two symmetrically coupled, identical, smooth one-dimensional maps to be soft or hard and describe a generic scenario for the transformations of the basin of attraction following a soft riddling bifurcation....
Very long period conduit oscillations induced by rockfalls at Kilauea Volcano, Hawaii
Chouet, Bernard A.; Dawson, Phillip B.
2013-01-01
Eruptive activity at the summit of Kilauea Volcano, Hawaii, beginning in 2010 and continuing to the present time is characterized by transient outgassing bursts accompanied by very long period (VLP) seismic signals triggered by rockfalls from the vent walls impacting a lava lake in a pit within the Halemaumau pit crater. We use raw data recorded with an 11-station broadband network to model the source mechanism of signals accompanying two large rockfalls on 29 August 2012 and two smaller average rockfalls obtained by stacking over all events with similar waveforms to improve the signal-to-noise ratio. To determine the source centroid location and source mechanism, we minimize the residual error between data and synthetics calculated by the finite difference method for a point source embedded in a homogeneous medium that takes topography into account. We apply a new waveform inversion method that accounts for the contributions from both translation and tilt in horizontal seismograms through the use of Green's functions representing the seismometer response to translation and tilt ground motions. This method enables a robust description of the source mechanism over the period range 1–1000 s. The VLP signals associated with the rockfalls originate in a source region ∼1 km below the eastern perimeter of the Halemaumau pit crater. The observed waveforms are well explained by a simple volumetric source with geometry composed of two intersecting cracks including an east striking crack (dike) dipping 80° to the north, intersecting a north striking crack (another dike) dipping 65° to the east. Each rockfall is marked by a similar step-like inflation trailed by decaying oscillations of the volumetric source, attributed to the efficient coupling at the source centroid location of the pressure and momentum changes induced by the rock mass impacting the top of the lava column. Assuming a simple lumped parameter representation of the shallow magmatic system, the
Energy Technology Data Exchange (ETDEWEB)
Linares, M.; Chakrabarty, D. [Massachusetts Institute of Technology, Kavli Institute for Astrophysics and Space Research, Cambridge, MA 02139 (United States); Altamirano, D. [Astronomical Institute ' Anton Pannekoek' , University of Amsterdam and Center for High-Energy Astrophysics, P.O. BOX 94249, 1090 GE Amsterdam (Netherlands); Cumming, A. [Department of Physics, McGill University, 3600 Rue University, Montreal, QC H3A 2T8 (Canada); Keek, L. [School of Physics and Astronomy, University of Minnesota, 116 Church Street SE, Minneapolis, MN 55455 (United States)
2012-04-01
We present a comprehensive study of the thermonuclear bursts and millihertz quasi-periodic oscillations (mHz QPOs) from the neutron star (NS) transient and 11 Hz X-ray pulsar IGR J17480-2446, located in the globular cluster Terzan 5. The increase in burst rate that we found during its 2010 outburst, when persistent luminosity rose from 0.1 to 0.5 times the Eddington limit, is in qualitative agreement with thermonuclear burning theory yet contrary to all previous observations of thermonuclear bursts. Thermonuclear bursts gradually evolved into a mHz QPO when the accretion rate increased, and vice versa. The mHz QPOs from IGR J17480-2446 resemble those previously observed in other accreting NSs, yet they feature lower frequencies (by a factor {approx}3) and occur when the persistent luminosity is higher (by a factor 4-25). We find four distinct bursting regimes and a steep (close to inverse cubic) decrease of the burst recurrence time with increasing persistent luminosity. We compare these findings to nuclear burning models and find evidence for a transition between the pure helium and mixed hydrogen/helium ignition regimes when the persistent luminosity was about 0.3 times the Eddington limit. We also point out important discrepancies between the observed bursts and theory, which predicts brighter and less frequent bursts, and suggest that an additional source of heat in the NS envelope is required to reconcile the observed and expected burst properties. We discuss the impact of NS magnetic field and spin on the expected nuclear burning regimes, in the context of this particular pulsar.
SOFT LAGS IN NEUTRON STAR kHz QUASI-PERIODIC OSCILLATIONS: EVIDENCE FOR REVERBERATION?
Energy Technology Data Exchange (ETDEWEB)
Barret, Didier, E-mail: didier.barret@irap.omp.eu [Universite de Toulouse, UPS-OMP, IRAP, F-31400 Toulouse (France); CNRS, Institut de Recherche en Astrophysique et Planetologie, 9 Av. colonel Roche, BP 44346, F-31028 Toulouse cedex 4 (France)
2013-06-10
High frequency soft reverberation lags have now been detected from stellar mass and supermassive black holes. Their interpretation involves reflection of a hard source of photons onto an accretion disk, producing a delayed reflected emission, with a time lag consistent with the light travel time between the irradiating source and the disk. Independently of the location of the clock, the kHz quasi-periodic oscillation (QPO) emission is thought to arise from the neutron star boundary layer. Here, we search for the signature of reverberation of the kHz QPO emission, by measuring the soft lags and the lag energy spectrum of the lower kHz QPOs from 4U1608-522. Soft lags, ranging from {approx}15 to {approx}40 {mu}s, between the 3-8 keV and 8-30 keV modulated emissions are detected between 565 and 890 Hz. The soft lags are not constant with frequency and show a smooth decrease between 680 Hz and 890 Hz. The broad band X-ray spectrum is modeled as the sum of a disk and a thermal Comptonized component, plus a broad iron line, expected from reflection. The spectral parameters follow a smooth relationship with the QPO frequency, in particular the fitted inner disk radius decreases steadily with frequency. Both the bump around the iron line in the lag energy spectrum and the consistency between the lag changes and the inferred changes of the inner disk radius, from either spectral fitting or the QPO frequency, suggest that the soft lags may indeed involve reverberation of the hard pulsating QPO source on the disk.
Periodic analysis of solar activity and its link with the Arctic oscillation phenomenon
Energy Technology Data Exchange (ETDEWEB)
Qu, Weizheng; Li, Chun; Du, Ling; Huang, Fei [Ocean University of China, 14-1' -601, 2117 Jinshui Road, Qingdao 266100 (China); Li, Yanfang, E-mail: quweizhe@ouc.edu.cn [Yantai Institute of Coastal Zone Research Chinese Academy of Sciences (China)
2014-12-01
Based on spectrum analysis, we provide the arithmetic expressions of the quasi 11 yr cycle, 110 yr century cycle of relative sunspot numbers, and quasi 22 yr cycle of solar magnetic field polarity. Based on a comparative analysis of the monthly average geopotential height, geopotential height anomaly, and temperature anomaly of the northern hemisphere at locations with an air pressure of 500 HPa during the positive and negative phases of AO (Arctic Oscillation), one can see that the abnormal warming period in the Arctic region corresponds to the negative phase of AO, while the anomalous cold period corresponds to its positive phase. This shows that the abnormal change in the Arctic region is an important factor in determining the anomalies of AO. In accordance with the analysis performed using the successive filtering method, one can see that the AO phenomenon occurring in January shows a clear quasi 88 yr century cycle and quasi 22 yr decadal cycle, which are closely related to solar activities. The results of our comparative analysis show that there is a close inverse relationship between the solar activities (especially the solar magnetic field index changes) and the changes in the 22 yr cycle of the AO occurring in January, and that the two trends are basically opposite of each other. That is to say, in most cases after the solar magnetic index MI rises from the lowest value, the solar magnetic field turns from north to south, and the high-energy particle flow entering the Earth's magnetosphere increases to heat the polar atmosphere, thus causing the AO to drop from the highest value; after the solar magnetic index MI drops from the highest value, the solar magnetic field turns from south to north, and the solar high-energy particle flow passes through the top of the Earth's magnetosphere rather than entering it to heat the polar atmosphere. Thus the polar temperature drops, causing the AO to rise from the lowest value. In summary, the variance
Mode locking and spatiotemporal chaos in periodically driven Gunn diodes
DEFF Research Database (Denmark)
Mosekilde, Erik; Feldberg, Rasmus; Knudsen, Carsten
1990-01-01
oscillation entrains with the external signal. This produces a devil’s staircase of frequency-locked solutions. At higher microwave amplitudes, period doubling and other forms of mode-converting bifurcations can be seen. In this interval the diode also exhibits spatiotemporal chaos. At still higher microwave...
Xiao, Min; Zheng, Wei Xing; Cao, Jinde
2013-01-01
Recent studies on Hopf bifurcations of neural networks with delays are confined to simplified neural network models consisting of only two, three, four, five, or six neurons. It is well known that neural networks are complex and large-scale nonlinear dynamical systems, so the dynamics of the delayed neural networks are very rich and complicated. Although discussing the dynamics of networks with a few neurons may help us to understand large-scale networks, there are inevitably some complicated problems that may be overlooked if simplified networks are carried over to large-scale networks. In this paper, a general delayed bidirectional associative memory neural network model with n + 1 neurons is considered. By analyzing the associated characteristic equation, the local stability of the trivial steady state is examined, and then the existence of the Hopf bifurcation at the trivial steady state is established. By applying the normal form theory and the center manifold reduction, explicit formulae are derived to determine the direction and stability of the bifurcating periodic solution. Furthermore, the paper highlights situations where the Hopf bifurcations are particularly critical, in the sense that the amplitude and the period of oscillations are very sensitive to errors due to tolerances in the implementation of neuron interconnections. It is shown that the sensitivity is crucially dependent on the delay and also significantly influenced by the feature of the number of neurons. Numerical simulations are carried out to illustrate the main results.
Bifurcations of Fibonacci generating functions
Energy Technology Data Exchange (ETDEWEB)
Ozer, Mehmet [Istanbul Kultur University, E5 Karayolu Uzeri Sirinevler, 34191 Istanbul (Turkey) and Semiconductor Physics Institute, LT-01108 and Vilnius Gediminas Technical University, Sauletekio 11, LT-10223 (Lithuania)]. E-mail: m.ozer@iku.edu.tr; Cenys, Antanas [Semiconductor Physics Institute, LT-01108 and Vilnius Gediminas Technical University, Sauletekio 11, LT-10223 (Lithuania); Polatoglu, Yasar [Istanbul Kultur University, E5 Karayolu Uzeri Sirinevler, 34191 Istanbul (Turkey); Hacibekiroglu, Guersel [Istanbul Kultur University, E5 Karayolu Uzeri Sirinevler, 34191 Istanbul (Turkey); Akat, Ercument [Yeditepe University, 26 Agustos Campus Kayisdagi Street, Kayisdagi 81120, Istanbul (Turkey); Valaristos, A. [Aristotle University of Thessaloniki, GR-54124, Thessaloniki (Greece); Anagnostopoulos, A.N. [Aristotle University of Thessaloniki, GR-54124, Thessaloniki (Greece)
2007-08-15
In this work the dynamic behaviour of the one-dimensional family of maps F{sub p,q}(x) = 1/(1 - px - qx {sup 2}) is examined, for specific values of the control parameters p and q. Lyapunov exponents and bifurcation diagrams are numerically calculated. Consequently, a transition from periodic to chaotic regions is observed at values of p and q, where the related maps correspond to Fibonacci generating functions associated with the golden-, the silver- and the bronze mean.
Bifurcations of Fibonacci generating functions
International Nuclear Information System (INIS)
Ozer, Mehmet; Cenys, Antanas; Polatoglu, Yasar; Hacibekiroglu, Guersel; Akat, Ercument; Valaristos, A.; Anagnostopoulos, A.N.
2007-01-01
In this work the dynamic behaviour of the one-dimensional family of maps F p,q (x) = 1/(1 - px - qx 2 ) is examined, for specific values of the control parameters p and q. Lyapunov exponents and bifurcation diagrams are numerically calculated. Consequently, a transition from periodic to chaotic regions is observed at values of p and q, where the related maps correspond to Fibonacci generating functions associated with the golden-, the silver- and the bronze mean
Poincare' maps of impulsed oscillators and two-dimensional dynamics
International Nuclear Information System (INIS)
Lupini, R.; Lenci, S.; Gardini, L.; Urbino Univ.
1996-01-01
The Poincare' map of one-dimensional linear oscillators subject to periodic, non-linear and time-delayed impulses is shown to reduce to a family of plane maps with possible non-uniqueness of the inverse. By restricting the analysis to a convenient form of the impulse function, a variety of interesting dynamical behaviours in this family are pointed out, including multistability and homoclinic bifurcations. Critical curves of two-dimensional endomorphisms are used to identify the structure of absorbing areas and their bifurcations
Hopf bifurcation for tumor-immune competition systems with delay
Directory of Open Access Journals (Sweden)
Ping Bi
2014-01-01
Full Text Available In this article, a immune response system with delay is considered, which consists of two-dimensional nonlinear differential equations. The main purpose of this paper is to explore the Hopf bifurcation of a immune response system with delay. The general formula of the direction, the estimation formula of period and stability of bifurcated periodic solution are also given. Especially, the conditions of the global existence of periodic solutions bifurcating from Hopf bifurcations are given. Numerical simulations are carried out to illustrate the the theoretical analysis and the obtained results.
Morre, D. James; Ternes, Philipp; Morre, Dorothy M.
2002-01-01
Rate of plant cell enlargement, measured at intervals of 3 min using a sensitive linear transducer, oscillates with a minimum period of about 24 min that parallels the 24-min periodicity observed with the oxidation of NADH by the external plasma membrane NADH oxidase and of single cells measured previously by video-enhanced light microscopy. Also exhibiting 24-min oscillations is the steady-state rate of cell enlargement induced by the addition of the auxin herbicide 2,4-dichlorophenoxyacetic acid (2,4-D) or the natural auxin indole-3-acetic acid (IAA). Immediately following 2,4-D addition, a very complex pattern of oscillations is frequently observed. However, after several hours a dominant 24-min period emerges. The length of the 24-min period is temperature compensated and remains constant at 24 min when measured at 15, 25 or 35 degrees C, despite the fact that the rate of cell enlargement approximately doubles for each 10 degree C rise over this same range of temperatures.
Periodic Solutions of the Duffing Harmonic Oscillator by He's Energy Balance Method
Directory of Open Access Journals (Sweden)
A. M. El-Naggar
2015-11-01
Full Text Available Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF and numerical solutions using Runge-Kutta method. The results show the presented method is potentially to solve high nonlinear oscillator equations.
Phase-locking regions in a forced model of slow insulin and glucose oscillations
DEFF Research Database (Denmark)
Sturis, Jeppe; Knudsen, Carsten; O'Meara, Niall M.
1995-01-01
We present a detailed numerical investigation of the phase-locking regions in a forced model of slow oscillations in human insulin secretion and blood glucose concentration. The bifurcation structures of period 2pi and 4pi tongues are mapped out and found to be qualitatively identical to those...
Phase-locking regions in a forced model of slow insulin and glucose oscillations
DEFF Research Database (Denmark)
Sturis, J.; Knudsen, C.; O'Meara, N.M.
1996-01-01
We present a detailed numerical investigation of the phase-locking regions in a forced model of slow oscillations in human insulin secretion and blood glucose concentration. The bifurcation structures of period 2pi and 4pi tongues are mapped out and found to be qualitatively identical to those...
Stochastic modeling of kHz quasi-periodic oscillation light curves
DEFF Research Database (Denmark)
Vio, R.; Rebusco, P.; Andreani, P.
2006-01-01
Kluzniak & Abramowicz explain the high frequency, double peak, "3:2" QPOs observed in neutron star and black hole sources in terms of a non-linear parametric resonance between radial and vertical epicyclic oscillations of an almost Keplerian accretion disk. The 3:2 ratio of epicyclic frequencies ...
Observation of a Pomeau-Manneville intermittent route to chaos in a nonlinear oscillator
International Nuclear Information System (INIS)
Jeffries, C.; Perez, J.
1982-01-01
For a driven nonlinear semiconductor oscillator which shows a period-doubling pitchfork bifurcation route to chaos, we report an additional route to chaos: the Pomeau-Manneville intermittency route, characterized by a periodic (laminar) phase interrupted by bursts of aperiodic behavior. This occurs near a tangent bifurcation as the system driving parameter is reduced by epsilon from the threshold value for a periodic window. Data are presented for the dependence of the average laminar length on epsilon, and also on additive random noise voltage. The results are in reasonable agreement with the intermittency theory of Hirsch, Huberman, and Scalapino. The distribution P(l) is also reported
Experimental Investigation of Bifurcations in a Thermoacoustic Engine
Directory of Open Access Journals (Sweden)
Vishnu R. Unni
2015-06-01
Full Text Available In this study, variation in the characteristics of the pressure oscillations in a thermoacoustic engine is explored as the input heat flux is varied. A bifurcation diagram is plotted to study the variation in the qualitative behavior of the acoustic oscillations as the input heat flux changes. At a critical input heat flux (60 Watt, the engine begins to produce acoustic oscillations in its fundamental longitudinal mode. As the input heat flux is increased, incommensurate frequencies appear in the power spectrum. The simultaneous presence of incommensurate frequencies results in quasiperiodic oscillations. On further increase of heat flux, the fundamental mode disappears and second mode oscillations are observed. These bifurcations in the characteristics of the pressure oscillations are the result of nonlinear interaction between multiple modes present in the thermoacoustic engine. Hysteresis in the bifurcation diagram suggests that the bifurcation is subcritical. Further, the qualitative analysis of different dynamic regimes is performed using nonlinear time series analysis. The physical reason for the observed nonlinear behavior is discussed. Suggestions to avert the variations in qualitative behavior of the pressure oscillations in thermoacoustic engines are also provided.
Shell structure and orbit bifurcations in finite fermion systems
Magner, A. G.; Yatsyshyn, I. S.; Arita, K.; Brack, M.
2011-10-01
We first give an overview of the shell-correction method which was developed by V.M. Strutinsky as a practicable and efficient approximation to the general self-consistent theory of finite fermion systems suggested by A.B. Migdal and collaborators. Then we present in more detail a semiclassical theory of shell effects, also developed by Strutinsky following original ideas of M.C. Gutzwiller. We emphasize, in particular, the influence of orbit bifurcations on shell structure. We first give a short overview of semiclassical trace formulae, which connect the shell oscillations of a quantum system with a sum over periodic orbits of the corresponding classical system, in what is usually called the "periodic orbit theory". We then present a case study in which the gross features of a typical double-humped nuclear fission barrier, including the effects of mass asymmetry, can be obtained in terms of the shortest periodic orbits of a cavity model with realistic deformations relevant for nuclear fission. Next we investigate shell structures in a spheroidal cavity model which is integrable and allows for far-going analytical computation. We show, in particular, how period-doubling bifurcations are closely connected to the existence of the so-called "superdeformed" energy minimum which corresponds to the fission isomer of actinide nuclei. Finally, we present a general class of radial power-law potentials which approximate well the shape of a Woods-Saxon potential in the bound region, give analytical trace formulae for it and discuss various limits (including the harmonic oscillator and the spherical box potentials).
Analysis of precision in chemical oscillators: implications for circadian clocks
International Nuclear Information System (INIS)
D'Eysmond, Thomas; De Simone, Alessandro; Naef, Felix
2013-01-01
Biochemical reaction networks often exhibit spontaneous self-sustained oscillations. An example is the circadian oscillator that lies at the heart of daily rhythms in behavior and physiology in most organisms including humans. While the period of these oscillators evolved so that it resonates with the 24 h daily environmental cycles, the precision of the oscillator (quantified via the Q factor) is another relevant property of these cell-autonomous oscillators. Since this quantity can be measured in individual cells, it is of interest to better understand how this property behaves across mathematical models of these oscillators. Current theoretical schemes for computing the Q factors show limitations for both high-dimensional models and in the vicinity of Hopf bifurcations. Here, we derive low-noise approximations that lead to numerically stable schemes also in high-dimensional models. In addition, we generalize normal form reductions that are appropriate near Hopf bifurcations. Applying our approximations to two models of circadian clocks, we show that while the low-noise regime is faithfully recapitulated, increasing the level of noise leads to species-dependent precision. We emphasize that subcomponents of the oscillator gradually decouple from the core oscillator as noise increases, which allows us to identify the subnetworks responsible for robust rhythms. (paper)
A Chaotic Oscillator Based on HP Memristor Model
Directory of Open Access Journals (Sweden)
Guangyi Wang
2015-01-01
Full Text Available This paper proposes a simple autonomous memristor-based oscillator for generating periodic signals. Applying an external sinusoidal excitation to the autonomous system, a nonautonomous oscillator is obtained, which contains HP memristor model and four linear circuit elements. This memristor-based oscillator can generate periodic, chaotic, and hyperchaotic signals under the periodic excitation and an appropriate set of circuit parameters. It also shows that the system exhibits alternately a hidden attractor with no equilibrium and a self-excited attractor with a line equilibrium as time goes on. Furthermore, some specialties including burst chaos, irregular periodic bifurcations, and nonintermittence chaos of the circuit are found by theoretical analysis and numerical simulations. Finally, a discrete model for the HP memristor is given and the main statistical properties of this memristor-based oscillator are verified via DSP chip experiments and NIST (National Institute of Standards and Technology tests.
Experimental Investigation of Bifurcations in a Thermoacoustic Engine
Vishnu R. Unni; Yogesh M. S. Prasaad; N. T. Ravi; S. Md Iqbal; Bala Pesala; R. I. Sujith
2015-01-01
In this study, variation in the characteristics of the pressure oscillations in a thermoacoustic engine is explored as the input heat flux is varied. A bifurcation diagram is plotted to study the variation in the qualitative behavior of the acoustic oscillations as the input heat flux changes. At a critical input heat flux (60 Watt), the engine begins to produce acoustic oscillations in its fundamental longitudinal mode. As the input heat flux is increased, incommensurate frequencies appear i...
A one-parametric formula relating the frequencies of twin-peak quasi-periodic oscillations
Török, Gabriel; Goluchová, Kateřina; Šrámková, Eva; Horák, Jiří; Bakala, Pavel; Urbanec, Martin
2017-12-01
Timing analysis of X-ray flux in more than a dozen low-mass X-ray binary systems containing a neutron star reveals remarkable correlations between frequencies of two characteristic peaks present in the power-density spectra. We find a simple analytic relation that well reproduces all these individual correlations. We link this relation to a physical model which involves accretion rate modulation caused by an oscillating torus.
Attractors near grazing–sliding bifurcations
International Nuclear Information System (INIS)
Glendinning, P; Kowalczyk, P; Nordmark, A B
2012-01-01
In this paper we prove, for the first time, that multistability can occur in three-dimensional Fillipov type flows due to grazing–sliding bifurcations. We do this by reducing the study of the dynamics of Filippov type flows around a grazing–sliding bifurcation to the study of appropriately defined one-dimensional maps. In particular, we prove the presence of three qualitatively different types of multiple attractors born in grazing–sliding bifurcations. Namely, a period-two orbit with a sliding segment may coexist with a chaotic attractor, two stable, period-two and period-three orbits with a segment of sliding each may coexist, or a non-sliding and period-three orbit with two sliding segments may coexist
Harmonic balance approach to the periodic solutions of the (an)harmonic relativistic oscillator
International Nuclear Information System (INIS)
Belendez, Augusto; Pascual, Carolina
2007-01-01
The first-order harmonic balance method via the first Fourier coefficient is used to construct two approximate frequency-amplitude relations for the relativistic oscillator for which the nonlinearity (anharmonicity) is a relativistic effect due to the time line dilation along the world line. Making a change of variable, a new nonlinear differential equation is obtained and two procedures are used to approximately solve this differential equation. In the first the differential equation is rewritten in a form that does not contain a square-root expression, while in the second the differential equation is solved directly. The approximate frequency obtained using the second procedure is more accurate than the frequency obtained with the first due to the fact that, in the second procedure, application of the harmonic balance method produces an infinite set of harmonics, while in the first procedure only two harmonics are produced. Both approximate frequencies are valid for the complete range of oscillation amplitudes, and excellent agreement of the approximate frequencies with the exact one are demonstrated and discussed. The discrepancy between the first-order approximate frequency obtained by means of the second procedure and the exact frequency never exceeds 1.6%. We also obtained the approximate frequency by applying the second-order harmonic balance method and in this case the relative error is as low 0.31% for all the range of values of amplitude of oscillation A
FFT Bifurcation Analysis of Routes to Chaos via Quasiperiodic Solutions
Directory of Open Access Journals (Sweden)
L. Borkowski
2015-01-01
Full Text Available The dynamics of a ring of seven unidirectionally coupled nonlinear Duffing oscillators is studied. We show that the FFT analysis presented in form of a bifurcation graph, that is, frequency distribution versus a control parameter, can provide a valuable and helpful complement to the corresponding typical bifurcation diagram and the course of Lyapunov exponents, especially in context of detailed identification of the observed attractors. As an example, bifurcation analysis of routes to chaos via 2-frequency and 3-frequency quasiperiodicity is demonstrated.
Directory of Open Access Journals (Sweden)
M. G. Manoj
2011-03-01
Full Text Available Atmospheric gravity waves, which are a manifestation of the fluctuations in buoyancy of the air parcels, are well known for their direct influence on concentration of atmospheric trace gases and aerosols, and also on oscillations of meteorological variables such as temperature, wind speed, visibility and so on. The present paper reports quasi-periodic oscillations in the lidar backscatter signal strength due to aerosol fluctuations in the nocturnal boundary layer, studied with a high space-time resolution polarimetric micro pulse lidar and concurrent meteorological parameters over a tropical station in India. The results of the spectral analysis of the data, archived on some typical clear-sky conditions during winter months of 2008 and 2009, exhibit a prominent periodicity of 20–40 min in lidar-observed aerosol variability and show close association with those observed in the near-surface temperature and wind at 5% statistical significance. Moreover, the lidar aerosol backscatter signal strength variations at different altitudes, which have been generated from the height-time series of the one-minute interval profiles at 2.4 m vertical resolution, indicate vertical propagation of these waves, exchanging energy between lower and higher height levels. Such oscillations are favoured by the stable atmospheric background condition and peculiar topography of the experimental site. Accurate representation of these buoyancy waves is essential in predicting the sporadic fluctuations of weather in the tropics.
Stability and bifurcation analysis in a delayed SIR model
International Nuclear Information System (INIS)
Jiang Zhichao; Wei Junjie
2008-01-01
In this paper, a time-delayed SIR model with a nonlinear incidence rate is considered. The existence of Hopf bifurcations at the endemic equilibrium is established by analyzing the distribution of the characteristic values. A explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form and the center manifold theory. Numerical simulations to support the analytical conclusions are carried out
Busschaert, C.; Falize, É.; Michaut, C.; Bonnet-Bidaud, J.-M.; Mouchet, M.
2015-07-01
Context. Magnetic cataclysmic variables are close binary systems containing a strongly magnetized white dwarf that accretes matter coming from an M-dwarf companion. The high magnetic field strength leads to the formation of an accretion column instead of an accretion disk. High-energy radiation coming from those objects is emitted from the column close to the white dwarf photosphere at the impact region. Its properties depend on the characteristics of the white dwarf and an accurate accretion column model allows the properties of the binary system to be inferred, such as the white dwarf mass, its magnetic field, and the accretion rate. Aims: We study the temporal and spectral behaviour of the accretion region and use the tools we developed to accurately connect the simulation results to the X-ray and optical astronomical observations. Methods: The radiation hydrodynamics code Hades was adapted to simulate this specific accretion phenomena. Classical approaches were used to model the radiative losses of the two main radiative processes: bremsstrahlung and cyclotron. Synthetic light curves and X-ray spectra were extracted from numerical simulations. A fast Fourier analysis was performed on the simulated light curves. The oscillation frequencies and amplitudes in the X-ray and optical domains are studied to compare those numerical results to observational ones. Different dimensional formulae were developed to complete the numerical evaluations. Results: The complete characterization of the emitting region is described for the two main radiative regimes: when only the bremsstrahlung losses and when both cyclotron and bremsstrahlung losses are considered. The effect of the non-linear cooling instability regime on the accretion column behaviour is analysed. Variation in luminosity on short timescales (~1 s quasi-periodic oscillations) is an expected consequence of this specific dynamic. The importance of secondary shock instability on the quasi-periodic oscillation
Improving the precision of noisy oscillators
Moehlis, Jeff
2014-04-01
We consider how the period of an oscillator is affected by white noise, with special attention given to the cases of additive noise and parameter fluctuations. Our treatment is based upon the concepts of isochrons, which extend the notion of the phase of a stable periodic orbit to the basin of attraction of the periodic orbit, and phase response curves, which can be used to understand the geometry of isochrons near the periodic orbit. This includes a derivation of the leading-order effect of noise on the statistics of an oscillator’s period. Several examples are considered in detail, which illustrate the use and validity of the theory, and demonstrate how to improve a noisy oscillator’s precision by appropriately tuning system parameters or operating away from a bifurcation point. It is also shown that appropriately timed impulsive kicks can give further improvements to oscillator precision.
Willett, R L; Pfeiffer, L N; West, K W
2009-06-02
A standing problem in low-dimensional electron systems is the nature of the 5/2 fractional quantum Hall (FQH) state: Its elementary excitations are a focus for both elucidating the state's properties and as candidates in methods to perform topological quantum computation. Interferometric devices may be used to manipulate and measure quantum Hall edge excitations. Here we use a small-area edge state interferometer designed to observe quasiparticle interference effects. Oscillations consistent in detail with the Aharonov-Bohm effect are observed for integer quantum Hall and FQH states (filling factors nu = 2, 5/3, and 7/3) with periods corresponding to their respective charges and magnetic field positions. With these factors as charge calibrations, periodic transmission through the device consistent with quasiparticle charge e/4 is observed at nu = 5/2 and at lowest temperatures. The principal finding of this work is that, in addition to these e/4 oscillations, periodic structures corresponding to e/2 are also observed at 5/2 nu and at lowest temperatures. Properties of the e/4 and e/2 oscillations are examined with the device sensitivity sufficient to observe temperature evolution of the 5/2 quasiparticle interference. In the model of quasiparticle interference, this presence of an effective e/2 period may empirically reflect an e/2 quasiparticle charge or may reflect multiple passes of the e/4 quasiparticle around the interferometer. These results are discussed within a picture of e/4 quasiparticle excitations potentially possessing non-Abelian statistics. These studies demonstrate the capacity to perform interferometry on 5/2 excitations and reveal properties important for understanding this state and its excitations.
Williams, Caitlin R. S.; Sorrentino, Francesco; Murphy, Thomas E.; Roy, Rajarshi
2013-12-01
We experimentally study the complex dynamics of a unidirectionally coupled ring of four identical optoelectronic oscillators. The coupling between these systems is time-delayed in the experiment and can be varied over a wide range of delays. We observe that as the coupling delay is varied, the system may show different synchronization states, including complete isochronal synchrony, cluster synchrony, and two splay-phase states. We analyze the stability of these solutions through a master stability function approach, which we show can be effectively applied to all the different states observed in the experiment. Our analysis supports the experimentally observed multistability in the system.
Crenelated fast oscillatory outputs of a two-delay electro-optic oscillator.
Weicker, Lionel; Erneux, Thomas; Jacquot, Maxime; Chembo, Yanne; Larger, Laurent
2012-02-01
An electro-optic oscillator subject to two distinct delayed feedbacks has been designed to develop pronounced broadband chaotic output. Its route to chaos starts with regular pulsating gigahertz oscillations that we investigate both experimentally and theoretically. Of particular physical interest are the transitions to various crenelated fast time-periodic oscillations, prior to the onset of chaotic regimes. The two-delay problem is described mathematically by two coupled delay-differential equations, which we analyze by using multiple-time-scale methods. We show that the interplay of a large delay and a relatively small delay is responsible for the onset of fast oscillations modulated by a slowly varying square-wave envelope. As the bifurcation parameter progressively increases, this envelope undergoes a sequence of bifurcations that corresponds to successive fixed points of a sine map.
Bifurcation theory for finitely smooth planar autonomous differential systems
Han, Maoan; Sheng, Lijuan; Zhang, Xiang
2018-03-01
In this paper we establish bifurcation theory of limit cycles for planar Ck smooth autonomous differential systems, with k ∈ N. The key point is to study the smoothness of bifurcation functions which are basic and important tool on the study of Hopf bifurcation at a fine focus or a center, and of Poincaré bifurcation in a period annulus. We especially study the smoothness of the first order Melnikov function in degenerate Hopf bifurcation at an elementary center. As we know, the smoothness problem was solved for analytic and C∞ differential systems, but it was not tackled for finitely smooth differential systems. Here, we present their optimal regularity of these bifurcation functions and their asymptotic expressions in the finite smooth case.
Vuille, M.
1999-11-01
The atmospheric circulation over the Bolivian Altiplano during composite WET and DRY periods and during HIGH and LOW index phases of the Southern Oscillation was investigated using daily radiosonde data from Antofagasta (Chile), Salta (Argentina), Lima (Peru) and La Paz (Bolivia), daily precipitation data from the Bolivian/Chilean border between 18° and 19°S and monthly NCEP (National Centers for Environmental Prediction) reanalysis data between 1960 and 1998. In austral summer (DJF) the atmosphere during WET periods is characterized by easterly wind anomalies in the middle and upper troposphere over the Altiplano, resulting in increased moisture influx from the interior of the continent near the Altiplano surface. The Bolivian High is intensified and displaced southward. On the other hand, westerly winds usually prevail during DRY summer periods, preventing the moisture transport from the east from reaching the western Altiplano. Precipitation tends to be deficient over the western Bolivian Altiplano during LOW index summers and above average during HIGH and LOW+1 summers, but the relation is weak and statistically insignificant. LOW summers feature broadly similar atmospheric circulation anomalies as DRY periods and can be regarded as an extended DRY period or as a summer with increased occurrence of DRY episodes. HIGH summers, and to a lesser degree LOW+1 summers, are characterized by broadly opposite atmospheric characteristics, featuring a more pronounced Bolivian High located significantly further south, and easterly wind anomalies over the Altiplano. In winter (JJA) precipitation events are rare; these are associated with increased northerly and westerly wind components, reduced pressure and temperature, and increased specific humidity over the entire Altiplano. Atmospheric circulation anomalies during LOW periods are less pronounced in austral winter (JJA) than in summer, but generally feature similar changes (increased temperatures and a vertically
International Nuclear Information System (INIS)
Dudetskiy, V Yu; Lariontsev, E G; Chekina, S N
2014-01-01
The effect of pump noise on the synchronisation of selfmodulation oscillations in a solid-state ring laser with periodic pump modulation is studied numerically and experimentally. It is found that, in contrast to desynchronisation that usually occurs under action of noise in the case of 1/1 synchronisation of self-oscillations by a periodic signal, the effect of noise on 1/2 synchronisation may be positive, namely, at a sufficiently low intensity, pump noise is favourable for synchronisation of self-oscillations, for narrowing of their spectrum, and for increasing the signal-to-noise ratio. (lasers)
Directory of Open Access Journals (Sweden)
Jinmi Koo
2015-09-01
Full Text Available BackgroundIn mammals, the master circadian pacemaker is localized in an area of the ventral hypothalamus known as the suprachiasmatic nucleus (SCN. Previous studies have shown that pacemaker neurons in the SCN are highly coupled to one another, and this coupling is crucial for intrinsic self-sustainability of the SCN central clock, which is distinguished from peripheral oscillators. One plausible mechanism underlying the intercellular communication may involve direct electrical connections mediated by gap junctions.MethodsWe examined the effect of mefloquine, a neuronal gap junction blocker, on circadian Period 2 (Per2 gene oscillation in SCN slice cultures prepared from Per2::luciferase (PER2::LUC knock-in mice using a real-time bioluminescence measurement system.ResultsAdministration of mefloquine causes instability in the pulse period and a slight reduction of amplitude in cyclic PER2::LUC expression. Blockade of gap junctions uncouples PER2::LUC-expressing cells, in terms of phase transition, which weakens synchrony among individual cellular rhythms.ConclusionThese findings suggest that neuronal gap junctions play an important role in synchronizing the central pacemaker neurons and contribute to the distinct self-sustainability of the SCN master clock.
Directory of Open Access Journals (Sweden)
S.W. Mason
2018-06-01
Full Text Available This paper seeks to adopt and solve the wave-equation for the radial propagation of light in three dimensions from the moment of the Big-Bang and during Earth-based experiments. The primary purpose is to model a propagating beam of light emitted from the singularity, outwards, and to show that its velocity is sinusoidal, meaning that its speed oscillates periodically, and is therefore variable rather than constant. It is additionally shown, by calculating an appropriate solution to the wave-equation, that the velocity of light is not only negatively damped according to the inverse radial law, 1/r, throughout its journey over space and time, but that this latter feature also exhibits amplitude convergence from a very large initial value to a value that is very close to what is now defined to be a constant, namely the current value denoted by c=299792458m/s. The possibility that such observations may also vary depending upon the inertial frame in which a measurement is carried out is similarly considered, along with a discussion of the related nature of mass and energy, and how the possible variability of the speed-of-light and the fabric of the space-time continuum may affect each other. Keywords: Wave-equation, Transverse, Electromagnetic-wave, Radial motion, Eigen-function, Radial-solution, Redshift-drift, Speed-of-light, Displacement, Variable-velocity, Periodic, Oscillation, Convergence, Limit, Big-bang, Space-time, Neutrinos, CERN, Gran Sasso, Experiment
Directory of Open Access Journals (Sweden)
Zhang Yong-Hua
2013-10-01
Full Text Available A two-dimensional unsteady computational fluid dynamics (CFD method using an unstructured, grid-based and unsteady Navier-Stokes solver with automatic adaptive re-meshing to compute the unsteady flow was adopted to study the hydrodynamic interaction between a periodic oscillating plate and a rigid undulating fin in tandem arrangement. The user-defined function (UDF program was compiled to define the undulating and oscillating motion. First, the influence of the distance between the anterior oscillating plate and the posterior undulating fin on the non-dimensional drag coefficient of the fin was investigated. Ten different distances, D=0.2L, 0.4L, 0.6L, 0.8L, 1.0L, 1.2L, 1.4L, 1.6L, 1.8L and 2.0L, were considered. The performance of the fin for different distances (D is different. Second, the plate oscillating angle (5.7°, 10°, 20°, 30°, 40°, 45°, 50° and frequency (0.5 Hz, 1.0 Hz, 1.5 Hz, 2.0 Hz, 2.5 Hz, 3.0 Hz, 3.5 Hz, 4.0 Hz effects on the non-dimensional drag coefficient of the fin were also implemented. The pressure distribution on the fin was computed and integrated to provide fin forces, which were decomposed into lift and thrust. Meanwhile, the flow field was demonstrated and analysed. Based on the flow structures, the reasons for different undulating performances were discussed. It shows that the results largely depend on the distance between the two objects. The plate oscillating angle and frequency also make a certain contribution to the performance of the posterior undulating fin. The results are similar to the interaction between two undulating objects in tandem arrangement and they may provide a physical insight into the understanding of fin interaction in fishes or bio-robotic underwater propulsors that are propelled by multi fins.
Bifurcations of transition states: Morse bifurcations
International Nuclear Information System (INIS)
MacKay, R S; Strub, D C
2014-01-01
A transition state for a Hamiltonian system is a closed, invariant, oriented, codimension-2 submanifold of an energy level that can be spanned by two compact codimension-1 surfaces of unidirectional flux whose union, called a dividing surface, locally separates the energy level into two components and has no local recrossings. For this to happen robustly to all smooth perturbations, the transition state must be normally hyperbolic. The dividing surface then has locally minimal geometric flux through it, giving an upper bound on the rate of transport in either direction. Transition states diffeomorphic to S 2m−3 are known to exist for energies just above any index-1 critical point of a Hamiltonian of m degrees of freedom, with dividing surfaces S 2m−2 . The question addressed here is what qualitative changes in the transition state, and consequently the dividing surface, may occur as the energy or other parameters are varied? We find that there is a class of systems for which the transition state becomes singular and then regains normal hyperbolicity with a change in diffeomorphism class. These are Morse bifurcations. Various examples are considered. Firstly, some simple examples in which transition states connect or disconnect, and the dividing surface may become a torus or other. Then, we show how sequences of Morse bifurcations producing various interesting forms of transition state and dividing surface are present in reacting systems, by considering a hypothetical class of bimolecular reactions in gas phase. (paper)
Periodic oscillations of discrete NLS solitons in the presence of diffraction management
International Nuclear Information System (INIS)
Panayotaros, Panayotis; Pelinovsky, Dmitry
2008-01-01
We consider the discrete NLS equation with a small-amplitude time-periodic diffraction coefficient which models diffraction management in nonlinear lattices. In the space of one dimension and at the zero-amplitude diffraction management, multi-peak localized modes (called discrete solitons or discrete breathers) are stationary solutions of the discrete NLS equation which are uniquely continued from the anti-continuum limit, where they are compactly supported on finitely many non-zero nodes. We prove that the multi-peak localized modes are uniquely continued to the time-periodic space-localized solutions for small-amplitude diffraction management if the period of the diffraction coefficient is not multiple to the period of the stationary solution. The same result is extended to multi-peaked localized modes in the space of two and three dimensions (which include discrete vortices) under additional non-degeneracy assumptions on the stationary solutions in the anti-continuum limit
Cavitation bubble oscillation period as a process diagnostic during the laser shock peening process
CSIR Research Space (South Africa)
Glaser, Daniel
2017-09-01
Full Text Available bubble can be used to characterize effective and repeatable energy delivery to the target. High-speed shadowgraphy is implemented to show that variations in the bubble period occur before visual observations of dielectric breakdown in water...
Kalmbach, K.; Booth, V.; Behn, C. G. Diniz
2017-01-01
The structure of human sleep changes across development as it consolidates from the polyphasic sleep of infants to the single nighttime sleep period typical in adults. Across this same developmental period, time scales of the homeostatic sleep drive, the physiological drive to sleep that increases with time spent awake, also change and presumably govern the transition from polyphasic to monophasic sleep behavior. Using a physiologically-based, sleep-wake regulatory network model for human sle...
International Nuclear Information System (INIS)
Karaoglu, Esra; Merdan, Huseyin
2014-01-01
Highlights: • A ratio-dependent predator–prey system involving two discrete maturation time delays is studied. • Hopf bifurcations are analyzed by choosing delay parameters as bifurcation parameters. • When a delay parameter passes through a critical value, Hopf bifurcations occur. • The direction of bifurcation, the period and the stability of periodic solution are also obtained. - Abstract: In this paper we give a detailed Hopf bifurcation analysis of a ratio-dependent predator–prey system involving two different discrete delays. By analyzing the characteristic equation associated with the model, its linear stability is investigated. Choosing delay terms as bifurcation parameters the existence of Hopf bifurcations is demonstrated. Stability of the bifurcating periodic solutions is determined by using the center manifold theorem and the normal form theory introduced by Hassard et al. Furthermore, some of the bifurcation properties including direction, stability and period are given. Finally, theoretical results are supported by some numerical simulations
Rabi oscillations a quantum dot exposed to quantum light
International Nuclear Information System (INIS)
Magyarov, A.; Slepyan, G.Ya.; Maksimenko, S.A.; Hoffmann, A.
2007-01-01
The influence of the local field on the excitonic Rabi oscillations in an isolated quantum dot driven by the coherent state of light has been theoretically investigated. Local field is predicted to entail the appearance of two oscillatory regimes in the Rabi effect separated by the bifurcation. In the first regime Rabi oscillations are periodic and do not reveal collapse-revivals phenomenon, while in the second one collapse and revivals appear, showing significant difference as compared to those predicted by the standard Jaynes-Cummings model
Using a Gradient Vector to Find Multiple Periodic Oscillations in Suspension Bridge Models
Humphreys, L. D.; McKenna, P. J.
2005-01-01
This paper describes how the method of steepest descent can be used to find periodic solutions of differential equations. Applications to two suspension bridge models are discussed, and the method is used to find non-obvious large-amplitude solutions.
Quasi-Periodic Oscillations in the X-ray Light Curves of Blazars Paul ...
Indian Academy of Sciences (India)
the quasi-periodic component could provide a powerful tool for diagnosing the jet's structure. ... tent with the red-noise seen in most power spectra of AGN variability; QPOs would ... A statistical analysis of the periodogram for that observation yields a peak at ... (2008) also employed structure functions to try to characterize.
Bifurcation structure of an optical ring cavity
DEFF Research Database (Denmark)
Kubstrup, C.; Mosekilde, Erik
1996-01-01
One- and two-dimensional continuation techniques are applied to determine the basic bifurcation structure for an optical ring cavity with a nonlinear absorbing element (the Ikeda Map). By virtue of the periodic structure of the map, families of similar solutions develop in parameter space. Within...
International Nuclear Information System (INIS)
Altamirano, D.; Van der Klis, M.; Wijnands, R.; Ingram, A.; Linares, M.; Homan, J.
2012-01-01
We report on six RXTE observations taken during the 2010 outburst of the 11 Hz accreting pulsar IGR J17480–2446 located in the globular cluster Terzan 5. During these observations we find power spectra which resemble those seen in Z-type high-luminosity neutron star low-mass X-ray binaries, with a quasi-periodic oscillation (QPO) in the 35-50 Hz range simultaneous with a kHz QPO and broadband noise. Using well-known frequency-frequency correlations, we identify the 35-50 Hz QPOs as the horizontal branch oscillations, which were previously suggested to be due to Lense-Thirring (LT) precession. As IGR J17480–2446 spins more than an order of magnitude more slowly than any of the other neutron stars where these QPOs were found, this QPO cannot be explained by frame dragging. By extension, this casts doubt on the LT precession model for other low-frequency QPOs in neutron stars and perhaps even black hole systems.
Altamirano, D.; Ingram, A.; van der Klis, M.; Wijnands, R.; Linares, M.; Homan, J.
2012-11-01
We report on six RXTE observations taken during the 2010 outburst of the 11 Hz accreting pulsar IGR J17480-2446 located in the globular cluster Terzan 5. During these observations we find power spectra which resemble those seen in Z-type high-luminosity neutron star low-mass X-ray binaries, with a quasi-periodic oscillation (QPO) in the 35-50 Hz range simultaneous with a kHz QPO and broadband noise. Using well-known frequency-frequency correlations, we identify the 35-50 Hz QPOs as the horizontal branch oscillations, which were previously suggested to be due to Lense-Thirring (LT) precession. As IGR J17480-2446 spins more than an order of magnitude more slowly than any of the other neutron stars where these QPOs were found, this QPO cannot be explained by frame dragging. By extension, this casts doubt on the LT precession model for other low-frequency QPOs in neutron stars and perhaps even black hole systems.
Energetics and monsoon bifurcations
Seshadri, Ashwin K.
2017-01-01
Monsoons involve increases in dry static energy (DSE), with primary contributions from increased shortwave radiation and condensation of water vapor, compensated by DSE export via horizontal fluxes in monsoonal circulations. We introduce a simple box-model characterizing evolution of the DSE budget to study nonlinear dynamics of steady-state monsoons. Horizontal fluxes of DSE are stabilizing during monsoons, exporting DSE and hence weakening the monsoonal circulation. By contrast latent heat addition (LHA) due to condensation of water vapor destabilizes, by increasing the DSE budget. These two factors, horizontal DSE fluxes and LHA, are most strongly dependent on the contrast in tropospheric mean temperature between land and ocean. For the steady-state DSE in the box-model to be stable, the DSE flux should depend more strongly on the temperature contrast than LHA; stronger circulation then reduces DSE and thereby restores equilibrium. We present conditions for this to occur. The main focus of the paper is describing conditions for bifurcation behavior of simple models. Previous authors presented a minimal model of abrupt monsoon transitions and argued that such behavior can be related to a positive feedback called the `moisture advection feedback'. However, by accounting for the effect of vertical lapse rate of temperature on the DSE flux, we show that bifurcations are not a generic property of such models despite these fluxes being nonlinear in the temperature contrast. We explain the origin of this behavior and describe conditions for a bifurcation to occur. This is illustrated for the case of the July-mean monsoon over India. The default model with mean parameter estimates does not contain a bifurcation, but the model admits bifurcation as parameters are varied.
Kori, Hiroshi; Kiss, István Z.; Jain, Swati; Hudson, John L.
2018-04-01
Experiments and supporting theoretical analysis are presented to describe the synchronization patterns that can be observed with a population of globally coupled electrochemical oscillators close to a homoclinic, saddle-loop bifurcation, where the coupling is repulsive in the electrode potential. While attractive coupling generates phase clusters and desynchronized states, repulsive coupling results in synchronized oscillations. The experiments are interpreted with a phenomenological model that captures the waveform of the oscillations (exponential increase) followed by a refractory period. The globally coupled autocatalytic integrate-and-fire model predicts the development of partially synchronized states that occur through attracting heteroclinic cycles between out-of-phase two-cluster states. Similar behavior can be expected in many other systems where the oscillations occur close to a saddle-loop bifurcation, e.g., with Morris-Lecar neurons.
Travelling waves and their bifurcations in the Lorenz-96 model
van Kekem, Dirk L.; Sterk, Alef E.
2018-03-01
In this paper we study the dynamics of the monoscale Lorenz-96 model using both analytical and numerical means. The bifurcations for positive forcing parameter F are investigated. The main analytical result is the existence of Hopf or Hopf-Hopf bifurcations in any dimension n ≥ 4. Exploiting the circulant structure of the Jacobian matrix enables us to reduce the first Lyapunov coefficient to an explicit formula from which it can be determined when the Hopf bifurcation is sub- or supercritical. The first Hopf bifurcation for F > 0 is always supercritical and the periodic orbit born at this bifurcation has the physical interpretation of a travelling wave. Furthermore, by unfolding the codimension two Hopf-Hopf bifurcation it is shown to act as an organising centre, explaining dynamics such as quasi-periodic attractors and multistability, which are observed in the original Lorenz-96 model. Finally, the region of parameter values beyond the first Hopf bifurcation value is investigated numerically and routes to chaos are described using bifurcation diagrams and Lyapunov exponents. The observed routes to chaos are various but without clear pattern as n → ∞.
Chemical reaction systems with a homoclinic bifurcation: an inverse problem
Czech Academy of Sciences Publication Activity Database
Plesa, T.; Vejchodský, Tomáš; Erban, R.
2016-01-01
Roč. 54, č. 10 (2016), s. 1884-1915 ISSN 0259-9791 EU Projects: European Commission(XE) 328008 - STOCHDETBIOMODEL Institutional support: RVO:67985840 Keywords : nonnegative dynamical systems * bifurcations * oscillations Subject RIV: BA - General Mathematics Impact factor: 1.308, year: 2016 http://link.springer.com/article/10.1007%2Fs10910-016-0656-1
Viral infection model with periodic lytic immune response
International Nuclear Information System (INIS)
Wang Kaifa; Wang Wendi; Liu Xianning
2006-01-01
Dynamical behavior and bifurcation structure of a viral infection model are studied under the assumption that the lytic immune response is periodic in time. The infection-free equilibrium is globally asymptotically stable when the basic reproductive ratio of virus is less than or equal to one. There is a non-constant periodic solution if the basic reproductive ratio of the virus is greater than one. It is found that period doubling bifurcations occur as the amplitude of lytic component is increased. For intermediate birth rates, the period triplication occurs and then period doubling cascades proceed gradually toward chaotic cycles. For large birth rate, the period doubling cascade proceeds gradually toward chaotic cycles without the period triplication, and the inverse period doubling can be observed. These results can be used to explain the oscillation behaviors of virus population, which was observed in chronic HBV or HCV carriers
NEAR-INFRARED AND X-RAY QUASI-PERIODIC OSCILLATIONS IN NUMERICAL MODELS OF Sgr A*
International Nuclear Information System (INIS)
Dolence, Joshua C.; Gammie, Charles F.; Shiokawa, Hotaka; Noble, Scott C.
2012-01-01
We report transient quasi-periodic oscillations (QPOs) on minute timescales in relativistic, radiative models of the galactic center source Sgr A*. The QPOs result from nonaxisymmetric m = 1 structure in the accretion flow excited by MHD turbulence. Near-infrared (NIR) and X-ray power spectra show significant peaks at frequencies comparable to the orbital frequency at the innermost stable circular orbit (ISCO) f o . The excess power is associated with inward propagating magnetic filaments inside the ISCO. The amplitudes of the QPOs are sensitive to the electron distribution function. We argue that transient QPOs appear at a range of frequencies in the neighborhood of f o and that the power spectra, averaged over long times, likely show a broad bump near f o rather than distinct, narrow QPO features.
International Nuclear Information System (INIS)
Lu, Guangfeng; Wang, Zhiguo; Fan, Zhenfang; Luo, Hui
2014-01-01
Periodic rotation noise in the outputs of multi-oscillator ring laser gyros (MRLGs) is investigated in this paper for the first time. It is proved theoretically and experimentally that noise is induced by the crosstalk between two beat-frequency signals, which are combined from the left and right circularly polarized counter-propagating beams in MRLGs. Theoretical analysis and experimental results also indicate that the fundamental frequency of this noise is equal to the frequency difference between the two beat-frequency signals and the amplitude of the fundamental component is proportional to the crosstalk ratio between the two beat-frequency signals. Further, the amplitude of the nth-order component is proportional to the nth power of the crosstalk ratio. (paper)
Analysis of Quasi-periodic Oscillations and Time Lag in Ultraluminous X-Ray Sources with XMM-Newton
Energy Technology Data Exchange (ETDEWEB)
Li, Zi-Jian; Xiao, Guang-Cheng; Zhang, Shu; Ma, Xiang; Yan, Lin-Li; Qu, Jin-Lu [Key Laboratory for Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, 19B Yuquan Road, Beijing 100049 (China); Chen, Li; Bu, Qing-Cui; Zhang, Liang, E-mail: lizijian@ihep.ac.cn, E-mail: qujl@ihep.ac.cn [Department of Astronomy, Beijing Normal University, Beijing 100875 (China)
2017-04-10
We investigated the power density spectrum (PDS) and time lag of ultraluminous X-ray sources (ULXs) observed by XMM-Newton . We determined the PDSs for each ULX and found that five of them show intrinsic variability due to obvious quasi-periodic oscillations (QPOs) of mHz–1 Hz, consistent with previous reports. We further investigated these five ULXs to determine their possible time lag. The ULX QPOs exhibit a soft time lag that is linearly related to the QPO frequency. We discuss the likelihood of the ULX QPOs being type-C QPO analogs, and the time lag models. The ULXs might harbor intermediate-mass black holes if their QPOs are type-C QPO analogs. We suggest that the soft lag and the linearity may be due to reverberation.
Detection of solar radio brightness oscillations with 160.01-min period from direct measurements
International Nuclear Information System (INIS)
Efanov, V.A.; Moiseev, I.G.; Nesterov, N.S.
1983-01-01
It is shown that direct measurements of the quiet Sun brightness at 8.2 and 13.5 mm wavelengths corrected for extinction in the Earth atmosphere by means of the Bouguer law reveal the 160.01-min periodic component. The relative amplitudes of variations are of approximately 6x10 -4 at the shorter wavelength and of 10 -3 at the longer one. The brightness maximum coincides with the phase of the maximal radius of the photosphere as derived from the optical data
Xu, Chang
2017-04-01
The intrinsic random variability of an astronomical source hampers the detection of possible periodicities that we are interested in. We find that a simple first-order autoregressive [AR(1)] process gives a poor fit to the power decay in the observed spectrum for astrophysical sources and geodetic observations. Thus, appropriate background noise models have to be chosen for significance tests to distinguish real features from the intrinsic variability of the source. Here we recall the wavelet analysis with significance and confidence testing but extend it with the generalized Gauss Markov stochastic model as the null hypothesis, which includes AR(1) and a power law as special cases. We exemplify this discussion with real data, such as sunspot number data, geomagnetic indices, X-ray observations, as well as a Global Positioning System (GPS) position time series.
Analysis of a Stochastic Chemical System Close to a SNIPER Bifurcation of Its Mean-Field Model
Erban, Radek
2009-01-01
A framework for the analysis of stochastic models of chemical systems for which the deterministic mean-field description is undergoing a saddle-node infinite period (SNIPER) bifurcation is presented. Such a bifurcation occurs, for example, in the modeling of cell-cycle regulation. It is shown that the stochastic system possesses oscillatory solutions even for parameter values for which the mean-field model does not oscillate. The dependence of the mean period of these oscillations on the parameters of the model (kinetic rate constants) and the size of the system (number of molecules present) are studied. Our approach is based on the chemical Fokker-Planck equation. To gain some insight into the advantages and disadvantages of the method, a simple one-dimensional chemical switch is first analyzed, and then the chemical SNIPER problem is studied in detail. First, results obtained by solving the Fokker-Planck equation numerically are presented. Then an asymptotic analysis of the Fokker-Planck equation is used to derive explicit formulae for the period of oscillation as a function of the rate constants and as a function of the system size. © 2009 Society for Industrial and Applied Mathematics.
Chaos and loss of predictability in the periodically kicked linear oscillator
International Nuclear Information System (INIS)
Luna-Acosta, G.A.; Cantoral, E.
1989-01-01
Chernikov et.al. [2] have discovered new features in the dynamics of a periodically kicked LHO x'' + ω 0 2 x = ( K/ k 0 T 2 ) sin (k 0 x) x Σ n δ (t / T - n). They report that its phase space motion under exact resonance (p ω 0 = (2 π / T) q; p, q integers), and with initial conditions on the separatrix of the average Hamiltonian , accelerates unboundedly along a fractal stochastic web with q-fold symmetry. Here we investigate with numerical experiments the effects of small deviations from exact resonance on the diffusion and symmetry patterns. We show graphically that the stochastic webs are (topologically) unstable and thus the unbounded motion becomes considerably truncated. Moreover, we analyze numerically and analytically a simpler (integrable) version. We give its exact closed-form solution in complex numbers, realize that it accelerates unboundedly only when ω 0 = (2 π/T) q (q = ± 1,2,...), and show that for small uncertainties in these frequencies, total predictability is lost as time evolves. That is, trajectories of a set of systems, initially described by close neighboring points in phase space strongly diverge in a non-linear way. The great loss of predictability in the integrable model is due to the combination of translational and rotational symmetries, inherent in these systems. (Author)
Chaos and loss of predictability in the periodically kicked linear oscillator
Energy Technology Data Exchange (ETDEWEB)
Luna-Acosta, G A [Universidad Autonoma de Puebla (Mexico). Inst. de Ciencias; Cantoral, E [Universidad Autonoma de Puebla (Mexico). Escuela de Fisica
1989-01-01
Chernikov et.al. [2] have discovered new features in the dynamics of a periodically kicked LHO x'' + [omega] [sub 0] [sup 2] x = ( K/ k[sub 0] T [sup 2]) sin (k[sub 0] x) x [Sigma][sub n] [delta] (t / T - n). They report that its phase space motion under exact resonance (p [omega] [sub 0] = (2 [pi] / T) q; p, q integers), and with initial conditions on the separatrix of the average Hamiltonian , accelerates unboundedly along a fractal stochastic web with q-fold symmetry. Here we investigate with numerical experiments the effects of small deviations from exact resonance on the diffusion and symmetry patterns. We show graphically that the stochastic webs are (topologically) unstable and thus the unbounded motion becomes considerably truncated. Moreover, we analyze numerically and analytically a simpler (integrable) version. We give its exact closed-form solution in complex numbers, realize that it accelerates unboundedly only when [omega][sub 0] = (2 [pi]/T) q (q = [+-] 1,2,...), and show that for small uncertainties in these frequencies, total predictability is lost as time evolves. That is, trajectories of a set of systems, initially described by close neighboring points in phase space strongly diverge in a non-linear way. The great loss of predictability in the integrable model is due to the combination of translational and rotational symmetries, inherent in these systems. (Author).
Directory of Open Access Journals (Sweden)
Ajith Ananthakrishna Pillai
2012-03-01
Full Text Available Bifurcation percutaneous coronary intervention (PCI is still a difficult call for the interventionist despite advancements in the instrumentation, technical skill and the imaging modalities. With major cardiac events relate to the side-branch (SB compromise, the concept and practice of dedicated bifurcation stents seems exciting. Several designs of such dedicated stents are currently undergoing trials. This novel concept and pristine technology offers new hope notwithstanding the fact that we need to go a long way in widespread acceptance and practice of these gadgets. Some of these designs even though looks enterprising, the mere complex delivering technique and the demanding knowledge of the exact coronary anatomy makes their routine use challenging.
Numerical analysis of bifurcations
International Nuclear Information System (INIS)
Guckenheimer, J.
1996-01-01
This paper is a brief survey of numerical methods for computing bifurcations of generic families of dynamical systems. Emphasis is placed upon algorithms that reflect the structure of the underlying mathematical theory while retaining numerical efficiency. Significant improvements in the computational analysis of dynamical systems are to be expected from more reliance of geometric insight coming from dynamical systems theory. copyright 1996 American Institute of Physics
Geometrically Induced Interactions and Bifurcations
Binder, Bernd
2010-01-01
In order to evaluate the proper boundary conditions in spin dynamics eventually leading to the emergence of natural and artificial solitons providing for strong interactions and potentials with monopole charges, the paper outlines a new concept referring to a curvature-invariant formalism, where superintegrability is given by a special isometric condition. Instead of referring to the spin operators and Casimir/Euler invariants as the generator of rotations, a curvature-invariant description is introduced utilizing a double Gudermann mapping function (generator of sine Gordon solitons and Mercator projection) cross-relating two angular variables, where geometric phases and rotations arise between surfaces of different curvature. Applying this stereographic projection to a superintegrable Hamiltonian can directly map linear oscillators to Kepler/Coulomb potentials and/or monopoles with Pöschl-Teller potentials and vice versa. In this sense a large scale Kepler/Coulomb (gravitational, electro-magnetic) wave dynamics with a hyperbolic metric could be mapped as a geodesic vertex flow to a local oscillator singularity (Dirac monopole) with spherical metrics and vice versa. Attracting fixed points and dynamic constraints are given by special isometries with magic precession angles. The nonlinear angular encoding directly provides for a Shannon mutual information entropy measure of the geodesic phase space flow. The emerging monopole patterns show relations to spiral Fresnel holography and Berry/Aharonov-Bohm geometric phases subject to bifurcation instabilities and singularities from phase ambiguities due to a local (entropy) overload. Neutral solitons and virtual patterns emerging and mediating in the overlap region between charged or twisted holographic patterns are visualized and directly assigned to the Berry geometric phase revealing the role of photons, neutrons, and neutrinos binding repulsive charges in Coulomb, strong and weak interaction.
Kido, M.; Matsui, R.; Imano, M.; Honsho, C.
2017-12-01
In the GNSS/acoustic measurement, sound speed in ocean plays a key role of accuracy of final positioning. We have shown than longer period sound speed undulation can be properly estimated from GNSS-A analysis itself in our previous work. In this work, we have carried out intensive XBT measurement to get temporal variation of sound speed in short period to be compared with GNSS-A derived one. In the individual temperature profile obtained by intensive XBT measurements (10 minutes interval up to 12 times of cast), clear vertical oscillation up to 20 m of amplitude in the shallow part were observed. These can be interpreted as gravitational internal wave with short-period and hence short wavelength anomaly. Kido et al. (2007) proposed that horizontal variation of the ocean structure can be considered employing five or more transponders at once if the structure is expressed by two quantities, i.e., horizontal gradient in x/y directions. However, this hypothesis requires that the variation must has a large spatial scale (> 2-5km) so that the horizontal variation can be regarded as linear within the extent of acoustic path to seafloor transponders. Therefore the wavelength of the above observed internal wave is getting important. The observed period of internal wave was 30-60 minute. However its wavelength cannot be directly measured. It must be estimate based on density profile of water column. In the comparison between sound speed change and positioning, the delay of their phases were 90 degree, which indicates that most steep horizontal slope of internal wave correspond to largest apparent positioning shift.
An Optical Low-frequency Quasi-Periodic Oscillation in the Kepler Light Curve of an Active Galaxy
Mushotzky, Richard; Smith, Krista Lynne; Boyd, Patricia; Wagoner, Robert
2018-01-01
We report the discovery of a candidate quasi-periodic oscillation (QPO) in the optical light curve of KIC 9650712, a Seyfert 1 galaxy in the original Kepler field. After the development and application of a pipeline for Kepler data specific to active galactic nuclei (AGN), one of our sample of 21 AGN selected by infrared photometry and X-ray flux demonstrates a peak in the power spectrum at 10-6.58 Hz, corresponding to a temporal period of 44 days. >From optical spectroscopy, we measure the black hole mass of this AGN as log M = 8.17 M_sun. Despite this high mass, the optical spectrum of KIC 9650712 bears many similarities to Narrow Line Seyfert 1 (NLS1) galaxies, including strong Fe II emission and a low [O III]/Hβ ratio. So far, X-ray QPOs have primarily been seen in NLS1 galaxies. Finally, we find that this frequency lies along a correlation between low-frequency QPOs and black hole mass from stellar and intermediate mass black holes to AGN, similar to the known correlation in high-frequency QPOs.
Zhioua, M.; El Aroudi, A.; Belghith, S.; Bosque-Moncusí, J. M.; Giral, R.; Al Hosani, K.; Al-Numay, M.
A study of a DC-DC boost converter fed by a photovoltaic (PV) generator and supplying a constant voltage load is presented. The input port of the converter is controlled using fixed frequency pulse width modulation (PWM) based on the loss-free resistor (LFR) concept whose parameter is selected with the aim to force the PV generator to work at its maximum power point. Under this control strategy, it is shown that the system can exhibit complex nonlinear behaviors for certain ranges of parameter values. First, using the nonlinear models of the converter and the PV source, the dynamics of the system are explored in terms of some of its parameters such as the proportional gain of the controller and the output DC bus voltage. To present a comprehensive approach to the overall system behavior under parameter changes, a series of bifurcation diagrams are computed from the circuit-level switched model and from a simplified model both implemented in PSIM© software showing a remarkable agreement. These diagrams show that the first instability that takes place in the system period-1 orbit when a primary parameter is varied is a smooth period-doubling bifurcation and that the nonlinearity of the PV generator is irrelevant for predicting this phenomenon. Different bifurcation scenarios can take place for the resulting period-2 subharmonic regime depending on a secondary bifurcation parameter. The boundary between the desired period-1 orbit and subharmonic oscillation resulting from period-doubling in the parameter space is obtained by calculating the eigenvalues of the monodromy matrix of the simplified model. The results from this model have been validated with time-domain numerical simulation using the circuit-level switched model and also experimentally from a laboratory prototype. This study can help in selecting the parameter values of the circuit in order to delimit the region of period-1 operation of the converter which is of practical interest in PV systems.
Analysis of a Stochastic Chemical System Close to a SNIPER Bifurcation of Its Mean-Field Model
Erban, Radek; Chapman, S. Jonathan; Kevrekidis, Ioannis G.; Vejchodský , Tomá š
2009-01-01
A framework for the analysis of stochastic models of chemical systems for which the deterministic mean-field description is undergoing a saddle-node infinite period (SNIPER) bifurcation is presented. Such a bifurcation occurs, for example
Attractors of the periodically forced Rayleigh system
Directory of Open Access Journals (Sweden)
Petre Bazavan
2011-07-01
Full Text Available The autonomous second order nonlinear ordinary differential equation(ODE introduced in 1883 by Lord Rayleigh, is the equation whichappears to be the closest to the ODE of the harmonic oscillator withdumping.In this paper we present a numerical study of the periodic andchaotic attractors in the dynamical system associated with the generalized Rayleigh equation. Transition between periodic and quasiperiodic motion is also studied. Numerical results describe the system dynamics changes (in particular bifurcations, when the forcing frequency is varied and thus, periodic, quasiperiodic or chaotic behaviour regions are predicted.
Model Reduction of Nonlinear Aeroelastic Systems Experiencing Hopf Bifurcation
Abdelkefi, Abdessattar
2013-06-18
In this paper, we employ the normal form to derive a reduced - order model that reproduces nonlinear dynamical behavior of aeroelastic systems that undergo Hopf bifurcation. As an example, we consider a rigid two - dimensional airfoil that is supported by nonlinear springs in the pitch and plunge directions and subjected to nonlinear aerodynamic loads. We apply the center manifold theorem on the governing equations to derive its normal form that constitutes a simplified representation of the aeroelastic sys tem near flutter onset (manifestation of Hopf bifurcation). Then, we use the normal form to identify a self - excited oscillator governed by a time - delay ordinary differential equation that approximates the dynamical behavior while reducing the dimension of the original system. Results obtained from this oscillator show a great capability to predict properly limit cycle oscillations that take place beyond and above flutter as compared with the original aeroelastic system.
International Nuclear Information System (INIS)
Zhang Hailong; Zhang Ning; Wang Enrong; Min Fuhong
2016-01-01
The magneto-rheological damper (MRD) is a promising device used in vehicle semi-active suspension systems, for its continuous adjustable damping output. However, the innate nonlinear hysteresis characteristic of MRD may cause the nonlinear behaviors. In this work, a two-degree-of-freedom (2-DOF) MR suspension system was established first, by employing the modified Bouc–Wen force–velocity (F–v) hysteretic model. The nonlinear dynamic response of the system was investigated under the external excitation of single-frequency harmonic and bandwidth-limited stochastic road surface. The largest Lyapunov exponent (LLE) was used to detect the chaotic area of the frequency and amplitude of harmonic excitation, and the bifurcation diagrams, time histories, phase portraits, and power spectrum density (PSD) diagrams were used to reveal the dynamic evolution process in detail. Moreover, the LLE and Kolmogorov entropy (K entropy) were used to identify whether the system response was random or chaotic under stochastic road surface. The results demonstrated that the complex dynamical behaviors occur under different external excitation conditions. The oscillating mechanism of alternating periodic oscillations, quasi-periodic oscillations, and chaotic oscillations was observed in detail. The chaotic regions revealed that chaotic motions may appear in conditions of mid-low frequency and large amplitude, as well as small amplitude and all frequency. The obtained parameter regions where the chaotic motions may appear are useful for design of structural parameters of the vibration isolation, and the optimization of control strategy for MR suspension system. (paper)
Bifurcation of solutions to Hamiltonian boundary value problems
McLachlan, R. I.; Offen, C.
2018-06-01
A bifurcation is a qualitative change in a family of solutions to an equation produced by varying parameters. In contrast to the local bifurcations of dynamical systems that are often related to a change in the number or stability of equilibria, bifurcations of boundary value problems are global in nature and may not be related to any obvious change in dynamical behaviour. Catastrophe theory is a well-developed framework which studies the bifurcations of critical points of functions. In this paper we study the bifurcations of solutions of boundary-value problems for symplectic maps, using the language of (finite-dimensional) singularity theory. We associate certain such problems with a geometric picture involving the intersection of Lagrangian submanifolds, and hence with the critical points of a suitable generating function. Within this framework, we then study the effect of three special cases: (i) some common boundary conditions, such as Dirichlet boundary conditions for second-order systems, restrict the possible types of bifurcations (for example, in generic planar systems only the A-series beginning with folds and cusps can occur); (ii) integrable systems, such as planar Hamiltonian systems, can exhibit a novel periodic pitchfork bifurcation; and (iii) systems with Hamiltonian symmetries or reversing symmetries can exhibit restricted bifurcations associated with the symmetry. This approach offers an alternative to the analysis of critical points in function spaces, typically used in the study of bifurcation of variational problems, and opens the way to the detection of more exotic bifurcations than the simple folds and cusps that are often found in examples.
Generating macroscopic chaos in a network of globally coupled phase oscillators
So, Paul; Barreto, Ernest
2011-01-01
We consider an infinite network of globally coupled phase oscillators in which the natural frequencies of the oscillators are drawn from a symmetric bimodal distribution. We demonstrate that macroscopic chaos can occur in this system when the coupling strength varies periodically in time. We identify period-doubling cascades to chaos, attractor crises, and horseshoe dynamics for the macroscopic mean field. Based on recent work that clarified the bifurcation structure of the static bimodal Kuramoto system, we qualitatively describe the mechanism for the generation of such complicated behavior in the time varying case. PMID:21974662
Modified jailed balloon technique for bifurcation lesions.
Saito, Shigeru; Shishido, Koki; Moriyama, Noriaki; Ochiai, Tomoki; Mizuno, Shingo; Yamanaka, Futoshi; Sugitatsu, Kazuya; Tobita, Kazuki; Matsumi, Junya; Tanaka, Yutaka; Murakami, Masato
2017-12-04
We propose a new systematic approach in bifurcation lesions, modified jailed balloon technique (M-JBT), and report the first clinical experience. Side branch occlusion brings with a serious complication and occurs in more than 7.0% of cases during bifurcation stenting. A jailed balloon (JB) is introduced into the side branch (SB), while a stent is placed in the main branch (MB) as crossing SB. The size of the JB is half of the MB stent size. While the proximal end of JB attaching to MB stent, both stent and JB are simultaneously inflated with same pressure. JB is removed and then guidewires are recrossed. Kissing balloon dilatation (KBD) and/or T and protrusion (TAP) stenting are applied as needed. Between February 2015 and February 2016, 233 patients (254 bifurcation lesions including 54 left main trunk disease) underwent percutaneous coronary intervention (PCI) using this technique. Procedure success was achieved in all cases. KBD was performed for 183 lesions and TAP stenting was employed for 31 lesions. Occlusion of SV was not observed in any of the patients. Bench test confirmed less deformity of MB stent in M-JBT compared with conventional-JBT. This is the first report for clinical experiences by using modified jailed balloon technique. This novel M-JBT is safe and effective in the preservation of SB patency during bifurcation stenting. © 2017 Wiley Periodicals, Inc.
DETECTION OF VERY LOW-FREQUENCY, QUASI-PERIODIC OSCILLATIONS IN THE 2015 OUTBURST OF V404 CYGNI
Energy Technology Data Exchange (ETDEWEB)
Huppenkothen, D. [Center for Data Science, New York University, 726 Broadway, 7th Floor, New York, NY 10003 (United States); Younes, G.; Kouveliotou, C. [Department of Physics, The George Washington University, Washington, DC 20052 (United States); Ingram, A.; Van der Klis, M. [Anton Pannekoek Institute, University of Amsterdam, Science Park 904, 1098 XH Amsterdam (Netherlands); Göğüş, E. [Sabancı University, Orhanlı-Tuzla, İstanbul 34956 (Turkey); Bachetti, M. [INAF/Osservatorio Astronomico di Cagliari, via della Scienza 5, I-09047 Selargius (Italy); Sánchez-Fernández, C.; Kuulkers, E. [European Space Astronomy Centre (ESA/ESAC), Science Operations Department, E-28691 Villanueva de la Cañada, Madrid (Spain); Chenevez, J. [DTU Space—National Space Institute, Technical University of Denmark, Elektrovej 327-328, DK-2800 Lyngby (Denmark); Motta, S. [University of Oxford, Department of Physics, Astrophysics, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH (United Kingdom); Granot, J. [Department of Natural Sciences, The Open University of Israel, 1 University Road, P.O. Box 808, Raanana 43537 (Israel); Gehrels, N. [Astrophysics Science Division, NASA Goddard Space Flight Center, Mail Code 661, Greenbelt, MD 20771 (United States); Tomsick, J. A. [Space Sciences Laboratory, 7 Gauss Way, University of California, Berkeley, CA 94720-7450 (United States); Walton, D. J., E-mail: daniela.huppenkothen@nyu.edu [Cahill Center for Astronomy and Astrophysics, California Institute of Technology, Pasadena, CA 91125 (United States)
2017-01-01
In 2015 June, the black hole X-ray binary (BHXRB) V404 Cygni went into outburst for the first time since 1989. Here, we present a comprehensive search for quasi-periodic oscillations (QPOs) of V404 Cygni during its recent outburst, utilizing data from six instruments on board five different X-ray missions: Swift /XRT, Fermi /GBM, Chandra /ACIS, INTEGRAL ’s IBIS/ISGRI and JEM-X, and NuSTAR . We report the detection of a QPO at 18 mHz simultaneously with both Fermi /GBM and Swift /XRT, another example of a rare but slowly growing new class of mHz-QPOs in BHXRBs linked to sources with a high orbital inclination. Additionally, we find a duo of QPOs in a Chandra /ACIS observation at 73 mHz and 1.03 Hz, as well as a QPO at 136 mHz in a single Swift /XRT observation that can be interpreted as standard Type-C QPOs. Aside from the detected QPOs, there is significant structure in the broadband power, with a strong feature observable in the Chandra observations between 0.1 and 1 Hz. We discuss our results in the context of current models for QPO formation.
Quasi-periodic oscillations in short recurring bursts of the soft gamma repeater J1550–5418
Energy Technology Data Exchange (ETDEWEB)
Huppenkothen, D.; D' Angelo, C.; Watts, A. L.; Heil, L.; Van der Klis, M.; Van der Horst, A. J. [Astronomical Institute " Anton Pannekoek," University of Amsterdam, Postbus 94249, 1090 GE Amsterdam (Netherlands); Kouveliotou, C. [Astrophysics Office, ZP 12, NASA-Marshall Space Flight Center, Huntsville, AL 35812 (United States); Baring, M. G. [Department of Physics and Astronomy, Rice University, MS-108, P.O. Box 1892, Houston, TX 77251 (United States); Göğüş, E.; Kaneko, Y. [SabancıUniversity, Orhanlı-Tuzla, İstanbul 34956 (Turkey); Granot, J. [Department of Natural Sciences, The Open University of Israel, 1 University Road, P.O. Box 808, Ra' anana 43537 (Israel); Lin, L. [François Arago Centre, APC, 10 rue Alice Domon et Léonie Duquet, F-75205 Paris (France); Von Kienlin, A. [Max-Planck-Institut für extraterrestrische Physik, Giessenbachstrasse 1, D-85748 Garching (Germany); Younes, G., E-mail: D.Huppenkothen@uva.nl [NSSTC, 320 Sparkman Drive, Huntsville, AL 35805 (United States)
2014-06-01
The discovery of quasi-periodic oscillations (QPOs) in magnetar giant flares has opened up prospects for neutron star asteroseismology. The scarcity of giant flares makes a search for QPOs in the shorter, far more numerous bursts from soft gamma repeaters (SGRs) desirable. In Huppenkothen et al., we developed a Bayesian method for searching for QPOs in short magnetar bursts, taking into account the effects of the complicated burst structure, and have shown its feasibility on a small sample of bursts. Here we apply the same method to a much larger sample from a burst storm of 286 bursts from SGR J1550–5418. We report a candidate signal at 260 Hz in a search of the individual bursts, which is fairly broad. We also find two QPOs at ∼93 Hz, and one at 127 Hz, when averaging periodograms from a number of bursts in individual triggers, at frequencies close to QPOs previously observed in magnetar giant flares. Finally, for the first time, we explore the overall burst variability in the sample and report a weak anti-correlation between the power-law index of the broadband model characterizing aperiodic burst variability and the burst duration: shorter bursts have steeper power-law indices than longer bursts. This indicates that longer bursts vary over a broader range of timescales and are not simply longer versions of the short bursts.
Energy Technology Data Exchange (ETDEWEB)
Cunha, M. S.; Avelino, P. P. [Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, 4150-762 Porto (Portugal); Stello, D. [Sydney Institute for Astronomy (SIfA), School of Physics, University of Sydney, NSW 2006 (Australia); Christensen-Dalsgaard, J. [Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C (Denmark); Townsend, R. H. D., E-mail: mcunha@astro.up.pt [Department of Astronomy, University of Wisconsin–Madison, 2535 Sterling Hall, 475 N. Charter Street, Madison, WI 53706 (United States)
2015-06-01
With recent advances in asteroseismology it is now possible to peer into the cores of red giants, potentially providing a way to study processes such as nuclear burning and mixing through their imprint as sharp structural variations—glitches—in the stellar cores. Here we show how such core glitches can affect the oscillations we observe in red giants. We derive an analytical expression describing the expected frequency pattern in the presence of a glitch. This formulation also accounts for the coupling between acoustic and gravity waves. From an extensive set of canonical stellar models we find glitch-induced variation in the period spacing and inertia of non-radial modes during several phases of red giant evolution. Significant changes are seen in the appearance of mode amplitude and frequency patterns in asteroseismic diagrams such as the power spectrum and the échelle diagram. Interestingly, along the red giant branch glitch-induced variation occurs only at the luminosity bump, potentially providing a direct seismic indicator of stars in that particular evolution stage. Similarly, we find the variation at only certain post-helium-ignition evolution stages, namely, in the early phases of helium core burning and at the beginning of helium shell burning, signifying the asymptotic giant branch bump. Based on our results, we note that assuming stars to be glitch-free, while they are not, can result in an incorrect estimate of the period spacing. We further note that including diffusion and mixing beyond classical Schwarzschild could affect the characteristics of the glitches, potentially providing a way to study these physical processes.
You, Bei; Bursa, Michal; Życki, Piotr T.
2018-05-01
We develop a Monte Carlo code to compute the Compton-scattered X-ray flux arising from a hot inner flow that undergoes Lense–Thirring precession. The hot flow intercepts seed photons from an outer truncated thin disk. A fraction of the Comptonized photons will illuminate the disk, and the reflected/reprocessed photons will contribute to the observed spectrum. The total spectrum, including disk thermal emission, hot flow Comptonization, and disk reflection, is modeled within the framework of general relativity, taking light bending and gravitational redshift into account. The simulations are performed in the context of the Lense–Thirring precession model for the low-frequency quasi-periodic oscillations, so the inner flow is assumed to precess, leading to periodic modulation of the emitted radiation. In this work, we concentrate on the energy-dependent X-ray variability of the model and, in particular, on the evolution of the variability during the spectral transition from hard to soft state, which is implemented by the decrease of the truncation radius of the outer disk toward the innermost stable circular orbit. In the hard state, where the Comptonizing flow is geometrically thick, the Comptonization is weakly variable with a fractional variability amplitude of ≤10% in the soft state, where the Comptonizing flow is cooled down and thus becomes geometrically thin, the fractional variability of the Comptonization is highly variable, increasing with photon energy. The fractional variability of the reflection increases with energy, and the reflection emission for low spin is counterintuitively more variable than the one for high spin.
International Nuclear Information System (INIS)
Svirskii, M.S.
1985-01-01
Oscillations with a period equal to the normal or superconducting flux quantum occur in the current density and the orbital parts of the energy and the magnetic moment in cyclic systems. Transitions between these regimes can be induced by changing the number of electrons or by switching between states with different energies
Symmetry breaking bifurcations of a current sheet
International Nuclear Information System (INIS)
Parker, R.D.; Dewar, R.L.; Johnson, J.L.
1990-01-01
Using a time evolution code with periodic boundary conditions, the viscoresistive hydromagnetic equations describing an initially static, planar current sheet with large Lundquist number have been evolved for times long enough to reach a steady state. A cosh 2 x resistivity model was used. For long periodicity lengths L p , the resistivity gradient drives flows that cause forced reconnection at X point current sheets. Using L p as a bifurcation parameter, two new symmetry breaking bifurcations were found: a transition to an asymmetric island chain with nonzero, positive, or negative phase velocity, and a transition to a static state with alternating large and small islands. These states are reached after a complex transient behavior, which involves a competition between secondary current sheet instability and coalescence
Symmetry breaking bifurcations of a current sheet
International Nuclear Information System (INIS)
Parker, R.D.; Dewar, R.L.; Johnson, J.L.
1988-08-01
Using a time evolution code with periodic boundary conditions, the viscoresistive hydromagnetic equations describing an initially static, planar current sheet with large Lundquist number have been evolved for times long enough to reach a steady state. A cosh 2 x resistivity model was used. For long periodicity lengths, L p , the resistivity gradient drives flows which cause forced reconnection at X point current sheets. Using L p as a bifurcation parameter, two new symmetry breaking bifurcations were found - a transition to an asymmetric island chain with nonzero, positive or negative phase velocity, and a transition to a static state with alternating large and small islands. These states are reached after a complex transient behavior which involves a competition between secondary current sheet instability and coalescence. 31 refs., 6 figs
Bubble transport in bifurcations
Bull, Joseph; Qamar, Adnan
2017-11-01
Motivated by a developmental gas embolotherapy technique for cancer treatment, we examine the transport of bubbles entrained in liquid. In gas embolotherapy, infarction of tumors is induced by selectively formed vascular gas bubbles that originate from acoustic vaporization of vascular droplets. In the case of non-functionalized droplets with the objective of vessel occlusion, the bubbles are transported by flow through vessel bifurcations, where they may split prior to eventually reach vessels small enough that they become lodged. This splitting behavior affects the distribution of bubbles and the efficacy of flow occlusion and the treatment. In these studies, we investigated bubble transport in bifurcations using computational and theoretical modeling. The model reproduces the variety of experimentally observed splitting behaviors. Splitting homogeneity and maximum shear stress along the vessel walls is predicted over a variety of physical parameters. Maximum shear stresses were found to decrease with increasing Reynolds number. The initial bubble length was found to affect the splitting behavior in the presence of gravitational asymmetry. This work was supported by NIH Grant R01EB006476.
Asymptotic representation of relaxation oscillations in lasers
Grigorieva, Elena V
2017-01-01
In this book we analyze relaxation oscillations in models of lasers with nonlinear elements controlling light dynamics. The models are based on rate equations taking into account periodic modulation of parameters, optoelectronic delayed feedback, mutual coupling between lasers, intermodal interaction and other factors. With the aim to study relaxation oscillations we present the special asymptotic method of integration for ordinary differential equations and differential-difference equations. As a result, they are reduced to discrete maps. Analyzing the maps we describe analytically such nonlinear phenomena in lasers as multistability of large-amplitude relaxation cycles, bifurcations of cycles, controlled switching of regimes, phase synchronization in an ensemble of coupled systems and others. The book can be fruitful for students and technicians in nonlinear laser dynamics and in differential equations.
Co-existing hidden attractors in a radio-physical oscillator system
DEFF Research Database (Denmark)
Kuznetsov, A. P.; Kuznetsov, S. P.; Mosekilde, Erik
2015-01-01
The term `hidden attractor' relates to a stable periodic, quasiperiodic or chaotic state whose basin of attraction does not overlap with the neighborhood of an unstable equilibrium point. Considering a three-dimensional oscillator system that does not allow for the existence of an equilibrium point...... frequency, describe the bifurcations through which hidden attractors of different type arise and disappear, and illustrate the form of the basins of attraction....
Liu, Han-Chun; Reichl, C; Wegscheider, W; Mani, R G
2018-05-18
We report the observation of dc-current-bias-induced B-periodic Hall resistance oscillations and Hall plateaus in the GaAs/AlGaAs 2D system under combined microwave radiation- and dc bias excitation at liquid helium temperatures. The Hall resistance oscillations and plateaus appear together with concomitant oscillations also in the diagonal magnetoresistance. The periods of Hall and diagonal resistance oscillations are nearly identical, and source power (P) dependent measurements demonstrate sub-linear relationship of the oscillation amplitude with P over the span 0 < P ≤ 20 mW.
Bunch lengthening with bifurcation in electron storage rings
Energy Technology Data Exchange (ETDEWEB)
Kim, Eun-San; Hirata, Kohji [National Lab. for High Energy Physics, Tsukuba, Ibaraki (Japan)
1996-08-01
The mapping which shows equilibrium particle distribution in synchrotron phase space for electron storage rings is discussed with respect to some localized constant wake function based on the Gaussian approximation. This mapping shows multi-periodic states as well as double bifurcation in dynamical states of the equilibrium bunch length. When moving around parameter space, the system shows a transition/bifurcation which is not always reversible. These results derived by mapping are confirmed by multiparticle tracking. (author)
Bifurcation Analysis and Chaos Control in a Discrete Epidemic System
Directory of Open Access Journals (Sweden)
Wei Tan
2015-01-01
Full Text Available The dynamics of discrete SI epidemic model, which has been obtained by the forward Euler scheme, is investigated in detail. By using the center manifold theorem and bifurcation theorem in the interior R+2, the specific conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation have been derived. Numerical simulation not only presents our theoretical analysis but also exhibits rich and complex dynamical behavior existing in the case of the windows of period-1, period-3, period-5, period-6, period-7, period-9, period-11, period-15, period-19, period-23, period-34, period-42, and period-53 orbits. Meanwhile, there appears the cascade of period-doubling 2, 4, 8 bifurcation and chaos sets from the fixed point. These results show the discrete model has more richer dynamics compared with the continuous model. The computations of the largest Lyapunov exponents more than 0 confirm the chaotic behaviors of the system x→x+δ[rN(1-N/K-βxy/N-(μ+mx], y→y+δ[βxy/N-(μ+dy]. Specifically, the chaotic orbits at an unstable fixed point are stabilized by using the feedback control method.
Energy Technology Data Exchange (ETDEWEB)
Török, Gabriel; Goluchová, Katerina; Urbanec, Martin, E-mail: gabriel.torok@gmail.com, E-mail: katka.g@seznam.cz, E-mail: martin.urbanec@physics.cz [Research Centre for Computational Physics and Data Processing, Institute of Physics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo nám. 13, CZ-746, 01 Opava (Czech Republic); and others
2016-12-20
Twin-peak quasi-periodic oscillations (QPOs) are observed in the X-ray power-density spectra of several accreting low-mass neutron star (NS) binaries. In our previous work we have considered several QPO models. We have identified and explored mass–angular-momentum relations implied by individual QPO models for the atoll source 4U 1636-53. In this paper we extend our study and confront QPO models with various NS equations of state (EoS). We start with simplified calculations assuming Kerr background geometry and then present results of detailed calculations considering the influence of NS quadrupole moment (related to rotationally induced NS oblateness) assuming Hartle–Thorne spacetimes. We show that the application of concrete EoS together with a particular QPO model yields a specific mass–angular-momentum relation. However, we demonstrate that the degeneracy in mass and angular momentum can be removed when the NS spin frequency inferred from the X-ray burst observations is considered. We inspect a large set of EoS and discuss their compatibility with the considered QPO models. We conclude that when the NS spin frequency in 4U 1636-53 is close to 580 Hz, we can exclude 51 of the 90 considered combinations of EoS and QPO models. We also discuss additional restrictions that may exclude even more combinations. Namely, 13 EOS are compatible with the observed twin-peak QPOs and the relativistic precession model. However, when considering the low-frequency QPOs and Lense–Thirring precession, only 5 EOS are compatible with the model.
Energy Technology Data Exchange (ETDEWEB)
Bu, Qingcui; Chen, Li [Department of Astronomy, Beijing Normal University, Beijing 100875 (China); Belloni, T. M. [INAF-Osservatorio Astronomico di Brera, Via E, Bianchi 46, I-23807 Merate (Italy); Qu, Jinlu, E-mail: buqc@mail.bnu.edu.cn, E-mail: tomaso.belloni@brera.inaf.it, E-mail: chenli@bnu.edu.cn, E-mail: qujl@ihep.ac.cn [Laboratory for Particle Astrophysics, CAS, Beijing 100049 (China)
2017-06-01
Using archival Rossi X-ray Timing Explorer ( RXTE ) data, we studied the low-frequency quasi-periodic oscillations (LFQPOs) in the neutron star low-mass X-ray binary (LMXB) Cir X-1 and examined their contribution to frequency–frequency correlations for Z sources. We also studied the orbital phase effects on the LFQPO properties and found them to be phase independent. Comparing LFQPO frequencies in different classes of LMXBs, we found that systems that show both Z and atoll states form a common track with atoll/BH sources in the so-called WK correlation, while persistent Z systems are offset by a factor of about two. We found that neither source luminosity nor mass accretion rate is related to the shift of persistent Z systems. We discuss the possibility of a misidentification of fundamental frequency for horizontal branch oscillations from persistent Z systems and interpreted the oscillations in terms of models based on relativistic precession.
Chaos in periodically forced Holling type II predator-prey system with impulsive perturbations
International Nuclear Information System (INIS)
Zhang Shuwen; Tan Dejun; Chen Lansun
2006-01-01
The effect of periodic forcing and impulsive perturbations on predator-prey model with Holling type II functional response is investigated. The periodic forcing is affected by assuming a periodic variation in the intrinsic growth rate of prey. The impulsive perturbation is affected by introducing periodic constant impulsive immigration of predator. The dynamical behavior of the system is simulated and bifurcation diagrams are obtained for different parameters. The results show that periodic forcing and impulsive perturbation can very easily give rise to complex dynamics, including (1) quasi-periodic oscillating, (2) period doubling cascade, (3) chaos, (4) period halfing cascade, (5) non-unique dynamics
Chaos in periodically forced Holling type IV predator-prey system with impulsive perturbations
International Nuclear Information System (INIS)
Zhang Shuwen; Tan Dejun; Chen Lansun
2006-01-01
The effect of periodic forcing and impulsive perturbations on predator-prey model with Holling type IV functional response is investigated. The periodic forcing is affected by assuming a periodic variation in the intrinsic growth rate of the prey. The impulsive perturbations are affected by introducing periodic constant impulsive immigration of predator. The dynamical behavior of the system is simulated and bifurcation diagrams are obtained for different parameters. The results show that periodic forcing and impulsive perturbation can easily give rise to complex dynamics, including (1) quasi-periodic oscillating, (2) period doubling cascade, (3) chaos, (4) period halfing cascade
International Nuclear Information System (INIS)
Kalkofen, W.
1985-01-01
The assumptions of Ayres' model of the upper solar atmosphere are examined. It is found that the bistable character of his model is postulated - through the assumptions concerning the opacity sources and the effect of mechanical waves, which are allowed to destroy the CO molecules but not to heat the gas. The neglect of cooling by metal lines is based on their reduced local cooling rate, but it ignores the increased depth over which this cooling occurs. Thus, the bifurcated model of the upper solar atmosphere consists of two models, one cold at the temperature minimum, with a kinetic temperature of 2900 K, and the other hot, with a temperature of 4900 K. 8 references
Stochastic Bifurcation Analysis of an Elastically Mounted Flapping Airfoil
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Bose Chandan
2018-01-01
Full Text Available The present paper investigates the effects of noisy flow fluctuations on the fluid-structure interaction (FSI behaviour of a span-wise flexible wing modelled as a two degree-of-freedom elastically mounted flapping airfoil. In the sterile flow conditions, the system undergoes a Hopf bifurcation as the free-stream velocity exceeds a critical limit resulting in a stable limit-cycle oscillation (LCO from a fixed point response. On the other hand, the qualitative dynamics changes from a stochastic fixed point to a random LCO through an intermittent state in the presence of irregular flow fluctuations. The probability density function depicts the most probable system state in the phase space. A phenomenological bifurcation (P-bifurcation analysis based on the transition in the topology associated with the structure of the joint probability density function (pdf of the response variables has been carried out. The joint pdf corresponding to the stochastic fixed point possesses a Dirac delta function like structure with a sharp single peak around zero. As the mean flow speed crosses the critical value, the joint pdf bifurcates to a crater-like structure indicating the occurrence of a P-bifurcation. The intermittent state is characterized by the co-existence of the unimodal as well as the crater like structure.
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Martić-Bursać Nataša M.
2017-01-01
Full Text Available Periodicity of temperature on three stations in the Nisava River valley in period 1949-2014, has been analyzed by means of Fourier and wavelet transforms. Combined periodogram based on fast Fourier transform shows considerable similarity among individual series and identifies significant periods on 2.2, 2.7, 3.3, 5, 6-7, and 8.2 years in all datasets. Wavelet coherence analysis connects strongest 6-7 years spectral component to Mediterranean oscillation, starting in 1980s. Combined periodogram of Mediterranean oscillation index reveals 6-7 years spectral component as a dominant mode in period 1949-2014. Wavelet power spectra and partial combined periodograms show absence of 6-7 years component before 1975, after which this component becomes dominant in the spectrum. Consistency between alternation in temperature trend in the Nisava River valley and change in periodicity of Mediterranean oscillation was found. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. OI176008
Bifurcations sights, sounds, and mathematics
Matsumoto, Takashi; Kokubu, Hiroshi; Tokunaga, Ryuji
1993-01-01
Bifurcation originally meant "splitting into two parts. " Namely, a system under goes a bifurcation when there is a qualitative change in the behavior of the sys tem. Bifurcation in the context of dynamical systems, where the time evolution of systems are involved, has been the subject of research for many scientists and engineers for the past hundred years simply because bifurcations are interesting. A very good way of understanding bifurcations would be to see them first and study theories second. Another way would be to first comprehend the basic concepts and theories and then see what they look like. In any event, it is best to both observe experiments and understand the theories of bifurcations. This book attempts to provide a general audience with both avenues toward understanding bifurcations. Specifically, (1) A variety of concrete experimental results obtained from electronic circuits are given in Chapter 1. All the circuits are very simple, which is crucial in any experiment. The circuits, howev...
Analysis of stability and Hopf bifurcation for a viral infectious model with delay
International Nuclear Information System (INIS)
Sun Chengjun; Cao Zhijie; Lin Yiping
2007-01-01
In this paper, a four-dimensional viral infectious model with delay is considered. The stability of the two equilibria and the existence of Hopf bifurcation are investigated. It is found that there are stability switches and Hopf bifurcations occur when the delay τ passes through a sequence of critical values. Using the normal form theory and center manifold argument [Hassard B, Kazarino D, Wan Y. Theory and applications of Hopf bifurcation. Cambridge: Cambridge University Press; 1981], the explicit formulaes which determine the stability, the direction and the period of bifurcating periodic solutions are derived. Numerical simulations are carried out to illustrate the validity of the main results
Stability and bifurcation analysis in a kind of business cycle model with delay
International Nuclear Information System (INIS)
Zhang Chunrui; Wei Junjie
2004-01-01
A kind of business cycle model with delay is considered. Firstly, the linear stability of the model is studied and bifurcation set is drawn in the appropriate parameter plane. It is found that there exist Hopf bifurcations when the delay passes a sequence of critical values. Then the explicit algorithm for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived, using the normal form method and center manifold theorem. Finally, a group conditions to guarantee the global existence of periodic solutions is given, and numerical simulations are performed to illustrate the analytical results found
An alternative bifurcation analysis of the Rose-Hindmarsh model
International Nuclear Information System (INIS)
Nikolov, Svetoslav
2005-01-01
The paper presents an alternative study of the bifurcation behavior of the Rose-Hindmarsh model using Lyapunov-Andronov's theory. This is done on the basis of the obtained analytical formula expressing the first Lyapunov's value (this is not Lyapunov exponent) at the boundary of stability. From the obtained results the following new conclusions are made: Transition to chaos and the occurrence of chaotic oscillations in the Rose-Hindmarsh system take place under hard stability loss
Complex dynamics analysis of impulsively coupled Duffing oscillators with ring structure
International Nuclear Information System (INIS)
Jiang Hai-Bo; Zhang Li-Ping; Yu Jian-Jiang
2015-01-01
Impulsively coupled systems are high-dimensional non-smooth systems that can exhibit rich and complex dynamics. This paper studies the complex dynamics of a non-smooth system which is unidirectionally impulsively coupled by three Duffing oscillators in a ring structure. By constructing a proper Poincaré map of the non-smooth system, an analytical expression of the Jacobian matrix of Poincaré map is given. Two-parameter Hopf bifurcation sets are obtained by combining the shooting method and the Runge–Kutta method. When the period is fixed and the coupling strength changes, the system undergoes stable, periodic, quasi-periodic, and hyper-chaotic solutions, etc. Floquet theory is used to study the stability of the periodic solutions of the system and their bifurcations. (paper)
Wang, D. H.; Chen, L.; Zhang, C. M.; Lei, Y. J.; Qu, J. L.
2014-02-01
We collect the data of twin kilohertz quasi-periodic oscillations (kHz QPOs) published before 2012 from 26 neutron star (NS) low-mass X-ray binary (LMXB) sources, then we analyze the centroid frequency (ν) distribution of twin kHz QPOs (lower frequency ν_1 and upper frequency ν_2) both for Atoll and Z sources. For the data without shift-and-add, we find that Atoll and Z sources show different distributions of ν_1, ν_2 and ν_2/ν_1, but the same distribution of Δν (difference of twin kHz QPOs), which indicates that twin kHz QPOs may share the common properties of LXMBs and have the same physical origins. The distribution of Δν is quite different from a constant value, so is ν_2/ν_1 from a constant ratio. The weighted mean values and maxima of ν_1 and ν_2 in Atoll sources are slightly higher than those in Z sources. We also find that shift-and-add technique can reconstruct the distributions of ν_1 and Δν. The K-S test results of ν_1 and Δν between Atoll and Z sources from data with shift-and-add are quite different from those without it, and we think that this may be caused by the selection biases of the sample. We also study the properties of the quality factor (Q) and the root-mean-squared (rms) amplitude of 4U 0614+09 with data from the two observational methods, but the errors are too big to make a robust conclusion. The NS spin frequency (ν_s) distribution of 28 NS-LMXBs show a bigger mean value (˜ 408 Hz) than that (˜ 281 Hz) of the radio binary millisecond pulsars (MSPs), which may be due to the lack of the spin detections from Z sources (systematically lower than 281 Hz). Furthermore, on the relations between the kHz QPOs and NS spin frequency ν_s, we find the approximate correlations of the mean values of Δν with NS spin and its half, respectively.
An oscillating dynamic model of collective cells in a monolayer
Lin, Shao-Zhen; Xue, Shi-Lei; Li, Bo; Feng, Xi-Qiao
2018-03-01
Periodic oscillations of collective cells occur in the morphogenesis and organogenesis of various tissues and organs. In this paper, an oscillating cytodynamic model is presented by integrating the chemomechanical interplay between the RhoA effector signaling pathway and cell deformation. We show that both an isolated cell and a cell aggregate can undergo spontaneous oscillations as a result of Hopf bifurcation, upon which the system evolves into a limit cycle of chemomechanical oscillations. The dynamic characteristics are tailored by the mechanical properties of cells (e.g., elasticity, contractility, and intercellular tension) and the chemical reactions involved in the RhoA effector signaling pathway. External forces are found to modulate the oscillation intensity of collective cells in the monolayer and to polarize their oscillations along the direction of external tension. The proposed cytodynamic model can recapitulate the prominent features of cell oscillations observed in a variety of experiments, including both isolated cells (e.g., spreading mouse embryonic fibroblasts, migrating amoeboid cells, and suspending 3T3 fibroblasts) and multicellular systems (e.g., Drosophila embryogenesis and oogenesis).
Complex oscillatory behaviour in a delayed protein cross talk model with periodic forcing
International Nuclear Information System (INIS)
Nikolov, Svetoslav
2009-01-01
The purpose of this paper is to examine the effects of periodic forcing on the time delay protein cross talk model behaviour. We assume periodic variation for the plasma membrane permeability. The dynamic behaviour of the system is simulated and bifurcation diagrams are obtained for different parameters. The results show that periodic forcing can very easily give rise to complex dynamics, including a period-doubling cascade, chaos, quasi-periodic oscillating, and periodic windows. Finally, we calculate the maximal Lyapunov exponent in the regions of the parameter space where chaotic motion of delayed protein cross talk model with periodic forcing exists.
Energy Technology Data Exchange (ETDEWEB)
Varniere, Peggy [APC, AstroParticule et Cosmologie, Universite Paris Diderot, CNRS/IN2P3, CEA/Irfu, Observatoire de Paris, Sorbonne Paris Cité, 10, rue Alice Domon et Lonie Duquet, F-75205 Paris Cedex 13 (France); Vincent, Frederic H., E-mail: varniere@apc.univ-paris7.fr [Observatoire de Paris/LESIA, 5, place Jules Janssen, F-92195 Meudon Cedex (France)
2017-01-10
While it has been observed that the parameters intrinsic to the type C low-frequency quasi-periodic oscillations are related in a nonlinear manner among themselves, there has been, up to now, no model to explain or reproduce how the frequency, the FWHM, and the rms amplitude of the type C low-frequency quasi-periodic oscillations behave with respect to one another. Here we are using a simple toy model representing the emission from a standard disk and a spiral such as that caused by the accretion–ejection instability to reproduce the overall observed behavior and shed some light on its origin. This allows us to prove the ability of such a spiral structure to be at the origin of flux modulation over more than an order of magnitude in frequency.
Photon–phonon parametric oscillation induced by quadratic coupling in an optomechanical resonator
International Nuclear Information System (INIS)
Zhang, Lin; Ji, Fengzhou; Zhang, Xu; Zhang, Weiping
2017-01-01
A direct photon–phonon parametric effect of quadratic coupling on the mean-field dynamics of an optomechanical resonator in the large-scale-movement regime is found and investigated. Under a weak pumping power, the mechanical resonator damps to a steady state with a nonlinear static response sensitively modified by the quadratic coupling. When the driving power increases beyond the static energy balance, the steady states lose their stabilities via Hopf bifurcations, and the resonator produces stable self-sustained oscillation (limit-circle behavior) of discrete energies with step-like amplitudes due to the parametric effect of quadratic coupling, which can be understood roughly by the power balance between gain and loss on the resonator. A further increase in the pumping power can induce a chaotic dynamic of the resonator via a typical routine of period-doubling bifurcation, but which can be stabilized by the parametric effect through an inversion-bifurcation process back to the limit-circle states. The bifurcation-to-inverse-bifurcation transitions are numerically verified by the maximal Lyapunov exponents of the dynamics, which indicate an efficient way of suppressing the chaotic behavior of the optomechanical resonator by quadratic coupling. Furthermore, the parametric effect of quadratic coupling on the dynamic transitions of an optomechanical resonator can be conveniently detected or traced by the output power spectrum of the cavity field. (paper)
Heterogeneity induces spatiotemporal oscillations in reaction-diffusion systems
Krause, Andrew L.; Klika, Václav; Woolley, Thomas E.; Gaffney, Eamonn A.
2018-05-01
We report on an instability arising in activator-inhibitor reaction-diffusion (RD) systems with a simple spatial heterogeneity. This instability gives rise to periodic creation, translation, and destruction of spike solutions that are commonly formed due to Turing instabilities. While this behavior is oscillatory in nature, it occurs purely within the Turing space such that no region of the domain would give rise to a Hopf bifurcation for the homogeneous equilibrium. We use the shadow limit of the Gierer-Meinhardt system to show that the speed of spike movement can be predicted from well-known asymptotic theory, but that this theory is unable to explain the emergence of these spatiotemporal oscillations. Instead, we numerically explore this system and show that the oscillatory behavior is caused by the destabilization of a steady spike pattern due to the creation of a new spike arising from endogeneous activator production. We demonstrate that on the edge of this instability, the period of the oscillations goes to infinity, although it does not fit the profile of any well-known bifurcation of a limit cycle. We show that nearby stationary states are either Turing unstable or undergo saddle-node bifurcations near the onset of the oscillatory instability, suggesting that the periodic motion does not emerge from a local equilibrium. We demonstrate the robustness of this spatiotemporal oscillation by exploring small localized heterogeneity and showing that this behavior also occurs in the Schnakenberg RD model. Our results suggest that this phenomenon is ubiquitous in spatially heterogeneous RD systems, but that current tools, such as stability of spike solutions and shadow-limit asymptotics, do not elucidate understanding. This opens several avenues for further mathematical analysis and highlights difficulties in explaining how robust patterning emerges from Turing's mechanism in the presence of even small spatial heterogeneity.
Riddling bifurcation and interstellar journeys
International Nuclear Information System (INIS)
Kapitaniak, Tomasz
2005-01-01
We show that riddling bifurcation which is characteristic for low-dimensional attractors embedded in higher-dimensional phase space can give physical mechanism explaining interstellar journeys described in science-fiction literature
Stability and Hopf Bifurcation in a Delayed SEIRS Worm Model in Computer Network
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Zizhen Zhang
2013-01-01
Full Text Available A delayed SEIRS epidemic model with vertical transmission in computer network is considered. Sufficient conditions for local stability of the positive equilibrium and existence of local Hopf bifurcation are obtained by analyzing distribution of the roots of the associated characteristic equation. Furthermore, the direction of the local Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by using the normal form theory and center manifold theorem. Finally, a numerical example is presented to verify the theoretical analysis.
Dynamic bifurcations on financial markets
International Nuclear Information System (INIS)
Kozłowska, M.; Denys, M.; Wiliński, M.; Link, G.; Gubiec, T.; Werner, T.R.; Kutner, R.; Struzik, Z.R.
2016-01-01
We provide evidence that catastrophic bifurcation breakdowns or transitions, preceded by early warning signs such as flickering phenomena, are present on notoriously unpredictable financial markets. For this we construct robust indicators of catastrophic dynamical slowing down and apply these to identify hallmarks of dynamical catastrophic bifurcation transitions. This is done using daily closing index records for the representative examples of financial markets of small and mid to large capitalisations experiencing a speculative bubble induced by the worldwide financial crisis of 2007-08.
International Nuclear Information System (INIS)
Suarez Antola, R.
2011-01-01
One of the goals of nuclear power systems design and operation is to restrict the possible states of certain critical subsystems, during steady operation and during transients, to remain inside a certain bounded set of admissible states and state variations. Also, during transients, certain restrictions must be imposed on the time scale of evolution of the critical subsystem's state. A classification of the different solution types concerning their relation with the operational safety of the power plant is done by distributing the different solution types in relation with the exclusion region of the power-flow map. In the framework of an analytic or numerical modeling process of a boiling water reactor (BWR) power plant, this could imply first to find an suitable approximation to the solution manifold of the differential equations describing the stability behavior of this nonlinear system, and then a classification of the different solution types concerning their relation with the operational safety of the power plant, by distributing the different solution types in relation with the exclusion region of the power-flow map. Inertial manifold theory gives a foundation for the construction and use of reduced order models (ROM's) of reactor dynamics to discover and characterize meaningful bifurcations that may pass unnoticed during digital simulations done with full scale computer codes of the nuclear power plant. The March-Leuba's BWR ROM is used to exemplify the analytical approach developed here. The equation for excess void reactivity of this ROM is generalized. A nonlinear integral-differential equation in the logarithmic power is derived, including the generalized thermal-hydraulics feedback on the reactivity. Introducing a Krilov- Bogoliubov-Mitropolsky (KBM) ansatz with both amplitude and phase being slowly varying functions of time relative to the center period of oscillation, a coupled set of nonlinear ordinary differential equations for amplitude and phase
Balaji, Nidish Narayanaa; Krishna, I. R. Praveen; Padmanabhan, C.
2018-05-01
The Harmonic Balance Method (HBM) is a frequency-domain based approximation approach used for obtaining the steady state periodic behavior of forced dynamical systems. Intrinsically these systems are non-autonomous and the method offers many computational advantages over time-domain methods when the fundamental period of oscillation is known (generally fixed as the forcing period itself or a corresponding sub-harmonic if such behavior is expected). In the current study, a modified approach, based on He's Energy Balance Method (EBM), is applied to obtain the periodic solutions of conservative systems. It is shown that by this approach, periodic solutions of conservative systems on iso-energy manifolds in the phase space can be obtained very efficiently. The energy level provides the additional constraint on the HBM formulation, which enables the determination of the period of the solutions. The method is applied to the linear harmonic oscillator, a couple of nonlinear oscillators, the elastic pendulum and the Henon-Heiles system. The approach is used to trace the bifurcations of the periodic solutions of the last two, being 2 degree-of-freedom systems demonstrating very rich dynamical behavior. In the process, the advantages offered by the current formulation of the energy balance is brought out. A harmonic perturbation approach is used to evaluate the stability of the solutions for the bifurcation diagram.
Simple Chaotic Oscillator: From Mathematical Model to Practical Experiment
Directory of Open Access Journals (Sweden)
S. Hanus
2006-04-01
Full Text Available This paper shows the circuitry implementation and practical verification of the autonomous nonlinear oscillator. Since it is described by a single third-order differential equation, its state variables can be considered as the position, velocity and acceleration and thus have direct connection to a real physical system. Moreover, for some specific configurations of internal system parameters, it can exhibit a period doubling bifurcation leading to chaos. Two different structures of the nonlinear element were verified by a comparison of numerically integrated trajectory with the oscilloscope screenshots .
Directory of Open Access Journals (Sweden)
Fuhong Min
2016-08-01
Full Text Available The bifurcation and Lyapunov exponent for a single-machine-infinite bus system with excitation model are carried out by varying the mechanical power, generator damping factor and the exciter gain, from which periodic motions, chaos and the divergence of system are observed respectively. From given parameters and different initial conditions, the coexisting motions are developed in power system. The dynamic behaviors in power system may switch freely between the coexisting motions, which will bring huge security menace to protection operation. Especially, the angle divergences due to the break of stable chaotic oscillation are found which causes the instability of power system. Finally, a new adaptive backstepping sliding mode controller is designed which aims to eliminate the angle divergences and make the power system run in stable orbits. Numerical simulations are illustrated to verify the effectivity of the proposed method.
Energy Technology Data Exchange (ETDEWEB)
Min, Fuhong, E-mail: minfuhong@njnu.edu.cn; Wang, Yaoda; Peng, Guangya; Wang, Enrong [School of Electrical and Automation Engineering, Nanjing Normal University, Jiangsu, 210042 (China)
2016-08-15
The bifurcation and Lyapunov exponent for a single-machine-infinite bus system with excitation model are carried out by varying the mechanical power, generator damping factor and the exciter gain, from which periodic motions, chaos and the divergence of system are observed respectively. From given parameters and different initial conditions, the coexisting motions are developed in power system. The dynamic behaviors in power system may switch freely between the coexisting motions, which will bring huge security menace to protection operation. Especially, the angle divergences due to the break of stable chaotic oscillation are found which causes the instability of power system. Finally, a new adaptive backstepping sliding mode controller is designed which aims to eliminate the angle divergences and make the power system run in stable orbits. Numerical simulations are illustrated to verify the effectivity of the proposed method.
Energy Technology Data Exchange (ETDEWEB)
Hagedorn, R
1957-03-07
A mechanical system of two degrees of freedom is considered which can be described by a system of canonical differential equations. The Hamiltonian is assumed to be explicitly time-dependent with period 2. The aim is to bring this system by a sequence of canonical and periodical transformations into a form where the new Hamiltonian is constant and as simple as possible. The general theory is then brought to a stage where it becomes immediately applicable to given particular cases, particularly to circular particle accelerators. More general results are given on exciting strengths of different subresonance lines of equal order, on symmetry relations and on the one-dimensional case. An example is also given where the theory is overstressed and its predictions become wrong.
Bifurcation and Fractal of the Coupled Logistic Map
Wang, Xingyuan; Luo, Chao
The nature of the fixed points of the coupled Logistic map is researched, and the boundary equation of the first bifurcation of the coupled Logistic map in the parameter space is given out. Using the quantitative criterion and rule of system chaos, i.e., phase graph, bifurcation graph, power spectra, the computation of the fractal dimension, and the Lyapunov exponent, the paper reveals the general characteristics of the coupled Logistic map transforming from regularity to chaos, the following conclusions are shown: (1) chaotic patterns of the coupled Logistic map may emerge out of double-periodic bifurcation and Hopf bifurcation, respectively; (2) during the process of double-period bifurcation, the system exhibits self-similarity and scale transform invariability in both the parameter space and the phase space. From the research of the attraction basin and Mandelbrot-Julia set of the coupled Logistic map, the following conclusions are indicated: (1) the boundary between periodic and quasiperiodic regions is fractal, and that indicates the impossibility to predict the moving result of the points in the phase plane; (2) the structures of the Mandelbrot-Julia sets are determined by the control parameters, and their boundaries have the fractal characteristic.
Shells, orbit bifurcations, and symmetry restorations in Fermi systems
Energy Technology Data Exchange (ETDEWEB)
Magner, A. G., E-mail: magner@kinr.kiev.ua; Koliesnik, M. V. [NASU, Institute for Nuclear Research (Ukraine); Arita, K. [Nagoya Institute of Technology, Department of Physics (Japan)
2016-11-15
The periodic-orbit theory based on the improved stationary-phase method within the phase-space path integral approach is presented for the semiclassical description of the nuclear shell structure, concerning themain topics of the fruitful activity ofV.G. Soloviev. We apply this theory to study bifurcations and symmetry breaking phenomena in a radial power-law potential which is close to the realistic Woods–Saxon one up to about the Fermi energy. Using the realistic parametrization of nuclear shapes we explain the origin of the double-humped fission barrier and the asymmetry in the fission isomer shapes by the bifurcations of periodic orbits. The semiclassical origin of the oblate–prolate shape asymmetry and tetrahedral shapes is also suggested within the improved periodic-orbit approach. The enhancement of shell structures at some surface diffuseness and deformation parameters of such shapes are explained by existence of the simple local bifurcations and new non-local bridge-orbit bifurcations in integrable and partially integrable Fermi-systems. We obtained good agreement between the semiclassical and quantum shell-structure components of the level density and energy for several surface diffuseness and deformation parameters of the potentials, including their symmetry breaking and bifurcation values.
Global Hopf Bifurcation for a Predator-Prey System with Three Delays
Jiang, Zhichao; Wang, Lin
2017-06-01
In this paper, a delayed predator-prey model is considered. The existence and stability of the positive equilibrium are investigated by choosing the delay τ = τ1 + τ2 as a bifurcation parameter. We see that Hopf bifurcation can occur as τ crosses some critical values. The direction of the Hopf bifurcations and the stability of the bifurcation periodic solutions are also determined by using the center manifold and normal form theory. Furthermore, based on the global Hopf bifurcation theorem for general function differential equations, which was established by J. Wu using fixed point theorem and degree theory methods, the existence of global Hopf bifurcation is investigated. Finally, numerical simulations to support the analytical conclusions are carried out.
Stability, bifurcation and a new chaos in the logistic differential equation with delay
International Nuclear Information System (INIS)
Jiang Minghui; Shen Yi; Jian Jigui; Liao Xiaoxin
2006-01-01
This Letter is concerned with bifurcation and chaos in the logistic delay differential equation with a parameter r. The linear stability of the logistic equation is investigated by analyzing the associated characteristic transcendental equation. Based on the normal form approach and the center manifold theory, the formula for determining the direction of Hopf bifurcation and the stability of bifurcation periodic solution in the first bifurcation values is obtained. By theoretical analysis and numerical simulation, we found a new chaos in the logistic delay differential equation
Dynamics of a model of two delay-coupled relaxation oscillators
Ruelas, R. E.; Rand, R. H.
2010-08-01
This paper investigates the dynamics of a new model of two coupled relaxation oscillators. The model replaces the usual DDE (differential-delay equation) formulation with a discrete-time approach with jumps. Existence, bifurcation and stability of in-phase periodic motions is studied. Simple periodic motions, which involve exactly two jumps per period, are found to have large plateaus in parameter space. These plateaus are separated by regions of complicated dynamics, reminiscent of the Devil's Staircase. Stability of motions in the in-phase manifold are contrasted with stability of motions in the full phase space.
Energy Technology Data Exchange (ETDEWEB)
Bhatta, Gopal, E-mail: gopalbhatta716@gmail.com [Astronomical Observatory of the Jagiellonian University, ul. Orla 171, 30-244 Kraków (Poland); Mt. Suhora Observatory, Pedagogical University, ul. Podchorazych 2, 30-084 Kraków (Poland)
2017-09-20
In this work, we explore the long-term variability properties of the blazar PKS 0219−164 in the radio and the γ -ray regime, utilizing the OVRO 15 GHz and the Fermi /LAT observations from the period 2008–2017. We found that γ -ray emission is more variable than the radio emission implying that γ -ray emission possibly originated in more compact regions while the radio emission represented continuum emission from the large-scale jets. Also, in the γ -ray, the source exhibited spectral variability, characterized by the softer-when-brighter trend, a less frequently observed feature in the high-energy emission by BL Lacs. In radio, using Lomb–Scargle periodogram and weighted wavelet z -transform, we detected a strong signal of quasi-periodic oscillation (QPO) with a periodicity of 270 ± 26 days with possible harmonics of 550 ± 42 and 1150 ± 157 day periods. At a time when detections of QPOs in blazars are still under debate, the observed QPO with high statistical significance (∼97%–99% global significance over underlying red-noise processes) and persistent over nearly 10 oscillations could make one of the strongest cases for the detection of QPOs in blazar light curves. We discuss various blazar models that might lead to the γ -ray and radio variability, QPO, and the achromatic behavior seen in the high-energy emission from the source.
Double Hopf bifurcation in delay differential equations
Directory of Open Access Journals (Sweden)
Redouane Qesmi
2014-07-01
Full Text Available The paper addresses the computation of elements of double Hopf bifurcation for retarded functional differential equations (FDEs with parameters. We present an efficient method for computing, simultaneously, the coefficients of center manifolds and normal forms, in terms of the original FDEs, associated with the double Hopf singularity up to an arbitrary order. Finally, we apply our results to a nonlinear model with periodic delay. This shows the applicability of the methodology in the study of delay models arising in either natural or technological problems.
Quantitative angiography methods for bifurcation lesions
DEFF Research Database (Denmark)
Collet, Carlos; Onuma, Yoshinobu; Cavalcante, Rafael
2017-01-01
Bifurcation lesions represent one of the most challenging lesion subsets in interventional cardiology. The European Bifurcation Club (EBC) is an academic consortium whose goal has been to assess and recommend the appropriate strategies to manage bifurcation lesions. The quantitative coronary...... angiography (QCA) methods for the evaluation of bifurcation lesions have been subject to extensive research. Single-vessel QCA has been shown to be inaccurate for the assessment of bifurcation lesion dimensions. For this reason, dedicated bifurcation software has been developed and validated. These software...
A Pendulum-Like Motion of Nanofiber Gel Actuator Synchronized with External Periodic pH Oscillation
Directory of Open Access Journals (Sweden)
Shuji Hasimoto
2011-02-01
Full Text Available In this study, we succeeded in manufacturing a novel nanofiber hydrogel actuator that caused a bending and stretching motion synchronized with external pH oscillation, based on a bromate/sulfite/ferrocyanide reaction. The novel nanofiber gel actuator was composed of electrospun nanofibers synthesized by copolymerizing acrylic acid and hydrophobic butyl methacrylate as a solubility control site. By changing the electrospinning flow rate, the nanofiber gel actuator introduced an anisotropic internal structure into the gel. Therefore, the unsymmetrical motion of the nanofiber actuator was generated.
Karkar , Sami; Vergez , Christophe; Cochelin , Bruno
2012-01-01
International audience; We propose a new approach based on numerical continuation and bifurcation analysis for the study of physical models of instruments that produce self- sustained oscillation. Numerical continuation consists in following how a given solution of a set of equations is modified when one (or several) parameter of these equations are allowed to vary. Several physical models (clarinet, saxophone, and violin) are formulated as nonlinear dynamical systems, whose periodic solution...
Magneto-elastic dynamics and bifurcation of rotating annular plate*
International Nuclear Information System (INIS)
Hu Yu-Da; Piao Jiang-Min; Li Wen-Qiang
2017-01-01
In this paper, magneto-elastic dynamic behavior, bifurcation, and chaos of a rotating annular thin plate with various boundary conditions are investigated. Based on the thin plate theory and the Maxwell equations, the magneto-elastic dynamic equations of rotating annular plate are derived by means of Hamilton’s principle. Bessel function as a mode shape function and the Galerkin method are used to achieve the transverse vibration differential equation of the rotating annular plate with different boundary conditions. By numerical analysis, the bifurcation diagrams with magnetic induction, amplitude and frequency of transverse excitation force as the control parameters are respectively plotted under different boundary conditions such as clamped supported sides, simply supported sides, and clamped-one-side combined with simply-anotherside. Poincaré maps, time history charts, power spectrum charts, and phase diagrams are obtained under certain conditions, and the influence of the bifurcation parameters on the bifurcation and chaos of the system is discussed. The results show that the motion of the system is a complicated and repeated process from multi-periodic motion to quasi-period motion to chaotic motion, which is accompanied by intermittent chaos, when the bifurcation parameters change. If the amplitude of transverse excitation force is bigger or magnetic induction intensity is smaller or boundary constraints level is lower, the system can be more prone to chaos. (paper)
Stability and Hopf bifurcations in a competitive Lotka-Volterra system with two delays
International Nuclear Information System (INIS)
Song Yongli; Han Maoan; Peng Yahong
2004-01-01
We consider a Lotka-Volterra competition system with two delays. We first investigate the stability of the positive equilibrium and the existence of Hopf bifurcations, and then using the normal form theory and center manifold argument, derive the explicit formulas which determine the stability, direction and other properties of bifurcating periodic solutions
Hopf bifurcation in a dynamic IS-LM model with time delay
International Nuclear Information System (INIS)
Neamtu, Mihaela; Opris, Dumitru; Chilarescu, Constantin
2007-01-01
The paper investigates the impact of delayed tax revenues on the fiscal policy out-comes. Choosing the delay as a bifurcation parameter we study the direction and the stability of the bifurcating periodic solutions. We show when the system is stable with respect to the delay. Some numerical examples are given to confirm the theoretical results
Pierce instability and bifurcating equilibria
International Nuclear Information System (INIS)
Godfrey, B.B.
1981-01-01
The report investigates the connection between equilibrium bifurcations and occurrence of the Pierce instability. Electrons flowing from one ground plane to a second through an ion background possess a countable infinity of static equilibria, of which only one is uniform and force-free. Degeneracy of the uniform and simplest non-uniform equilibria at a certain ground plan separation marks the onset of the Pierce instability, based on a newly derived dispersion relation appropriate to all the equilibria. For large ground plane separations the uniform equilibrium is unstable and the non-uniform equilibrium is stable, the reverse of their stability properties at small separations. Onset of the Pierce instability at the first bifurcation of equilibria persists in more complicated geometries, providing a general criterion for marginal stability. It seems probable that bifurcation analysis can be a useful tool in the overall study of stable beam generation in diodes and transport in finite cavities
Fujiwara, Katsuo; Kiyota, Takeo; Mammadova, Aida; Yaguchi, Chie
2011-01-01
We investigated age-related changes and sex differences in adaptability of anticipatory postural control in children. Subjects comprised 449 children (4-12 years old) and 109 young adults (18-29 years old). Subjects stood with eyes closed on a force-platform fixed to a floor oscillator. We conducted five trials of 1-minute oscillation (0.5 Hz frequency, 2.5 cm amplitude) in the anteroposterior direction. Postural steadiness was quantified as the mean speed of the center of pressure in the anteroposterior direction (CoPy). In young adults, CoPy speed decreased rapidly until the third trial for both sexes. Adaptability was evaluated by changes in steadiness. The adaptability of children was categorized as "good," "moderate," and "poor," compared with a standard variation of the mean CoPy speed regression line between the first and fifth trials in young adults. Results were as follows: (1) anticipatory postural control adaptability starts to develop from age 6 in boys and 5 in girls, and greatly improves at age 7-8 in boys and 6 in girls; (2) the adaptability of children at age 11-12 (74% of boys and 63% of girls were categorized as "good") has not yet reached the same level as for young adults; (3) the adaptability at age 11-12 for girls is temporarily disturbed due to early puberty.
Different types of bursting calcium oscillations in non-excitable cells
International Nuclear Information System (INIS)
Perc, Matjaz; Marhl, Marko
2003-01-01
In the paper different types of bursting Ca 2+ oscillations are presented. We analyse bursting behaviour in four recent mathematical models for Ca 2+ oscillations in non-excitable cells. Separately, regular, quasi-periodic, and chaotic bursting Ca 2+ oscillations are classified into several subtypes. The classification is based on the dynamics of separated fast and slow subsystems, the so-called fast-slow burster analysis. For regular bursting Ca 2+ oscillations two types of bursting are specified: Point-Point and Point-Cycle bursting. In particular, the slow passage effect, important for the Hopf-Hopf and SubHopf-SubHopf bursting subtypes, is explained by local divergence calculated for the fast subsystem. Quasi-periodic bursting Ca 2+ oscillations can be found in only one of the four studied mathematical models and appear via a homoclinic bifurcation with a homoclinic torus structure. For chaotic bursting Ca 2+ oscillations, we found that bursting patterns resulting from the period doubling root to chaos considerably differ from those appearing via intermittency and have to be treated separately. The analysis and classification of different types of bursting Ca 2+ oscillations provides better insight into mechanisms of complex intra- and intercellular Ca 2+ signalling. This improves our understanding of several important biological phenomena in cellular signalling like complex frequency-amplitude signal encoding and synchronisation of intercellular signal transduction between coupled cells in tissue
International Nuclear Information System (INIS)
Hsu, Tzu-Fang; Jao, Kuan-Hsuan; Hung, Yao-Chen
2014-01-01
Phase synchronization (PS) in a periodically pump-modulated two-mode solid state laser is investigated. Although PS in the laser system has been demonstrated in response to a periodic modulation with the main relaxation oscillation (RO) frequency of the free-running laser, little is known about the case of modulation with minor RO frequencies. In this Letter, the empirical mode decomposition (EMD) method is utilized to decompose the laser time series into a set of orthogonal modes and to examine the intrinsic PS near the frequency of the second RO. The degree of PS is quantified by means of a histogram of phase differences and the analysis of Shannon entropy. - Highlights: • We study the intrinsic phase synchronization in a periodically pump-modulated two-mode solid state laser. • The empirical mode decomposition method is utilized to define the intrinsic phase synchronization. • The degree of phase synchronization is quantified by a proposed synchronization coefficient
Solvable model for chimera states of coupled oscillators.
Abrams, Daniel M; Mirollo, Rennie; Strogatz, Steven H; Wiley, Daniel A
2008-08-22
Networks of identical, symmetrically coupled oscillators can spontaneously split into synchronized and desynchronized subpopulations. Such chimera states were discovered in 2002, but are not well understood theoretically. Here we obtain the first exact results about the stability, dynamics, and bifurcations of chimera states by analyzing a minimal model consisting of two interacting populations of oscillators. Along with a completely synchronous state, the system displays stable chimeras, breathing chimeras, and saddle-node, Hopf, and homoclinic bifurcations of chimeras.
International Nuclear Information System (INIS)
Qu, J. L.; Lu, F. J.; Lu, Y.; Song, L. M.; Zhang, S.; Wang, J. M.; Ding, G. Q.
2010-01-01
We present a study of the centroid frequencies and phase lags of quasi-periodic oscillations (QPOs) as functions of photon energy for GRS 1915+105. It is found that the centroid frequencies of the 0.5-10 Hz QPOs and their phase lags are both energy dependent, and there exists an anticorrelation between the QPO frequency and phase lag. These new results challenge the popular QPO models, because none of them can fully explain the observed properties. We suggest that the observed QPO phase lags are partially due to the variation of the QPO frequency with energy, especially for those with frequency higher than 3.5 Hz.
Hailong, Zhang; Enrong, Wang; Fuhong, Min; Ning, Zhang
2016-03-01
The magneto-rheological damper (MRD) is a promising device used in vehicle semi-active suspension systems, for its continuous adjustable damping output. However, the innate nonlinear hysteresis characteristic of MRD may cause the nonlinear behaviors. In this work, a two-degree-of-freedom (2-DOF) MR suspension system was established first, by employing the modified Bouc-Wen force-velocity (F-v) hysteretic model. The nonlinear dynamic response of the system was investigated under the external excitation of single-frequency harmonic and bandwidth-limited stochastic road surface. The largest Lyapunov exponent (LLE) was used to detect the chaotic area of the frequency and amplitude of harmonic excitation, and the bifurcation diagrams, time histories, phase portraits, and power spectrum density (PSD) diagrams were used to reveal the dynamic evolution process in detail. Moreover, the LLE and Kolmogorov entropy (K entropy) were used to identify whether the system response was random or chaotic under stochastic road surface. The results demonstrated that the complex dynamical behaviors occur under different external excitation conditions. The oscillating mechanism of alternating periodic oscillations, quasi-periodic oscillations, and chaotic oscillations was observed in detail. The chaotic regions revealed that chaotic motions may appear in conditions of mid-low frequency and large amplitude, as well as small amplitude and all frequency. The obtained parameter regions where the chaotic motions may appear are useful for design of structural parameters of the vibration isolation, and the optimization of control strategy for MR suspension system. Projects supported by the National Natural Science Foundation of China (Grant Nos. 51475246, 51277098, and 51075215), the Research Innovation Program for College Graduates of Jiangsu Province China (Grant No. KYLX15 0725), and the Natural Science Foundation of Jiangsu Province of China (Grant No. BK20131402).
Bifurcation in asymmetric plasma divided by a magnetic filter
International Nuclear Information System (INIS)
Ohi, K.; Naitou, H.; Tauchi, Y.; Fukumasa, O.
2001-05-01
A magnetic filter (MF) reflecting electrons from both sides can separate a low-temperature and low-density subplasma from a high-temperature and high-density main plasma. The one-dimensional numerical simulation by the particle-in-cell code revealed that, depending on the asymmetry, the plasma divided by the MF behaves dynamically or statically [K. Ohi et al., Physics of Plasmas 8, 23 (2001)]. The transition between the two bifurcated states is discontinuous. In the dynamic state, the autonomous potential oscillation in the subplasma is synchronized with the passage of the shock wave structure generated by the modulated ion beam from the main plasma. The stationary phase of the dynamic state appears after the amplitude of the potential oscillation in the subplasma grows exponentially from the thermal noise. In the static state, the system is stable to the growth of the potential oscillation in the subplasma. (author)
International Nuclear Information System (INIS)
Yamapi, R.; Moukam Kakmeni, F.M.; Aziz-Alaoui, M.A.
2005-07-01
We consider in this paper the dynamics of the self-sustained electromechanical system with multiple functions, consisting of an electrical Rayleigh-Duffing oscillator, magnetically coupled with linear mechanical oscillators. The averaging and the balance harmonic method are used to and the amplitudes of the oscillatory states respectively in the autonomous and non-autonomous cases, and analyze the condition in which the quenching of self-sustained oscillations appears. The effects of the number of linear mechanical oscillators on the behavior of the model are discussed. Various bifurcation structures, the stability chart and the variation of the Lyapunov exponent are obtained, using numerical simulations of the equations of motion. (author)
Delay-induced stochastic bifurcations in a bistable system under white noise
International Nuclear Information System (INIS)
Sun, Zhongkui; Fu, Jin; Xu, Wei; Xiao, Yuzhu
2015-01-01
In this paper, the effects of noise and time delay on stochastic bifurcations are investigated theoretically and numerically in a time-delayed Duffing-Van der Pol oscillator subjected to white noise. Due to the time delay, the random response is not Markovian. Thereby, approximate methods have been adopted to obtain the Fokker-Planck-Kolmogorov equation and the stationary probability density function for amplitude of the response. Based on the knowledge that stochastic bifurcation is characterized by the qualitative properties of the steady-state probability distribution, it is found that time delay and feedback intensity as well as noise intensity will induce the appearance of stochastic P-bifurcation. Besides, results demonstrated that the effects of the strength of the delayed displacement feedback on stochastic bifurcation are accompanied by the sensitive dependence on time delay. Furthermore, the results from numerical simulations best confirm the effectiveness of the theoretical analyses
Delay-induced stochastic bifurcations in a bistable system under white noise
Energy Technology Data Exchange (ETDEWEB)
Sun, Zhongkui, E-mail: sunzk@nwpu.edu.cn; Fu, Jin; Xu, Wei [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China); Xiao, Yuzhu [Department of Mathematics and Information Science, Chang' an University, Xi' an 710086 (China)
2015-08-15
In this paper, the effects of noise and time delay on stochastic bifurcations are investigated theoretically and numerically in a time-delayed Duffing-Van der Pol oscillator subjected to white noise. Due to the time delay, the random response is not Markovian. Thereby, approximate methods have been adopted to obtain the Fokker-Planck-Kolmogorov equation and the stationary probability density function for amplitude of the response. Based on the knowledge that stochastic bifurcation is characterized by the qualitative properties of the steady-state probability distribution, it is found that time delay and feedback intensity as well as noise intensity will induce the appearance of stochastic P-bifurcation. Besides, results demonstrated that the effects of the strength of the delayed displacement feedback on stochastic bifurcation are accompanied by the sensitive dependence on time delay. Furthermore, the results from numerical simulations best confirm the effectiveness of the theoretical analyses.
Analysis of stability and Hopf bifurcation for a delayed logistic equation
International Nuclear Information System (INIS)
Sun Chengjun; Han Maoan; Lin Yiping
2007-01-01
The dynamics of a logistic equation with discrete delay are investigated, together with the local and global stability of the equilibria. In particular, the conditions under which a sequence of Hopf bifurcations occur at the positive equilibrium are obtained. Explicit algorithm for determining the stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation are derived by using the theory of normal form and center manifold [Hassard B, Kazarino D, Wan Y. Theory and applications of Hopf bifurcation. Cambridge: Cambridge University Press; 1981.]. Global existence of periodic solutions is also established by using a global Hopf bifurcation result of Wu [Symmetric functional differential equations and neural networks with memory. Trans Amer Math Soc 350:1998;4799-38.
Bifurcation theory of ac electric arcing
International Nuclear Information System (INIS)
Christen, Thomas; Peinke, Emanuel
2012-01-01
The performance of alternating current (ac) electric arcing devices is related to arc extinction or its re-ignition at zero crossings of the current (so-called ‘current zero’, CZ). Theoretical investigations thus usually focus on the transient behaviour of arcs near CZ, e.g. by solving the modelling differential equations in the vicinity of CZ. This paper proposes as an alternative approach to investigate global mathematical properties of the underlying periodically driven dynamic system describing the electric circuit containing the arcing device. For instance, the uniqueness of the trivial solution associated with the insulating state indicates the extinction of any arc. The existence of non-trivial attractors (typically a time-periodic state) points to a re-ignition of certain arcs. The performance regions of arcing devices, such as circuit breakers and arc torches, can thus be identified with the regions of absence and existence, respectively, of non-trivial attractors. Most important for applications, the boundary of a performance region in the model parameter space is then associated with the bifurcation of the non-trivial attractors. The concept is illustrated for simple black-box arc models, such as the Mayr and the Cassie model, by calculating for various cases the performance boundaries associated with the bifurcation of ac arcs. (paper)
Secondary Channel Bifurcation Geometry: A Multi-dimensional Problem
Gaeuman, D.; Stewart, R. L.
2017-12-01
The construction of secondary channels (or side channels) is a popular strategy for increasing aquatic habitat complexity in managed rivers. Such channels, however, frequently experience aggradation that prevents surface water from entering the side channels near their bifurcation points during periods of relatively low discharge. This failure to maintain an uninterrupted surface water connection with the main channel can reduce the habitat value of side channels for fish species that prefer lotic conditions. Various factors have been proposed as potential controls on the fate of side channels, including water surface slope differences between the main and secondary channels, the presence of main channel secondary circulation, transverse bed slopes, and bifurcation angle. A quantitative assessment of more than 50 natural and constructed secondary channels in the Trinity River of northern California indicates that bifurcations can assume a variety of configurations that are formed by different processes and whose longevity is governed by different sets of factors. Moreover, factors such as bifurcation angle and water surface slope vary with discharge level and are continuously distributed in space, such that they must be viewed as a multi-dimensional field rather than a single-valued attribute that can be assigned to a particular bifurcation.
Global bifurcations in a piecewise-smooth Cournot duopoly game
International Nuclear Information System (INIS)
Tramontana, Fabio; Gardini, Laura; Puu, Toenu
2010-01-01
The object of the work is to perform the global analysis of the Cournot duopoly model with isoelastic demand function and unit costs, presented in Puu . The bifurcation of the unique Cournot fixed point is established, which is a resonant case of the Neimark-Sacker bifurcation. New properties associated with the introduction of horizontal branches are evidenced. These properties differ significantly when the constant value is zero or positive and small. The good behavior of the case with positive constant is proved, leading always to positive trajectories. Also when the Cournot fixed point is unstable, stable cycles of any period may exist.
Communication: Mode bifurcation of droplet motion under stationary laser irradiation
Energy Technology Data Exchange (ETDEWEB)
Takabatake, Fumi [Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502 (Japan); Department of Bioengineering and Robotics, Graduate School of Engineering, Tohoku University, Sendai, Miyagi 980-8579 (Japan); Yoshikawa, Kenichi [Faculty of Life and Medical Sciences, Doshisha University, Kyotanabe, Kyoto 610-0394 (Japan); Ichikawa, Masatoshi, E-mail: ichi@scphys.kyoto-u.ac.jp [Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502 (Japan)
2014-08-07
The self-propelled motion of a mm-sized oil droplet floating on water, induced by a local temperature gradient generated by CW laser irradiation is reported. The circular droplet exhibits two types of regular periodic motion, reciprocal and circular, around the laser spot under suitable laser power. With an increase in laser power, a mode bifurcation from rectilinear reciprocal motion to circular motion is caused. The essential aspects of this mode bifurcation are discussed in terms of spontaneous symmetry-breaking under temperature-induced interfacial instability, and are theoretically reproduced with simple coupled differential equations.
Bifurcation of steady tearing states
International Nuclear Information System (INIS)
Saramito, B.; Maschke, E.K.
1985-10-01
We apply the bifurcation theory for compact operators to the problem of the nonlinear solutions of the 3-dimensional incompressible visco-resistive MHD equations. For the plane plasma slab model we compute branches of nonlinear tearing modes, which are stationary for the range of parameters investigated up to now
Bifurcation of limit cycles for cubic reversible systems
Directory of Open Access Journals (Sweden)
Yi Shao
2014-04-01
Full Text Available This article is concerned with the bifurcation of limit cycles of a class of cubic reversible system having a center at the origin. We prove that this system has at least four limit cycles produced by the period annulus around the center under cubic perturbations
Hopf bifurcation and chaos in macroeconomic models with policy lag
International Nuclear Information System (INIS)
Liao Xiaofeng; Li Chuandong; Zhou Shangbo
2005-01-01
In this paper, we consider the macroeconomic models with policy lag, and study how lags in policy response affect the macroeconomic stability. The local stability of the nonzero equilibrium of this equation is investigated by analyzing the corresponding transcendental characteristic equation of its linearized equation. Some general stability criteria involving the policy lag and the system parameter are derived. By choosing the policy lag as a bifurcation parameter, the model is found to undergo a sequence of Hopf bifurcation. The direction and stability of the bifurcating periodic solutions are determined by using the normal form theory and the center manifold theorem. Moreover, we show that the government can stabilize the intrinsically unstable economy if the policy lag is sufficiently short, but the system become locally unstable when the policy lag is too long. We also find the chaotic behavior in some range of the policy lag
Directory of Open Access Journals (Sweden)
Yu-Xuan Fu
2018-02-01
Full Text Available The FitzHugh–Nagumo model is improved to consider the effect of the electromagnetic induction on single neuron. On the basis of investigating the Hopf bifurcation behavior of the improved model, stochastic resonance in the stochastic version is captured near the bifurcation point. It is revealed that a weak harmonic oscillation in the electromagnetic disturbance can be amplified through stochastic resonance, and it is the cooperative effect of random transition between the resting state and the large amplitude oscillating state that results in the resonant phenomenon. Using the noise dependence of the mean of interburst intervals, we essentially suggest a biologically feasible clue for detecting weak signal by means of neuron model with subcritical Hopf bifurcation. These observations should be helpful in understanding the influence of the magnetic field to neural electrical activity.
Nonlinear effects on Turing patterns: Time oscillations and chaos
Aragón, J. L.
2012-08-08
We show that a model reaction-diffusion system with two species in a monostable regime and over a large region of parameter space produces Turing patterns coexisting with a limit cycle which cannot be discerned from the linear analysis. As a consequence, the patterns oscillate in time. When varying a single parameter, a series of bifurcations leads to period doubling, quasiperiodic, and chaotic oscillations without modifying the underlying Turing pattern. A Ruelle-Takens-Newhouse route to chaos is identified. We also examine the Turing conditions for obtaining a diffusion-driven instability and show that the patterns obtained are not necessarily stationary for certain values of the diffusion coefficients. These results demonstrate the limitations of the linear analysis for reaction-diffusion systems. © 2012 American Physical Society.
Bistable Chimera Attractors on a Triangular Network of Oscillator Populations
DEFF Research Database (Denmark)
Martens, Erik Andreas
2010-01-01
. This triangular network is the simplest discretization of a continuous ring of oscillators. Yet it displays an unexpectedly different behavior: in contrast to the lone stable chimera observed in continuous rings of oscillators, we find that this system exhibits two coexisting stable chimeras. Both chimeras are......, as usual, born through a saddle-node bifurcation. As the coupling becomes increasingly local in nature they lose stability through a Hopf bifurcation, giving rise to breathing chimeras, which in turn get destroyed through a homoclinic bifurcation. Remarkably, one of the chimeras reemerges by a reversal...
Subharmonic Oscillations and Chaos in Dynamic Atomic Force Microscopy
Cantrell, John H.; Cantrell, Sean A.
2015-01-01
The increasing use of dynamic atomic force microscopy (d-AFM) for nanoscale materials characterization calls for a deeper understanding of the cantilever dynamics influencing scan stability, predictability, and image quality. Model development is critical to such understanding. Renormalization of the equations governing d- AFM provides a simple interpretation of cantilever dynamics as a single spring and mass system with frequency dependent cantilever stiffness and damping parameters. The renormalized model is sufficiently robust to predict the experimentally observed splitting of the free-space cantilever resonance into multiple resonances upon cantilever-sample contact. Central to the model is the representation of the cantilever sample interaction force as a polynomial expansion with coefficients F(sub ij) (i,j = 0, 1, 2) that account for the effective interaction stiffness parameter, the cantilever-to-sample energy transfer, and the amplitude of cantilever oscillation. Application of the Melnikov method to the model equation is shown to predict a homoclinic bifurcation of the Smale horseshoe type leading to a cascade of period doublings with increasing drive displacement amplitude culminating in chaos and loss of image quality. The threshold value of the drive displacement amplitude necessary to initiate subharmonic generation depends on the acoustic drive frequency, the effective damping coefficient, and the nonlinearity of the cantilever-sample interaction force. For parameter values leading to displacement amplitudes below threshold for homoclinic bifurcation other bifurcation scenarios can occur, some of which lead to chaos.
Bifurcation analysis of a product inhibition model of a continuous fermentation process
Energy Technology Data Exchange (ETDEWEB)
Lenbury, Y; Chiaranai, C
1987-03-01
A product inhibition model of a continuous fermentation process is considered. If the yield term is a variable function of ethanol concentration, oscillation in the cell and ethanol concentrations is shown to be a Hopf bifurcation in the underlying system of nonlinear, ordinary differential equations which comprises the model.
Bifurcation in a buoyant horizontal laminar jet
Arakeri, Jaywant H.; Das, Debopam; Srinivasan, J.
2000-06-01
The trajectory of a laminar buoyant jet discharged horizontally has been studied. The experimental observations were based on the injection of pure water into a brine solution. Under certain conditions the jet has been found to undergo bifurcation. The bifurcation of the jet occurs in a limited domain of Grashof number and Reynolds number. The regions in which the bifurcation occurs has been mapped in the Reynolds number Grashof number plane. There are three regions where bifurcation does not occur. The various mechanisms that prevent bifurcation have been proposed.
Farner, Snorre; Vergez, Christophe; Kergomard, Jean; Lizée, Aude
2006-03-01
The harmonic balance method (HBM) was originally developed for finding periodic solutions of electronical and mechanical systems under a periodic force, but has been adapted to self-sustained musical instruments. Unlike time-domain methods, this frequency-domain method does not capture transients and so is not adapted for sound synthesis. However, its independence of time makes it very useful for studying any periodic solution, whether stable or unstable, without care of particular initial conditions in time. A computer program for solving general problems involving nonlinearly coupled exciter and resonator, HARMBAL, has been developed based on the HBM. The method as well as convergence improvements and continuation facilities are thoroughly presented and discussed in the present paper. Applications of the method are demonstrated, especially on problems with severe difficulties of convergence: the Helmholtz motion (square signals) of single-reed instruments when no losses are taken into account, the reed being modeled as a simple spring.
Coupled slow and fast surface dynamics in an electrocatalytic oscillator: Model and simulations
International Nuclear Information System (INIS)
Nascimento, Melke A.; Nagao, Raphael; Eiswirth, Markus; Varela, Hamilton
2014-01-01
The co-existence of disparate time scales is pervasive in many systems. In particular for surface reactions, it has been shown that the long-term evolution of the core oscillator is decisively influenced by slow surface changes, such as progressing deactivation. Here we present an in-depth numerical investigation of the coupled slow and fast surface dynamics in an electrocatalytic oscillator. The model consists of four nonlinear coupled ordinary differential equations, investigated over a wide parameter range. Besides the conventional bifurcation analysis, the system was studied by means of high-resolution period and Lyapunov diagrams. It was observed that the bifurcation diagram changes considerably as the irreversible surface poisoning evolves, and the oscillatory region shrinks. The qualitative dynamics changes accordingly and the chaotic oscillations are dramatically suppressed. Nevertheless, periodic cascades are preserved in a confined region of the resistance vs. voltage diagram. Numerical results are compared to experiments published earlier and the latter reinterpreted. Finally, the comprehensive description of the time-evolution in the period and Lyapunov diagrams suggests further experimental studies correlating the evolution of the system's dynamics with changes of the catalyst structure
Stability and Hopf bifurcation in a simplified BAM neural network with two time delays.
Cao, Jinde; Xiao, Min
2007-03-01
Various local periodic solutions may represent different classes of storage patterns or memory patterns, and arise from the different equilibrium points of neural networks (NNs) by applying Hopf bifurcation technique. In this paper, a bidirectional associative memory NN with four neurons and multiple delays is considered. By applying the normal form theory and the center manifold theorem, analysis of its linear stability and Hopf bifurcation is performed. An algorithm is worked out for determining the direction and stability of the bifurcated periodic solutions. Numerical simulation results supporting the theoretical analysis are also given.
Bifurcation structures of a cobweb model with memory and competing technologies
Agliari, Anna; Naimzada, Ahmad; Pecora, Nicolò
2018-05-01
In this paper we study a simple model based on the cobweb demand-supply framework with costly innovators and free imitators. The evolutionary selection between technologies depends on a performance measure which is related to the degree of memory. The resulting dynamics is described by a two-dimensional map. The map has a fixed point which may lose stability either via supercritical Neimark-Sacker bifurcation or flip bifurcation and several multistability situations exist. We describe some sequences of global bifurcations involving attracting and repelling closed invariant curves. These bifurcations, characterized by the creation of homoclinic connections or homoclinic tangles, are described through several numerical simulations. Particular bifurcation phenomena are also observed when the parameters are selected inside a periodicity region.
C-type period-doubling transition in nephron autoregulation
DEFF Research Database (Denmark)
Laugesen, Jakob Lund; Mosekilde, Erik; Holstein-Rathlou, Niels-Henrik
2011-01-01
The functional units of the kidney, called nephrons, utilize mechanisms that allow the individual nephron to regulate the incoming blood flow in response to fluctuations in the arterial pressure. This regulation tends to be unstable and to generate self-sustained oscillations, period-doubling bif......The functional units of the kidney, called nephrons, utilize mechanisms that allow the individual nephron to regulate the incoming blood flow in response to fluctuations in the arterial pressure. This regulation tends to be unstable and to generate self-sustained oscillations, period......-doubling bifurcations, mode-locking and other nonlinear dynamic phenomena in the tubular pressures and flows. Using a simplified nephron model, the paper examines how the regulatory mechanisms react to an external periodic variation in arterial pressure near a region of resonance with one of the internally generated...
Bifurcation and complex dynamics of a discrete-time predator-prey system involving group defense
Directory of Open Access Journals (Sweden)
S. M. Sohel Rana
2015-09-01
Full Text Available In this paper, we investigate the dynamics of a discrete-time predator-prey system involving group defense. The existence and local stability of positive fixed point of the discrete dynamical system is analyzed algebraically. It is shown that the system undergoes a flip bifurcation and a Neimark-Sacker bifurcation in the interior of R+2 by using bifurcation theory. Numerical simulation results not only show the consistence with the theoretical analysis but also display the new and interesting dynamical behaviors, including phase portraits, period-7, 20-orbits, attracting invariant circle, cascade of period-doubling bifurcation from period-20 leading to chaos, quasi-periodic orbits, and sudden disappearance of the chaotic dynamics and attracting chaotic set. The Lyapunov exponents are numerically computed to characterize the complexity of the dynamical behaviors.
Bifurcation routes and economic stability
Czech Academy of Sciences Publication Activity Database
Vošvrda, Miloslav
2001-01-01
Roč. 8, č. 14 (2001), s. 43-59 ISSN 1212-074X R&D Projects: GA ČR GA402/00/0439; GA ČR GA402/01/0034; GA ČR GA402/01/0539 Institutional research plan: AV0Z1075907 Keywords : macroeconomic stability * foreign investment phenomenon * the Hopf bifurcation Subject RIV: AH - Economics
Regular and irregular patterns of self-localized excitation in arrays of coupled phase oscillators
Energy Technology Data Exchange (ETDEWEB)
Wolfrum, Matthias; Omel' chenko, Oleh E. [Weierstrass Institute, Mohrenstrasse 39, Berlin 10117 (Germany); Sieber, Jan [College of Engineering, Mathematics and Physical Sciences, University of Exeter, North Park Road, Exeter EX4 4QF (United Kingdom)
2015-05-15
We study a system of phase oscillators with nonlocal coupling in a ring that supports self-organized patterns of coherence and incoherence, called chimera states. Introducing a global feedback loop, connecting the phase lag to the order parameter, we can observe chimera states also for systems with a small number of oscillators. Numerical simulations show a huge variety of regular and irregular patterns composed of localized phase slipping events of single oscillators. Using methods of classical finite dimensional chaos and bifurcation theory, we can identify the emergence of chaotic chimera states as a result of transitions to chaos via period doubling cascades, torus breakup, and intermittency. We can explain the observed phenomena by a mechanism of self-modulated excitability in a discrete excitable medium.
Evans, Jennifer A; Elliott, Jeffrey A; Gorman, Michael R
2011-07-01
The endogenous circadian pacemaker of mammals is synchronized to the environmental day by the ambient cycle of relative light and dark. The present studies assessed the actions of light in a novel circadian entrainment paradigm where activity rhythms are bifurcated following exposure to a 24-h light:dark:light:dark (LDLD) cycle. Bifurcated entrainment under LDLD reflects the temporal dissociation of component oscillators that comprise the circadian system and is facilitated when daily scotophases are dimly lit rather than completely dark. Although bifurcation can be stably maintained in LDLD, it is quickly reversed under constant conditions. Here the authors examine whether dim scotophase illumination acts to maintain bifurcated entrainment under LDLD through potential interactions with the parametric actions of bright light during the two daily photophases. In three experiments, wheel-running rhythms of Syrian hamsters were bifurcated under LDLD with dimly lit scotophases, and after several weeks, dim scotophase illumination was either retained or extinguished. Additionally, "full" and "skeleton" photophases were employed under LDLD cycles with dimly lit or completely dark scotophases to distinguish parametric from nonparametric effects of bright light. Rhythm bifurcation was more stable in full versus skeleton LDLD cycles. Dim light facilitated the maintenance of bifurcated entrainment under full LDLD cycles but did not prevent the loss of rhythm bifurcation in skeleton LDLD cycles. These studies indicate that parametric actions of bright light maintain the bifurcated entrainment state; that dim scotophase illumination increases the stability of the bifurcated state; and that dim light interacts with the parametric effects of bright light to increase the stability of rhythm bifurcation under full LDLD cycles. A further understanding of the novel actions of dim light may lead to new strategies for understanding, preventing, and treating chronobiological
Bifurcation analysis on a delayed SIS epidemic model with stage structure
Directory of Open Access Journals (Sweden)
Kejun Zhuang
2007-05-01
Full Text Available In this paper, a delayed SIS (Susceptible Infectious Susceptible model with stage structure is investigated. We study the Hopf bifurcations and stability of the model. Applying the normal form theory and the center manifold argument, we derive the explicit formulas determining the properties of the bifurcating periodic solutions. The conditions to guarantee the global existence of periodic solutions are established. Also some numerical simulations for supporting the theoretical are given.
Kügler, Philipp; Bulelzai, M A K; Erhardt, André H
2017-04-04
Early afterdepolarizations (EADs) are pathological voltage oscillations during the repolarization phase of cardiac action potentials (APs). EADs are caused by drugs, oxidative stress or ion channel disease, and they are considered as potential precursors to cardiac arrhythmias in recent attempts to redefine the cardiac drug safety paradigm. The irregular behaviour of EADs observed in experiments has been previously attributed to chaotic EAD dynamics under periodic pacing, made possible by a homoclinic bifurcation in the fast subsystem of the deterministic AP system of differential equations. In this article we demonstrate that a homoclinic bifurcation in the fast subsystem of the action potential model is neither a necessary nor a sufficient condition for the genesis of chaotic EADs. We rather argue that a cascade of period doubling (PD) bifurcations of limit cycles in the full AP system paves the way to chaotic EAD dynamics across a variety of models including a) periodically paced and spontaneously active cardiomyocytes, b) periodically paced and non-active cardiomyocytes as well as c) unpaced and spontaneously active cardiomyocytes. Furthermore, our bifurcation analysis reveals that chaotic EAD dynamics may coexist in a stable manner with fully regular AP dynamics, where only the initial conditions decide which type of dynamics is displayed. EADs are a potential source of cardiac arrhythmias and hence are of relevance both from the viewpoint of drug cardiotoxicity testing and the treatment of cardiomyopathies. The model-independent association of chaotic EADs with period doubling cascades of limit cycles introduced in this article opens novel opportunities to study chaotic EADs by means of bifurcation control theory and inverse bifurcation analysis. Furthermore, our results may shed new light on the synchronization and propagation of chaotic EADs in homogeneous and heterogeneous multicellular and cardiac tissue preparations.
Modelling, singular perturbation and bifurcation analyses of bitrophic food chains.
Kooi, B W; Poggiale, J C
2018-04-20
Two predator-prey model formulations are studied: for the classical Rosenzweig-MacArthur (RM) model and the Mass Balance (MB) chemostat model. When the growth and loss rate of the predator is much smaller than that of the prey these models are slow-fast systems leading mathematically to singular perturbation problem. In contradiction to the RM-model, the resource for the prey are modelled explicitly in the MB-model but this comes with additional parameters. These parameter values are chosen such that the two models become easy to compare. In both models a transcritical bifurcation, a threshold above which invasion of predator into prey-only system occurs, and the Hopf bifurcation where the interior equilibrium becomes unstable leading to a stable limit cycle. The fast-slow limit cycles are called relaxation oscillations which for increasing differences in time scales leads to the well known degenerated trajectories being concatenations of slow parts of the trajectory and fast parts of the trajectory. In the fast-slow version of the RM-model a canard explosion of the stable limit cycles occurs in the oscillatory region of the parameter space. To our knowledge this type of dynamics has not been observed for the RM-model and not even for more complex ecosystem models. When a bifurcation parameter crosses the Hopf bifurcation point the amplitude of the emerging stable limit cycles increases. However, depending of the perturbation parameter the shape of this limit cycle changes abruptly from one consisting of two concatenated slow and fast episodes with small amplitude of the limit cycle, to a shape with large amplitude of which the shape is similar to the relaxation oscillation, the well known degenerated phase trajectories consisting of four episodes (concatenation of two slow and two fast). The canard explosion point is accurately predicted by using an extended asymptotic expansion technique in the perturbation and bifurcation parameter simultaneously where the small
International Nuclear Information System (INIS)
Yoshimura, H.
1979-01-01
A new dynamical model of the solar cycle has predicted that the cycle should have a hysteretic nature: the behavior of each 11 year cycle should depend on previous cycles. In the light of this new understanding of the dynamical mechanism of the solar cycle, Waldmeier's (hypothetical) law was examined as a yet unexplained characteristic of the cycle by studying the observed sunspot frequency curve. Contrary to this hypothetical law, however, it was found that sunspot cycle curves did not form a single-parameter family characterized by the maximum amplitude of the cycle. The evolutionary trajectories in period-amplitude phase space verified the hysteretic nature of the observed cycle and revealed long-term (55 year instead of the previously claimed 80 year) periodic modulations, called here 55 year grand cycles. Each 55 year grand cycle forms a loop in the phase space, and the characteristics of each 11 year cycle depend on its position in the ascending or descending phase of the grand cycle. This new law was analyzed by the nonlinear multiple-period dynamo oscillation model which has predicted the hysteretic nature. The era from cycle 11 to cycle 15 turned out to be an anomalous one characterized by alternating amplitudes for odd and even cycles. Cycles 16--20 seem to constitute one grand cycle. If this is true, cycle 21 would be the beginning of another grand maximum and the model predicts that its duration would be short
Synchronization and basin bifurcations in mutually coupled oscillators
Indian Academy of Sciences (India)
its motivation from its role in understanding the basic features of coupled nonlinear systems and in view of potential applications in communication systems, time ..... [21] U E Vincent, A N Njah, O Akinlade and A R T Solarin, Physica A360, 186 (2006). [22] U E Vincent, A N Njah, O Akinlade and A R T Solarin, Chaos 14, 1018 ...
On the New Scenario of Annihilation of the Cross-Well Chaotic Attractor in a Nonlinear Oscillator
International Nuclear Information System (INIS)
Szemplinska, W.; Zubrzycki, A.; Tyrkiel, E.
1999-01-01
The twin-well potential Duffing oscillator is considered and the investigations are focused on a new scenario of destruction of the cross-well chaotic attractor. The new phenomenon belongs to the category of subduction bifurcation and consists in replacement of the cross-well chaotic attractor by a pair of unsymmetric 2T-periodic attractors. It is shown that the new scenario forms a transition zone in the system control parameter plane, the zone, which separates the two known scenarios of annihilation of the cross-well chaotic attractor: the boundary crisis, and the subduction in which the two single-well T-periodic attractors are born in a saddle-node bifurcation. (author)
Equilibrium-torus bifurcation in nonsmooth systems
DEFF Research Database (Denmark)
Zhusubahyev, Z.T.; Mosekilde, Erik
2008-01-01
Considering a set of two coupled nonautonomous differential equations with discontinuous right-hand sides describing the behavior of a DC/DC power converter, we discuss a border-collision bifurcation that can lead to the birth of a two-dimensional invariant torus from a stable node equilibrium...... point. We obtain the chart of dynamic modes and show that there is a region of parameter space in which the system has a single stable node equilibrium point. Under variation of the parameters, this equilibrium may disappear as it collides with a discontinuity boundary between two smooth regions...... in the phase space. The disappearance of the equilibrium point is accompanied by the soft appearance of an unstable focus period-1 orbit surrounded by a resonant or ergodic torus. Detailed numerical calculations are supported by a theoretical investigation of the normal form map that represents the piecewise...
Nonlinear dynamics approach of modeling the bifurcation for aircraft wing flutter in transonic speed
DEFF Research Database (Denmark)
Matsushita, Hiroshi; Miyata, T.; Christiansen, Lasse Engbo
2002-01-01
The procedure of obtaining the two-degrees-of-freedom, finite dimensional. nonlinear mathematical model. which models the nonlinear features of aircraft flutter in transonic speed is reported. The model enables to explain every feature of the transonic flutter data of the wind tunnel tests...... conducted at National Aerospace Laboratory in Japan for a high aspect ratio wing. It explains the nonlinear features of the transonic flutter such as the subcritical Hopf bifurcation of a limit cycle oscillation (LCO), a saddle-node bifurcation, and an unstable limit cycle as well as a normal (linear...
International Nuclear Information System (INIS)
Ding Xiaohua; Su Huan; Liu Mingzhu
2008-01-01
The paper analyzes a discrete second-order, nonlinear delay differential equation with negative feedback. The characteristic equation of linear stability is solved, as a function of two parameters describing the strength of the feedback and the damping in the autonomous system. The existence of local Hopf bifurcations is investigated, and the direction and stability of periodic solutions bifurcating from the Hopf bifurcation of the discrete model are determined by the Hopf bifurcation theory of discrete system. Finally, some numerical simulations are performed to illustrate the analytical results found
Multistability and gluing bifurcation to butterflies in coupled networks with non-monotonic feedback
International Nuclear Information System (INIS)
Ma Jianfu; Wu Jianhong
2009-01-01
Neural networks with a non-monotonic activation function have been proposed to increase their capacity for memory storage and retrieval, but there is still a lack of rigorous mathematical analysis and detailed discussions of the impact of time lag. Here we consider a two-neuron recurrent network. We first show how supercritical pitchfork bifurcations and a saddle-node bifurcation lead to the coexistence of multiple stable equilibria (multistability) in the instantaneous updating network. We then study the effect of time delay on the local stability of these equilibria and show that four equilibria lose their stability at a certain critical value of time delay, and Hopf bifurcations of these equilibria occur simultaneously, leading to multiple coexisting periodic orbits. We apply centre manifold theory and normal form theory to determine the direction of these Hopf bifurcations and the stability of bifurcated periodic orbits. Numerical simulations show very interesting global patterns of periodic solutions as the time delay is varied. In particular, we observe that these four periodic solutions are glued together along the stable and unstable manifolds of saddle points to develop a butterfly structure through a complicated process of gluing bifurcations of periodic solutions
Stability and Hopf Bifurcation for a Delayed SLBRS Computer Virus Model
Directory of Open Access Journals (Sweden)
Zizhen Zhang
2014-01-01
Full Text Available By incorporating the time delay due to the period that computers use antivirus software to clean the virus into the SLBRS model a delayed SLBRS computer virus model is proposed in this paper. The dynamical behaviors which include local stability and Hopf bifurcation are investigated by regarding the delay as bifurcating parameter. Specially, direction and stability of the Hopf bifurcation are derived by applying the normal form method and center manifold theory. Finally, an illustrative example is also presented to testify our analytical results.
Stability and Hopf bifurcation for a delayed SLBRS computer virus model.
Zhang, Zizhen; Yang, Huizhong
2014-01-01
By incorporating the time delay due to the period that computers use antivirus software to clean the virus into the SLBRS model a delayed SLBRS computer virus model is proposed in this paper. The dynamical behaviors which include local stability and Hopf bifurcation are investigated by regarding the delay as bifurcating parameter. Specially, direction and stability of the Hopf bifurcation are derived by applying the normal form method and center manifold theory. Finally, an illustrative example is also presented to testify our analytical results.
Directory of Open Access Journals (Sweden)
Yan-Ke Du
2013-09-01
Full Text Available We study a class of discrete-time bidirectional ring neural network model with delay. We discuss the asymptotic stability of the origin and the existence of Neimark-Sacker bifurcations, by analyzing the corresponding characteristic equation. Employing M-matrix theory and the Lyapunov functional method, global asymptotic stability of the origin is derived. Applying the normal form theory and the center manifold theorem, the direction of the Neimark-Sacker bifurcation and the stability of bifurcating periodic solutions are obtained. Numerical simulations are given to illustrate the main results.
Stability and Hopf bifurcation on a model for HIV infection of CD4{sup +} T cells with delay
Energy Technology Data Exchange (ETDEWEB)
Wang Xia [College of Mathematics and Information Science, Xinyang Normal University, Xinyang, Henan 464000 (China)], E-mail: xywangxia@163.com; Tao Youde [College of Mathematics and Information Science, Xinyang Normal University, Xinyang, Henan 464000 (China); Beijing Institute of Information Control, Beijing 100037 (China); Song Xinyu [College of Mathematics and Information Science, Xinyang Normal University, Xinyang, Henan 464000 (China) and Research Institute of Forest Resource Information Techniques, Chinese Academy of Forestry, Beijing 100091 (China)], E-mail: xysong88@163.com
2009-11-15
In this paper, a delayed differential equation model that describes HIV infection of CD4{sup +} T cells is considered. The stability of the positive equilibrium and the existence of Hopf bifurcation are investigated. In succession, using the normal form theory and center manifold argument, we derive the explicit formulas which determine the stability, direction and other properties of bifurcating periodic solutions.
Stability and Hopf Bifurcation in a Computer Virus Model with Multistate Antivirus
Directory of Open Access Journals (Sweden)
Tao Dong
2012-01-01
Full Text Available By considering that people may immunize their computers with countermeasures in susceptible state, exposed state and using anti-virus software may take a period of time, a computer virus model with time delay based on an SEIR model is proposed. We regard time delay as bifurcating parameter to study the dynamical behaviors which include local asymptotical stability and local Hopf bifurcation. By analyzing the associated characteristic equation, Hopf bifurcation occurs when time delay passes through a sequence of critical value. The linerized model and stability of the bifurcating periodic solutions are also derived by applying the normal form theory and the center manifold theorem. Finally, an illustrative example is also given to support the theoretical results.
Bifurcation and synchronization of synaptically coupled FHN models with time delay
International Nuclear Information System (INIS)
Wang Qingyun; Lu Qishao; Chen Guanrong; Feng Zhaosheng; Duan Lixia
2009-01-01
This paper presents an investigation of dynamics of the coupled nonidentical FHN models with synaptic connection, which can exhibit rich bifurcation behavior with variation of the coupling strength. With the time delay being introduced, the coupled neurons may display a transition from the original chaotic motions to periodic ones, which is accompanied by complex bifurcation scenario. At the same time, synchronization of the coupled neurons is studied in terms of their mean frequencies. We also find that the small time delay can induce new period windows with the coupling strength increasing. Moreover, it is found that synchronization of the coupled neurons can be achieved in some parameter ranges and related to their bifurcation transition. Bifurcation diagrams are obtained numerically or analytically from the mathematical model and the parameter regions of different behavior are clarified.
Bifurcation in the Lengyel–Epstein system for the coupled reactors with diffusion
Directory of Open Access Journals (Sweden)
Shaban Aly
2016-01-01
Full Text Available The main goal of this paper is to continue the investigations of the important system of Fengqi et al. (2008. The occurrence of Turing and Hopf bifurcations in small homogeneous arrays of two coupled reactors via diffusion-linked mass transfer which described by a system of ordinary differential equations is considered. I study the conditions of the existence as well as stability properties of the equilibrium solutions and derive the precise conditions on the parameters to show that the Hopf bifurcation occurs. Analytically I show that a diffusion driven instability occurs at a certain critical value, when the system undergoes a Turing bifurcation, patterns emerge. The spatially homogeneous equilibrium loses its stability and two new spatially non-constant stable equilibria emerge which are asymptotically stable. Numerically, at a certain critical value of diffusion the periodic solution gets destabilized and two new spatially nonconstant periodic solutions arise by Turing bifurcation.
Hopf bifurcation and chaos from torus breakdown in voltage-mode controlled DC drive systems
International Nuclear Information System (INIS)
Dai Dong; Ma Xikui; Zhang Bo; Tse, Chi K.
2009-01-01
Period-doubling bifurcation and its route to chaos have been thoroughly investigated in voltage-mode and current-mode controlled DC motor drives under simple proportional control. In this paper, the phenomena of Hopf bifurcation and chaos from torus breakdown in a voltage-mode controlled DC drive system is reported. It has been shown that Hopf bifurcation may occur when the DC drive system adopts a more practical proportional-integral control. The phenomena of period-adding and phase-locking are also observed after the Hopf bifurcation. Furthermore, it is shown that the stable torus can breakdown and chaos emerges afterwards. The work presented in this paper provides more complete information about the dynamical behaviors of DC drive systems.
The Design Space of the Embryonic Cell Cycle Oscillator.
Mattingly, Henry H; Sheintuch, Moshe; Shvartsman, Stanislav Y
2017-08-08
One of the main tasks in the analysis of models of biomolecular networks is to characterize the domain of the parameter space that corresponds to a specific behavior. Given the large number of parameters in most models, this is no trivial task. We use a model of the embryonic cell cycle to illustrate the approaches that can be used to characterize the domain of parameter space corresponding to limit cycle oscillations, a regime that coordinates periodic entry into and exit from mitosis. Our approach relies on geometric construction of bifurcation sets, numerical continuation, and random sampling of parameters. We delineate the multidimensional oscillatory domain and use it to quantify the robustness of periodic trajectories. Although some of our techniques explore the specific features of the chosen system, the general approach can be extended to other models of the cell cycle engine and other biomolecular networks. Copyright © 2017 Biophysical Society. Published by Elsevier Inc. All rights reserved.
Bifurcation and chaos of an axially accelerating viscoelastic beam
International Nuclear Information System (INIS)
Yang Xiaodong; Chen Liqun
2005-01-01
This paper investigates bifurcation and chaos of an axially accelerating viscoelastic beam. The Kelvin-Voigt model is adopted to constitute the material of the beam. Lagrangian strain is used to account for the beam's geometric nonlinearity. The nonlinear partial-differential equation governing transverse motion of the beam is derived from the Newton second law. The Galerkin method is applied to truncate the governing equation into a set of ordinary differential equations. By use of the Poincare map, the dynamical behavior is identified based on the numerical solutions of the ordinary differential equations. The bifurcation diagrams are presented in the case that the mean axial speed, the amplitude of speed fluctuation and the dynamic viscoelasticity is respectively varied while other parameters are fixed. The Lyapunov exponent is calculated to identify chaos. From numerical simulations, it is indicated that the periodic, quasi-periodic and chaotic motions occur in the transverse vibrations of the axially accelerating viscoelastic beam
A bifurcation analysis for the Lugiato-Lefever equation
Godey, Cyril
2017-05-01
The Lugiato-Lefever equation is a cubic nonlinear Schrödinger equation, including damping, detuning and driving, which arises as a model in nonlinear optics. We study the existence of stationary waves which are found as solutions of a four-dimensional reversible dynamical system in which the evolutionary variable is the space variable. Relying upon tools from bifurcation theory and normal forms theory, we discuss the codimension 1 bifurcations. We prove the existence of various types of steady solutions, including spatially localized, periodic, or quasi-periodic solutions. Contribution to the Topical Issue: "Theory and Applications of the Lugiato-Lefever Equation", edited by Yanne K. Chembo, Damia Gomila, Mustapha Tlidi, Curtis R. Menyuk.
Effect of state-dependent delay on a weakly damped nonlinear oscillator.
Mitchell, Jonathan L; Carr, Thomas W
2011-04-01
We consider a weakly damped nonlinear oscillator with state-dependent delay, which has applications in models for lasers, epidemics, and microparasites. More generally, the delay-differential equations considered are a predator-prey system where the delayed term is linear and represents the proliferation of the predator. We determine the critical value of the delay that causes the steady state to become unstable to periodic oscillations via a Hopf bifurcation. Using asymptotic averaging, we determine how the system's behavior is influenced by the functional form of the state-dependent delay. Specifically, we determine whether the branch of periodic solutions will be either sub- or supercritical as well as an accurate estimation of the amplitude. Finally, we choose a few examples of state-dependent delay to test our analytical results by comparing them to numerical continuation.
Application of the bifurcation method to the modified Boussinesq equation
Directory of Open Access Journals (Sweden)
Shaoyong Li
2014-08-01
Firstly, we give a property of the solutions of the equation, that is, if $1+u(x, t$ is a solution, so is $1-u(x, t$. Secondly, by using the bifurcation method of dynamical systems we obtain some explicit expressions of solutions for the equation, which include kink-shaped solutions, blow-up solutions, periodic blow-up solutions and solitary wave solutions. Some previous results are extended.
Bifurcations of optimal vector fields: an overview
Kiseleva, T.; Wagener, F.; Rodellar, J.; Reithmeier, E.
2009-01-01
We develop a bifurcation theory for the solution structure of infinite horizon optimal control problems with one state variable. It turns out that qualitative changes of this structure are connected to local and global bifurcations in the state-costate system. We apply the theory to investigate an
Evidence for bifurcation and universal chaotic behavior in nonlinear semiconducting devices
International Nuclear Information System (INIS)
Testa, J.; Perez, J.; Jeffries, C.
1982-01-01
Bifurcations, chaos, and extensive periodic windows in the chaotic regime are observed for a driven LRC circuit, the capacitive element being a nonlinear varactor diode. Measurements include power spectral analysis; real time amplitude data; phase portraits; and a bifurcation diagram, obtained by sampling methods. The effects of added external noise are studied. These data yield experimental determinations of several of the universal numbers predicted to characterize nonlinear systems having this route to chaos
Stability and Hopf bifurcation in a delayed competitive web sites model
International Nuclear Information System (INIS)
Xiao Min; Cao Jinde
2006-01-01
The delayed differential equations modeling competitive web sites, based on the Lotka-Volterra competition equations, are considered. Firstly, the linear stability is investigated. It is found that there is a stability switch for time delay, and Hopf bifurcation occurs when time delay crosses through a critical value. Then the direction and stability of the bifurcated periodic solutions are determined, using the normal form theory and the center manifold reduction. Finally, some numerical simulations are carried out to illustrate the results found
Voltage stability, bifurcation parameters and continuation methods
Energy Technology Data Exchange (ETDEWEB)
Alvarado, F L [Wisconsin Univ., Madison, WI (United States)
1994-12-31
This paper considers the importance of the choice of bifurcation parameter in the determination of the voltage stability limit and the maximum power load ability of a system. When the bifurcation parameter is power demand, the two limits are equivalent. However, when other types of load models and bifurcation parameters are considered, the two concepts differ. The continuation method is considered as a method for determination of voltage stability margins. Three variants of the continuation method are described: the continuation parameter is the bifurcation parameter the continuation parameter is initially the bifurcation parameter, but is free to change, and the continuation parameter is a new `arc length` parameter. Implementations of voltage stability software using continuation methods are described. (author) 23 refs., 9 figs.
Observation of bifurcation phenomena in an electron beam plasma system
International Nuclear Information System (INIS)
Hayashi, N.; Tanaka, M.; Shinohara, S.; Kawai, Y.
1995-01-01
When an electron beam is injected into a plasma, unstable waves are excited spontaneously near the electron plasma frequency f pe by the electron beam plasma instability. The experiment on subharmonics in an electron beam plasma system was performed with a glow discharge tube. The bifurcation of unstable waves with the electron plasma frequency f pe and 1/2 f pe was observed using a double-plasma device. Furthermore, the period doubling route to chaos around the ion plasma frequency in an electron beam plasma system was reported. However, the physical mechanism of bifurcation phenomena in an electron beam plasma system has not been clarified so far. We have studied nonlinear behaviors of the electron beam plasma instability. It was found that there are some cases: the fundamental unstable waves and subharmonics of 2 period are excited by the electron beam plasma instability, the fundamental unstable waves and subharmonics of 3 period are excited. In this paper, we measured the energy distribution functions of electrons and the dispersion relation of test waves in order to examine the physical mechanism of bifurcation phenomena in an electron beam plasma system
Reverse bifurcation and fractal of the compound logistic map
Wang, Xingyuan; Liang, Qingyong
2008-07-01
The nature of the fixed points of the compound logistic map is researched and the boundary equation of the first bifurcation of the map in the parameter space is given out. Using the quantitative criterion and rule of chaotic system, the paper reveal the general features of the compound logistic map transforming from regularity to chaos, the following conclusions are shown: (1) chaotic patterns of the map may emerge out of double-periodic bifurcation and (2) the chaotic crisis phenomena and the reverse bifurcation are found. At the same time, we analyze the orbit of critical point of the compound logistic map and put forward the definition of Mandelbrot-Julia set of compound logistic map. We generalize the Welstead and Cromer's periodic scanning technology and using this technology construct a series of Mandelbrot-Julia sets of compound logistic map. We investigate the symmetry of Mandelbrot-Julia set and study the topological inflexibility of distributing of period region in the Mandelbrot set, and finds that Mandelbrot set contain abundant information of structure of Julia sets by founding the whole portray of Julia sets based on Mandelbrot set qualitatively.
Nonresonant Double Hopf Bifurcation in Toxic Phytoplankton-Zooplankton Model with Delay
Yuan, Rui; Jiang, Weihua; Wang, Yong
This paper investigates a toxic phytoplankton-zooplankton model with Michaelis-Menten type phytoplankton harvesting. The model has rich dynamical behaviors. It undergoes transcritical, saddle-node, fold, Hopf, fold-Hopf and double Hopf bifurcation, when the parameters change and go through some of the critical values, the dynamical properties of the system will change also, such as the stability, equilibrium points and the periodic orbit. We first study the stability of the equilibria, and analyze the critical conditions for the above bifurcations at each equilibrium. In addition, the stability and direction of local Hopf bifurcations, and the completion bifurcation set by calculating the universal unfoldings near the double Hopf bifurcation point are given by the normal form theory and center manifold theorem. We obtained that the stable coexistent equilibrium point and stable periodic orbit alternate regularly when the digestion time delay is within some finite value. That is, we derived the pattern for the occurrence, and disappearance of a stable periodic orbit. Furthermore, we calculated the approximation expression of the critical bifurcation curve using the digestion time delay and the harvesting rate as parameters, and determined a large range in terms of the harvesting rate for the phytoplankton and zooplankton to coexist in a long term.
Oscillations in stellar atmospheres
International Nuclear Information System (INIS)
Costa, A.; Ringuelet, A.E.; Fontenla, J.M.
1989-01-01
Atmospheric excitation and propagation of oscillations are analyzed for typical pulsating stars. The linear, plane-parallel approach for the pulsating atmosphere gives a local description of the phenomenon. From the local analysis of oscillations, the minimum frequencies are obtained for radially propagating waves. The comparison of the minimum frequencies obtained for a variety of stellar types is in good agreement with the observed periods of the oscillations. The role of the atmosphere in the globar stellar pulsations is thus emphasized. 7 refs
Seitz, F.; Kirschner, S.; Neubersch, D.
2012-12-01
Earth rotation has been monitored using space geodetic techniques since many decades. The geophysical interpretation of observed time series of Earth rotation parameters (ERP) polar motion and length-of-day is commonly based on numerical models that describe and balance variations of angular momentum in various subsystems of the Earth. Naturally, models are dependent on geometrical, rheological and physical parameters. Many of these are weakly determined from other models or observations. In our study we present an adaptive Kalman filter approach for the improvement of parameters of the dynamic Earth system model DyMEG which acts as a simulator of ERP. In particular we focus on the improvement of the pole tide Love number k2. In the frame of a sensitivity analysis k2 has been identified as one of the most crucial parameters of DyMEG since it directly influences the modeled Chandler oscillation. At the same time k2 is one of the most uncertain parameters in the model. Our simulations with DyMEG cover a period of 60 years after which a steady state of k2 is reached. The estimate for k2, accounting for the anelastic response of the Earth's mantle and the ocean, is 0.3531 + 0.0030i. We demonstrate that the application of the improved parameter k2 in DyMEG leads to significantly better results for polar motion than the original value taken from the Conventions of the International Earth Rotation and Reference Systems Service (IERS).
Energy Technology Data Exchange (ETDEWEB)
Homan, Jeroen; Remillard, Ronald A. [MIT Kavli Institute for Astrophysics and Space Research, 77 Massachusetts Avenue 37-582D, Cambridge, MA 02139 (United States); Fridriksson, Joel K., E-mail: jeroen@space.mit.edu [Anton Pannekoek Institute for Astronomy, University of Amsterdam, Postbus 94249, 1090 GE Amsterdam (Netherlands)
2015-10-10
We report on a detailed analysis of the so-called ∼1 Hz quasi-periodic oscillation (QPO) in the eclipsing and dipping neutron-star low-mass X-ray binary EXO 0748–676. This type of QPO has previously been shown to have a geometric origin. Our study focuses on the evolution of the QPO as the source moves through the color–color diagram in which it traces out an atoll-source-like track. The QPO frequency increases from ∼0.4 Hz in the hard state to ∼25 Hz as the source approaches the soft state. Combining power spectra based on QPO frequency reveals additional features that strongly resemble those seen in non-dipping/eclipsing atoll sources. We show that the low-frequency QPOs in atoll sources and the ∼1 Hz QPO in EXO 0748–676 follow similar relations with respect to the noise components in their power spectra. We conclude that the frequencies of both types of QPOs are likely set by (the same) precession of a misaligned inner accretion disk. For high-inclination systems like EXO 0748–676 this results in modulations of the neutron-star emission due to obscuration or scattering, while for lower-inclination systems the modulations likely arise from relativistic Doppler-boosting and light-bending effects.
de Avellar, Marcio G. B.
2017-06-01
The majority of attempts to explain the origin and phenomenology of the quasi-periodic oscillations (QPOs) detected in low-mass X-ray binaries invoke dynamical models, and it was just in recent years that renewed attention has been given on how radiative processes occurring in these extreme environments gives rise to the variability features observed in the X-ray light curves of these systems. The study of the dependence of the phase lags upon the energy and frequency of the QPOs is a step towards this end. The methodology we developed here allowed us to study for the first time these dependencies for all QPOs detected in the range of 1 to 1300 Hz in the low-mass X-ray binary 4U 1636-53 as the source changes its state during its cycle in the colour-colour diagram. Our results suggest that within the context of models of up-scattering Comptonization, the phase lags dependencies upon frequency and energy can be used to extract size scales and physical conditions of the medium that produces the lags.
International Nuclear Information System (INIS)
De Avellar, Marcio G B
2017-01-01
The majority of attempts to explain the origin and phenomenology of the quasi-periodic oscillations (QPOs) detected in low-mass X-ray binaries invoke dynamical models, and it was just in recent years that renewed attention has been given on how radiative processes occurring in these extreme environments gives rise to the variability features observed in the X-ray light curves of these systems. The study of the dependence of the phase lags upon the energy and frequency of the QPOs is a step towards this end. The methodology we developed here allowed us to study for the first time these dependencies for all QPOs detected in the range of 1 to 1300 Hz in the low-mass X-ray binary 4U 1636–53 as the source changes its state during its cycle in the colour-colour diagram. Our results suggest that within the context of models of up-scattering Comptonization, the phase lags dependencies upon frequency and energy can be used to extract size scales and physical conditions of the medium that produces the lags. (paper)
Forced phase-locked response of a nonlinear system with time delay after Hopf bifurcation
International Nuclear Information System (INIS)
Ji, J.C.; Hansen, Colin H.
2005-01-01
The trivial equilibrium of a nonlinear autonomous system with time delay may become unstable via a Hopf bifurcation of multiplicity two, as the time delay reaches a critical value. This loss of stability of the equilibrium is associated with two coincident pairs of complex conjugate eigenvalues crossing the imaginary axis. The resultant dynamic behaviour of the corresponding nonlinear non-autonomous system in the neighbourhood of the Hopf bifurcation is investigated based on the reduction of the infinite-dimensional problem to a four-dimensional centre manifold. As a result of the interaction between the Hopf bifurcating periodic solutions and the external periodic excitation, a primary resonance can occur in the forced response of the system when the forcing frequency is close to the Hopf bifurcating periodic frequency. The method of multiple scales is used to obtain four first-order ordinary differential equations that determine the amplitudes and phases of the phase-locked periodic solutions. The first-order approximations of the periodic solutions are found to be in excellent agreement with those obtained by direct numerical integration of the delay-differential equation. It is also found that the steady state solutions of the nonlinear non-autonomous system may lose their stability via either a pitchfork or Hopf bifurcation. It is shown that the primary resonance response may exhibit symmetric and asymmetric phase-locked periodic motions, quasi-periodic motions, chaotic motions, and coexistence of two stable motions
Nature's Autonomous Oscillators
Mayr, H. G.; Yee, J.-H.; Mayr, M.; Schnetzler, R.
2012-01-01
Nonlinearity is required to produce autonomous oscillations without external time dependent source, and an example is the pendulum clock. The escapement mechanism of the clock imparts an impulse for each swing direction, which keeps the pendulum oscillating at the resonance frequency. Among nature's observed autonomous oscillators, examples are the quasi-biennial oscillation and bimonthly oscillation of the Earth atmosphere, and the 22-year solar oscillation. The oscillations have been simulated in numerical models without external time dependent source, and in Section 2 we summarize the results. Specifically, we shall discuss the nonlinearities that are involved in generating the oscillations, and the processes that produce the periodicities. In biology, insects have flight muscles, which function autonomously with wing frequencies that far exceed the animals' neural capacity; Stretch-activation of muscle contraction is the mechanism that produces the high frequency oscillation of insect flight, discussed in Section 3. The same mechanism is also invoked to explain the functioning of the cardiac muscle. In Section 4, we present a tutorial review of the cardio-vascular system, heart anatomy, and muscle cell physiology, leading up to Starling's Law of the Heart, which supports our notion that the human heart is also a nonlinear oscillator. In Section 5, we offer a broad perspective of the tenuous links between the fluid dynamical oscillators and the human heart physiology.
Circle maps and the Devil's staircase in a periodically perturbed Oregonator
DEFF Research Database (Denmark)
Brøns, Morten; Gross, Peter; Bar-Eli, Kedma
1997-01-01
Markman and Bar-Eli has studied a periodically forced Oregonator numerically and found a parameter range with the following properties: (1) Only periodic solutions are found in frequency-locked steps, each with a certain pattern of large and small oscillations (2) Between any two steps there is a....... Using invariant manifold theory we argue that an invariant circle must indeed exist when, as in the present case, the unforced system is close to a saddle-loop bifurcation. Generalisations of the results are briefly discussed....
El-Nashar, Hassan F.
2017-06-01
We consider a system of three nonidentical coupled phase oscillators in a ring topology. We explore the conditions that must be satisfied in order to obtain the phases at the transition to a synchrony state. These conditions lead to the correct mathematical expressions of phases that aid to find a simple analytic formula for critical coupling when the oscillators transit to a synchronization state having a common frequency value. The finding of a simple expression for the critical coupling allows us to perform a linear stability analysis at the transition to the synchronization stage. The obtained analytic forms of the eigenvalues show that the three coupled phase oscillators with periodic boundary conditions transit to a synchrony state when a saddle-node bifurcation occurs.
Competition for synchronization in a phase oscillator system
Kazanovich, Yakov; Burylko, Oleksandr; Borisyuk, Roman
2013-10-01
A system of phase oscillators with a Central Oscillator (CO) and a set of n Peripheral Oscillators (POs) is considered. Feed-forward and feedback connections between the CO and POs are determined by two interaction functions which are assumed to be smooth, odd, and periodic. To describe the competition of POs for synchronization with the CO, we study the asymptotic stability of fixed points corresponding to in-phase synchronization of a group of k POs, while other POs are in anti-phase with the CO. It is shown that stability conditions can be formulated in terms of four parameters that describe the slopes of the interaction functions at zero and half-period points. Analytical description of stability in terms of the regions in 4-dimensional parameter space is given. Combining stability analysis with the detailed study of geometry of invariant manifolds, the bifurcations of fixed points are investigated. We show that various dynamical regimes such as multistability, heteroclinic orbits, and chaos are possible. Analytical stability conditions for global synchronization of POs with the CO are formulated for the systems with local connections between POs. It is shown that synchronization in a large system with local connections becomes unstable even under weak desynchronizing influence from the CO. The application of the results to modeling in neuroscience and, in particular, for modeling visual attention is discussed.
Kurin-Csörgei, Krisztina; Poros, Eszter; Csepiova, Julianna; Orbán, Miklós
2018-05-01
The coupling of acid-base type pH-dependent equilibria to pH-oscillators expanded significantly the number and type of species which can participate in oscillatory chemical processes. Here, we report a new version of oscillatory phenomena that can appear in coupled oscillators. Oscillations in the oxidation states of the center ion bound in a chelate complex were generated in a combined system, when the participants of the oscillator as dynamical unit and the components of the complex formation interacted with each other through redox reaction. It was demonstrated, when the BrO3- - SO32- pH-oscillator and the Co2+ - histidine complex were mixed in a continuous stirred tank reactor, periodic changes in the pH were accompanied with periodic transitions in the oxidation number of the cobalt ion between +2 and +3. The oscillatory build up and removal of the Co(III)-complex were followed by recording the light absorption at the wavelength characteristic for this species with simultaneous monitoring the pH-oscillations. The dual role of the SO32- ion in the explanation of this observation was pointed out. Its partial and consecutive total oxidations by BrO3- give rise to and maintain sustained pH-oscillations in the combined system and its presence induces the rapid conversion of the Co2+ to a highly inert Co(III)-histidine chelate when the system jumps to and remains in the high pH-state. The oscillatory cycle is completed when the Co(III)-complex is washed out from the reactor and the reagents are replenished by the flow during the time the system spends in the acidic range of pH. The idea, to couple a core oscillator to an equilibrium through a redox reaction that takes place between the constituents of the oscillator and the target species of the linked subsystem, may be generally used to bring about forced oscillations in many other combined chemical systems.
Bifurcation Analysis with Aerodynamic-Structure Uncertainties by the Nonintrusive PCE Method
Directory of Open Access Journals (Sweden)
Linpeng Wang
2017-01-01
Full Text Available An aeroelastic model for airfoil with a third-order stiffness in both pitch and plunge degree of freedom (DOF and the modified Leishman–Beddoes (LB model were built and validated. The nonintrusive polynomial chaos expansion (PCE based on tensor product is applied to quantify the uncertainty of aerodynamic and structure parameters on the aerodynamic force and aeroelastic behavior. The uncertain limit cycle oscillation (LCO and bifurcation are simulated in the time domain with the stochastic PCE method. Bifurcation diagrams with uncertainties were quantified. The Monte Carlo simulation (MCS is also applied for comparison. From the current work, it can be concluded that the nonintrusive polynomial chaos expansion can give an acceptable accuracy and have a much higher calculation efficiency than MCS. For aerodynamic model, uncertainties of aerodynamic parameters affect the aerodynamic force significantly at the stage from separation to stall at upstroke and at the stage from stall to reattach at return. For aeroelastic model, both uncertainties of aerodynamic parameters and structure parameters impact bifurcation position. Structure uncertainty of parameters is more sensitive for bifurcation. When the nonlinear stall flutter and bifurcation are concerned, more attention should be paid to the separation process of aerodynamics and parameters about pitch DOF in structure.
Local stability and Hopf bifurcation in small-world delayed networks
International Nuclear Information System (INIS)
Li Chunguang; Chen Guanrong
2004-01-01
The notion of small-world networks, recently introduced by Watts and Strogatz, has attracted increasing interest in studying the interesting properties of complex networks. Notice that, a signal or influence travelling on a small-world network often is associated with time-delay features, which are very common in biological and physical networks. Also, the interactions within nodes in a small-world network are often nonlinear. In this paper, we consider a small-world networks model with nonlinear interactions and time delays, which was recently considered by Yang. By choosing the nonlinear interaction strength as a bifurcation parameter, we prove that Hopf bifurcation occurs. We determine the stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation by applying the normal form theory and the center manifold theorem. Finally, we show a numerical example to verify the theoretical analysis
Local stability and Hopf bifurcation in small-world delayed networks
Energy Technology Data Exchange (ETDEWEB)
Li Chunguang E-mail: cgli@uestc.edu.cn; Chen Guanrong E-mail: gchen@ee.cityu.edu.hk
2004-04-01
The notion of small-world networks, recently introduced by Watts and Strogatz, has attracted increasing interest in studying the interesting properties of complex networks. Notice that, a signal or influence travelling on a small-world network often is associated with time-delay features, which are very common in biological and physical networks. Also, the interactions within nodes in a small-world network are often nonlinear. In this paper, we consider a small-world networks model with nonlinear interactions and time delays, which was recently considered by Yang. By choosing the nonlinear interaction strength as a bifurcation parameter, we prove that Hopf bifurcation occurs. We determine the stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation by applying the normal form theory and the center manifold theorem. Finally, we show a numerical example to verify the theoretical analysis.
Hopf bifurcation in a environmental defensive expenditures model with time delay
International Nuclear Information System (INIS)
Russu, Paolo
2009-01-01
In this paper a three-dimensional environmental defensive expenditures model with delay is considered. The model is based on the interactions among visitors V, quality of ecosystem goods E, and capital K, intended as accommodation and entertainment facilities, in Protected Areas (PAs). The tourism user fees (TUFs) are used partly as a defensive expenditure and partly to increase the capital stock. The stability and existence of Hopf bifurcation are investigated. It is that stability switches and Hopf bifurcation occurs when the delay t passes through a sequence of critical values, τ 0 . It has been that the introduction of a delay is a destabilizing process, in the sense that increasing the delay could cause the bio-economics to fluctuate. Formulas about the stability of bifurcating periodic solution and the direction of Hopf bifurcation are exhibited by applying the normal form theory and the center manifold theorem. Numerical simulations are given to illustrate the results.
Stability and Bifurcation Analysis of a Modified Epidemic Model for Computer Viruses
Directory of Open Access Journals (Sweden)
Chuandong Li
2014-01-01
Full Text Available We extend the three-dimensional SIR model to four-dimensional case and then analyze its dynamical behavior including stability and bifurcation. It is shown that the new model makes a significant improvement to the epidemic model for computer viruses, which is more reasonable than the most existing SIR models. Furthermore, we investigate the stability of the possible equilibrium point and the existence of the Hopf bifurcation with respect to the delay. By analyzing the associated characteristic equation, it is found that Hopf bifurcation occurs when the delay passes through a sequence of critical values. An analytical condition for determining the direction, stability, and other properties of bifurcating periodic solutions is obtained by using the normal form theory and center manifold argument. The obtained results may provide a theoretical foundation to understand the spread of computer viruses and then to minimize virus risks.
Stability and Hopf Bifurcation of a Reaction-Diffusion Neutral Neuron System with Time Delay
Dong, Tao; Xia, Linmao
2017-12-01
In this paper, a type of reaction-diffusion neutral neuron system with time delay under homogeneous Neumann boundary conditions is considered. By constructing a basis of phase space based on the eigenvectors of the corresponding Laplace operator, the characteristic equation of this system is obtained. Then, by selecting time delay and self-feedback strength as the bifurcating parameters respectively, the dynamic behaviors including local stability and Hopf bifurcation near the zero equilibrium point are investigated when the time delay and self-feedback strength vary. Furthermore, the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are obtained by using the normal form and the center manifold theorem for the corresponding partial differential equation. Finally, two simulation examples are given to verify the theory.
Beeftink, Martine M A; Spiering, Wilko; De Jong, Mark R; Doevendans, Pieter A; Blankestijn, Peter J; Elvan, Arif; Heeg, Jan-Evert; Bots, Michiel L; Voskuil, Michiel
2017-04-01
Renal denervation may be more effective if performed distal in the renal artery because of smaller distances between the lumen and perivascular nerves. The authors reviewed the angiographic results of 97 patients and compared blood pressure reduction in relation to the location of the denervation. No significant differences in blood pressure reduction or complications were found between patient groups divided according to their spatial distribution of the ablations (proximal to the bifurcation in both arteries, distal to the bifurcation in one artery and distal in the other artery, or distal to the bifurcation in both arteries), but systolic ambulatory blood pressure reduction was significantly related to the number of distal ablations. No differences in adverse events were observed. In conclusion, we found no reason to believe that renal denervation distal to the bifurcation poses additional risks over the currently advised approach of proximal denervation, but improved efficacy remains to be conclusively established. ©2017 Wiley Periodicals, Inc.
Stability and bifurcation in a simplified four-neuron BAM neural network with multiple delays
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available We first study the distribution of the zeros of a fourth-degree exponential polynomial. Then we apply the obtained results to a simplified bidirectional associated memory (BAM neural network with four neurons and multiple time delays. By taking the sum of the delays as the bifurcation parameter, it is shown that under certain assumptions the steady state is absolutely stable. Under another set of conditions, there are some critical values of the delay, when the delay crosses these critical values, the Hopf bifurcation occurs. Furthermore, some explicit formulae determining the stability and the direction of periodic solutions bifurcating from Hopf bifurcations are obtained by applying the normal form theory and center manifold reduction. Numerical simulations supporting the theoretical analysis are also included.
International Nuclear Information System (INIS)
Li, Jinhui; Teng, Zhidong; Wang, Guangqing; Zhang, Long; Hu, Cheng
2017-01-01
In this paper, we introduce the saturated treatment and logistic growth rate into an SIR epidemic model with bilinear incidence. The treatment function is assumed to be a continuously differential function which describes the effect of delayed treatment when the medical condition is limited and the number of infected individuals is large enough. Sufficient conditions for the existence and local stability of the disease-free and positive equilibria are established. And the existence of the stable limit cycles also is obtained. Moreover, by using the theory of bifurcations, it is shown that the model exhibits backward bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcations. Finally, the numerical examples are given to illustrate the theoretical results and obtain some additional interesting phenomena, involving double stable periodic solutions and stable limit cycles.
Recent perspective on coronary artery bifurcation interventions.
Dash, Debabrata
2014-01-01
Coronary bifurcation lesions are frequent in routine practice, accounting for 15-20% of all lesions undergoing percutaneous coronary intervention (PCI). PCI of this subset of lesions is technically challenging and historically has been associated with lower procedural success rates and worse clinical outcomes compared with non-bifurcation lesions. The introduction of drug-eluting stents has dramatically improved the outcomes. The provisional technique of implanting one stent in the main branch remains the default approach in most bifurcation lesions. Selection of the most effective technique for an individual bifurcation is important. The use of two-stent techniques as an intention to treat is an acceptable approach in some bifurcation lesions. However, a large amount of metal is generally left unapposed in the lumen with complex two-stent techniques, which is particularly concerning for the risk of stent thrombosis. New technology and dedicated bifurcation stents may overcome some of the limitations of two-stent techniques and revolutionise the management of bifurcation PCI in the future.
Limit cycles bifurcating from a perturbed quartic center
Energy Technology Data Exchange (ETDEWEB)
Coll, Bartomeu, E-mail: dmitcv0@ps.uib.ca [Dept. de Matematiques i Informatica, Universitat de les Illes Balears, Facultat de ciencies, 07071 Palma de Mallorca (Spain); Llibre, Jaume, E-mail: jllibre@mat.uab.ca [Dept. de Matematiques, Universitat Autonoma de Barcelona, Edifici Cc 08193 Bellaterra, Barcelona, Catalonia (Spain); Prohens, Rafel, E-mail: dmirps3@ps.uib.ca [Dept. de Matematiques i Informatica, Universitat de les Illes Balears, Facultat de ciencies, 07071 Palma de Mallorca (Spain)
2011-04-15
Highlights: We study polynomial perturbations of a quartic center. We get simultaneous upper and lower bounds for the bifurcating limit cycles. A higher lower bound for the maximum number of limit cycles is obtained. We obtain more limit cycles than the number obtained in the cubic case. - Abstract: We consider the quartic center x{sup .}=-yf(x,y),y{sup .}=xf(x,y), with f(x, y) = (x + a) (y + b) (x + c) and abc {ne} 0. Here we study the maximum number {sigma} of limit cycles which can bifurcate from the periodic orbits of this quartic center when we perturb it inside the class of polynomial vector fields of degree n, using the averaging theory of first order. We prove that 4[(n - 1)/2] + 4 {<=} {sigma} {<=} 5[(n - 1)/2] + 14, where [{eta}] denotes the integer part function of {eta}.
International Nuclear Information System (INIS)
Hajihosseini, Amirhossein; Maleki, Farzaneh; Rokni Lamooki, Gholam Reza
2011-01-01
Highlights: → We construct a recurrent neural network by generalizing a specific n-neuron network. → Several codimension 1 and 2 bifurcations take place in the newly constructed network. → The newly constructed network has higher capabilities to learn periodic signals. → The normal form theorem is applied to investigate dynamics of the network. → A series of bifurcation diagrams is given to support theoretical results. - Abstract: A class of recurrent neural networks is constructed by generalizing a specific class of n-neuron networks. It is shown that the newly constructed network experiences generic pitchfork and Hopf codimension one bifurcations. It is also proved that the emergence of generic Bogdanov-Takens, pitchfork-Hopf and Hopf-Hopf codimension two, and the degenerate Bogdanov-Takens bifurcation points in the parameter space is possible due to the intersections of codimension one bifurcation curves. The occurrence of bifurcations of higher codimensions significantly increases the capability of the newly constructed recurrent neural network to learn broader families of periodic signals.
Emergence of the bifurcation structure of a Langmuir–Blodgett transfer model
Köpf, Michael H
2014-10-07
© 2014 IOP Publishing Ltd & London Mathematical Society. We explore the bifurcation structure of a modified Cahn-Hilliard equation that describes a system that may undergo a first-order phase transition and is kept permanently out of equilibrium by a lateral driving. This forms a simple model, e.g., for the deposition of stripe patterns of different phases of surfactant molecules through Langmuir-Blodgett transfer. Employing continuation techniques the bifurcation structure is numerically investigated using the non-dimensional transfer velocity as the main control parameter. It is found that the snaking structure of steady front states is intertwined with a large number of branches of time-periodic solutions that emerge from Hopf or period-doubling bifurcations and end in global bifurcations (sniper and homoclinic). Overall the bifurcation diagram has a harp-like appearance. This is complemented by a two-parameter study in non-dimensional transfer velocity and domain size (as a measure of the distance to the phase transition threshold) that elucidates through which local and global codimension 2 bifurcations the entire harp-like structure emerges.
Barnett, William H; Cymbalyuk, Gennady S
2014-01-01
The dynamics of individual neurons are crucial for producing functional activity in neuronal networks. An open question is how temporal characteristics can be controlled in bursting activity and in transient neuronal responses to synaptic input. Bifurcation theory provides a framework to discover generic mechanisms addressing this question. We present a family of mechanisms organized around a global codimension-2 bifurcation. The cornerstone bifurcation is located at the intersection of the border between bursting and spiking and the border between bursting and silence. These borders correspond to the blue sky catastrophe bifurcation and the saddle-node bifurcation on an invariant circle (SNIC) curves, respectively. The cornerstone bifurcation satisfies the conditions for both the blue sky catastrophe and SNIC. The burst duration and interburst interval increase as the inverse of the square root of the difference between the corresponding bifurcation parameter and its bifurcation value. For a given set of burst duration and interburst interval, one can find the parameter values supporting these temporal characteristics. The cornerstone bifurcation also determines the responses of silent and spiking neurons. In a silent neuron with parameters close to the SNIC, a pulse of current triggers a single burst. In a spiking neuron with parameters close to the blue sky catastrophe, a pulse of current temporarily silences the neuron. These responses are stereotypical: the durations of the transient intervals-the duration of the burst and the duration of latency to spiking-are governed by the inverse-square-root laws. The mechanisms described here could be used to coordinate neuromuscular control in central pattern generators. As proof of principle, we construct small networks that control metachronal-wave motor pattern exhibited in locomotion. This pattern is determined by the phase relations of bursting neurons in a simple central pattern generator modeled by a chain of
Quantum entanglement and fixed-point bifurcations
International Nuclear Information System (INIS)
Hines, Andrew P.; McKenzie, Ross H.; Milburn, G.J.
2005-01-01
How does the classical phase-space structure for a composite system relate to the entanglement characteristics of the corresponding quantum system? We demonstrate how the entanglement in nonlinear bipartite systems can be associated with a fixed-point bifurcation in the classical dynamics. Using the example of coupled giant spins we show that when a fixed point undergoes a supercritical pitchfork bifurcation, the corresponding quantum state--the ground state--achieves its maximum amount of entanglement near the critical point. We conjecture that this will be a generic feature of systems whose classical limit exhibits such a bifurcation
A case study in bifurcation theory
Khmou, Youssef
This short paper is focused on the bifurcation theory found in map functions called evolution functions that are used in dynamical systems. The most well-known example of discrete iterative function is the logistic map that puts into evidence bifurcation and chaotic behavior of the topology of the logistic function. We propose a new iterative function based on Lorentizan function and its generalized versions, based on numerical study, it is found that the bifurcation of the Lorentzian function is of second-order where it is characterized by the absence of chaotic region.
Bifurcations of non-smooth systems
Angulo, Fabiola; Olivar, Gerard; Osorio, Gustavo A.; Escobar, Carlos M.; Ferreira, Jocirei D.; Redondo, Johan M.
2012-12-01
Non-smooth systems (namely piecewise-smooth systems) have received much attention in the last decade. Many contributions in this area show that theory and applications (to electronic circuits, mechanical systems, …) are relevant to problems in science and engineering. Specially, new bifurcations have been reported in the literature, and this was the topic of this minisymposium. Thus both bifurcation theory and its applications were included. Several contributions from different fields show that non-smooth bifurcations are a hot topic in research. Thus in this paper the reader can find contributions from electronics, energy markets and population dynamics. Also, a carefully-written specific algebraic software tool is presented.
Kato, Shoji
2016-01-01
This book presents the current state of research on disk oscillation theory, focusing on relativistic disks and tidally deformed disks. Since the launch of the Rossi X-ray Timing Explorer (RXTE) in 1996, many high-frequency quasiperiodic oscillations (HFQPOs) have been observed in X-ray binaries. Subsequently, similar quasi-periodic oscillations have been found in such relativistic objects as microquasars, ultra-luminous X-ray sources, and galactic nuclei. One of the most promising explanations of their origin is based on oscillations in relativistic disks, and a new field called discoseismology is currently developing. After reviewing observational aspects, the book presents the basic characteristics of disk oscillations, especially focusing on those in relativistic disks. Relativistic disks are essentially different from Newtonian disks in terms of several basic characteristics of their disk oscillations, including the radial distributions of epicyclic frequencies. In order to understand the basic processes...
Bifurcations and Chaos of AN Immersed Cantilever Beam in a Fluid and Carrying AN Intermediate Mass
AL-QAISIA, A. A.; HAMDAN, M. N.
2002-06-01
The concern of this work is the local stability and period-doubling bifurcations of the response to a transverse harmonic excitation of a slender cantilever beam partially immersed in a fluid and carrying an intermediate lumped mass. The unimodal form of the non-linear dynamic model describing the beam-mass in-plane large-amplitude flexural vibration, which accounts for axial inertia, non-linear curvature and inextensibility condition, developed in Al-Qaisia et al. (2000Shock and Vibration7 , 179-194), is analyzed and studied for the resonance responses of the first three modes of vibration, using two-term harmonic balance method. Then a consistent second order stability analysis of the associated linearized variational equation is carried out using approximate methods to predict the zones of symmetry breaking leading to period-doubling bifurcation and chaos on the resonance response curves. The results of the present work are verified for selected physical system parameters by numerical simulations using methods of the qualitative theory, and good agreement was obtained between the analytical and numerical results. Also, analytical prediction of the period-doubling bifurcation and chaos boundaries obtained using a period-doubling bifurcation criterion proposed in Al-Qaisia and Hamdan (2001 Journal of Sound and Vibration244, 453-479) are compared with those of computer simulations. In addition, results of the effect of fluid density, fluid depth, mass ratio, mass position and damping on the period-doubling bifurcation diagrams are studies and presented.
Pasham, Dheeraj R.; Strohmayer, Tod E.; Mushotzky, Richard F.
2013-01-01
We report the discovery with XMM-Newton of an approx.. = 7 mHz X-ray (0.3-10.0 keV) quasi-periodic oscillation (QPO) from the eclipsing, high-inclination black hole binary IC 10 X-1. The QPO is significant at >4.33 sigma confidence level and has a fractional amplitude (% rms) and a quality factor, Q is identical with nu/delta nu, of approx. = 11 and 4, respectively. The overall X-ray (0.3-10.0 keV) power spectrum in the frequency range 0.0001-0.1 Hz can be described by a power-law with an index of approx. = -2, and a QPO at 7 mHz. At frequencies approx. > 0.02 Hz there is no evidence for significant variability. The fractional amplitude (rms) of the QPO is roughly energy-independent in the energy range of 0.3-1.5 keV. Above 1.5 keV the low signal-to-noise ratio of the data does not allow us to detect the QPO. By directly comparing these properties with the wide range of QPOs currently known from accreting black hole and neutron stars, we suggest that the 7 mHz QPO of IC 10 X-1 may be linked to one of the following three categories of QPOs: (1) the "heartbeat" mHz QPOs of the black hole sources GRS 1915+105 and IGR J17091-3624, or (2) the 0.6-2.4 Hz "dipper QPOs" of high-inclination neutron star systems, or (3) the mHz QPOs of Cygnus X-3.
Modal bifurcation in a high-Tc superconducting levitation system
International Nuclear Information System (INIS)
Taguchi, D; Fujiwara, S; Sugiura, T
2011-01-01
This paper deals with modal bifurcation of a multi-degree-of-freedom high-T c superconducting levitation system. As modeling of large-scale high-T c superconducting levitation applications, where plural superconducting bulks are often used, it can be helpful to consider a system constituting of multiple oscillators magnetically coupled with each other. This paper investigates nonlinear dynamics of two permanent magnets levitated above high-T c superconducting bulks and placed between two fixed permanent magnets without contact. First, the nonlinear equations of motion of the levitated magnets were derived. Then the method of averaging was applied to them. It can be found from the obtained solutions that this nonlinear two degree-of-freedom system can have two asymmetric modes, in addition to a symmetric mode and an antisymmetric mode both of which also exist in the linearized system. One of the backbone curves in the frequency response shows a modal bifurcation where the two stable asymmetric modes mentioned above appear with destabilization of the antisymmetric mode, thus leading to modal localization. These analytical predictions have been confirmed in our numerical analysis and experiments of free vibration and forced vibration. These results, never predicted by linear analysis, can be important for application of high-T c superconducting levitation systems.
Noise transmission and delay-induced stochastic oscillations in biochemical network motifs
International Nuclear Information System (INIS)
Liu Sheng-Jun; Wang Qi; Liu Bo; Yan Shi-Wei; Sakata Fumihiko
2011-01-01
With the aid of stochastic delayed-feedback differential equations, we derive an analytic expression for the power spectra of reacting molecules included in a generic biological network motif that is incorporated with a feedback mechanism and time delays in gene regulation. We systematically analyse the effects of time delays, the feedback mechanism, and biological stochasticity on the power spectra. It has been clarified that the time delays together with the feedback mechanism can induce stochastic oscillations at the molecular level and invalidate the noise addition rule for a modular description of the noise propagator. Delay-induced stochastic resonance can be expected, which is related to the stability loss of the reaction systems and Hopf bifurcation occurring for solutions of the corresponding deterministic reaction equations. Through the analysis of the power spectrum, a new approach is proposed to estimate the oscillation period. (interdisciplinary physics and related areas of science and technology)
International Nuclear Information System (INIS)
Sriram, K.
2006-01-01
This paper describes both the experimental and numerical investigations on the effect of positive electrical feedback in the oscillating Belovsou-Zhabotinsky (BZ) reaction under batch conditions. Positive electrical feedback causes an increase in the amplitude and period of the oscillations with the corresponding increase of the feedback strength. Oregonator model with a positive feedback term suitably incorporated in one of the dynamical variables is used to account for these experimental observations. Further, the effect of positive feedback on the Hopf points are investigated numerically by constructing the bifurcation diagrams. In the absence of feedback, for a particular stoichiometric parameter, the model exhibits both supercritical and subcritical Hopf bifurcations with canard existing near the former Hopf point. In the presence of positive feedback it is observed that (i) both the Hopf points advances, (ii) the distance between the two Hopf points decreases linearly, while the period increases exponentially with the increase of feedback strength near the Hopf points, (iii) only supercritical Hopf point without canard survives for a very strong positive feedback strength and (iv) moderate feedback strength takes the system away from limit cycle to the canard regime. These observations are explained in terms of Field-Koeroes-Noyes mechanism of the Belousov-Zhabotinsky reaction. This may be the first instance where the advancement of Hopf points due to positive feedback is clearly shown
International Nuclear Information System (INIS)
Gritli, Hassène; Belghith, Safya
2017-01-01
Highlights: • We study the passive walking dynamics of the compass-gait model under OGY-based state-feedback control. • We analyze local bifurcations via a hybrid Poincaré map. • We show exhibition of the super(sub)-critical flip bifurcation, the saddle-node(saddle) bifurcation and a saddle-flip bifurcation. • An analysis via a two-parameter bifurcation diagram is presented. • Some new hidden attractors in the controlled passive walking dynamics are displayed. - Abstract: In our previous work, we have analyzed the passive dynamic walking of the compass-gait biped model under the OGY-based state-feedback control using the impulsive hybrid nonlinear dynamics. Such study was carried out through bifurcation diagrams. It was shown that the controlled bipedal gait exhibits attractive nonlinear phenomena such as the cyclic-fold (saddle-node) bifurcation, the period-doubling (flip) bifurcation and chaos. Moreover, we revealed that, using the controlled continuous-time dynamics, we encountered a problem in finding, identifying and hence following branches of (un)stable solutions in order to characterize local bifurcations. The present paper solves such problem and then provides a further investigation of the controlled bipedal walking dynamics using the developed analytical expression of the controlled hybrid Poincaré map. Thus, we show that analysis via such Poincaré map allows to follow branches of both stable and unstable fixed points in bifurcation diagrams and hence to explore the complete dynamics of the controlled compass-gait biped model. We demonstrate the generation, other than the conventional local bifurcations in bipedal walking, i.e. the flip bifurcation and the saddle-node bifurcation, of a saddle-saddle bifurcation, a subcritical flip bifurcation and a new type of a local bifurcation, the saddle-flip bifurcation. In addition, to further understand the occurrence of the local bifurcations, we present an analysis with a two-parameter bifurcation
Bifurcation Control of Chaotic Dynamical Systems
National Research Council Canada - National Science Library
Wang, Hua O; Abed, Eyad H
1992-01-01
A nonlinear system which exhibits bifurcations, transient chaos, and fully developed chaos is considered, with the goal of illustrating the role of two ideas in the control of chaotic dynamical systems...
Bifurcation structure of successive torus doubling
International Nuclear Information System (INIS)
Sekikawa, Munehisa; Inaba, Naohiko; Yoshinaga, Tetsuya; Tsubouchi, Takashi
2006-01-01
The authors discuss the 'embryology' of successive torus doubling via the bifurcation theory, and assert that the coupled map of a logistic map and a circle map has a structure capable of generating infinite number of torus doublings
Experimental Bifurcation Analysis Using Control-Based Continuation
DEFF Research Database (Denmark)
Bureau, Emil; Starke, Jens
The focus of this thesis is developing and implementing techniques for performing experimental bifurcation analysis on nonlinear mechanical systems. The research centers around the newly developed control-based continuation method, which allows to systematically track branches of stable...... the resulting behavior, we propose and test three different methods for assessing stability of equilibrium states during experimental continuation. We show that it is possible to determine the stability without allowing unbounded divergence, and that it is under certain circumstances possible to quantify...... and unstable equilibria under variation of parameters. As a test case we demonstrate that it is possible to track the complete frequency response, including the unstable branches, for a harmonically forced impact oscillator with hardening spring nonlinearity, controlled by electromagnetic actuators. The method...
Synchrony, waves and ripple in spatially coupled Kuramoto oscillators with Mexican hat connectivity.
Heitmann, Stewart; Ermentrout, G Bard
2015-06-01
Spatiotemporal waves of synchronized activity are known to arise in oscillatory neural networks with lateral inhibitory coupling. How such patterns respond to dynamic changes in coupling strength is largely unexplored. The present study uses analysis and simulation to investigate the evolution of wave patterns when the strength of lateral inhibition is varied dynamically. Neural synchronization was modeled by a spatial ring of Kuramoto oscillators with Mexican hat lateral coupling. Broad bands of coexisting stable wave solutions were observed at all levels of inhibition. The stability of these waves was formally analyzed in both the infinite ring and the finite ring. The broad range of multi-stability predicted hysteresis in transitions between neighboring wave solutions when inhibition is slowly varied. Numerical simulation confirmed the predicted transitions when inhibition was ramped down from a high initial value. However, non-wave solutions emerged from the uniform solution when inhibition was ramped upward from zero. These solutions correspond to spatially periodic deviations of phase that we call ripple states. Numerical continuation showed that stable ripple states emerge from synchrony via a supercritical pitchfork bifurcation. The normal form of this bifurcation was derived analytically, and its predictions compared against the numerical results. Ripple states were also found to bifurcate from wave solutions, but these were locally unstable. Simulation also confirmed the existence of hysteresis and ripple states in two spatial dimensions. Our findings show that spatial synchronization patterns can remain structurally stable despite substantial changes in network connectivity.
Meng, Xin-You; Wu, Yu-Qian
In this paper, a delayed differential algebraic phytoplankton-zooplankton-fish model with taxation and nonlinear fish harvesting is proposed. In the absence of time delay, the existence of singularity induced bifurcation is discussed by regarding economic interest as bifurcation parameter. A state feedback controller is designed to eliminate singularity induced bifurcation. Based on Liu’s criterion, Hopf bifurcation occurs at the interior equilibrium when taxation is taken as bifurcation parameter and is more than its corresponding critical value. In the presence of time delay, by analyzing the associated characteristic transcendental equation, the interior equilibrium loses local stability when time delay crosses its critical value. What’s more, the direction of Hopf bifurcation and stability of the bifurcating periodic solutions are investigated based on normal form theory and center manifold theorem, and nonlinear state feedback controller is designed to eliminate Hopf bifurcation. Furthermore, Pontryagin’s maximum principle has been used to obtain optimal tax policy to maximize the benefit as well as the conservation of the ecosystem. Finally, some numerical simulations are given to demonstrate our theoretical analysis.
Ternary choices in repeated games and border collision bifurcations
International Nuclear Information System (INIS)
Dal Forno, Arianna; Gardini, Laura; Merlone, Ugo
2012-01-01
Highlights: ► We extend a model of binary choices with externalities to include more alternatives. ► Introducing one more option affects the complexity of the dynamics. ► We find bifurcation structures which where impossible to observe in binary choices. ► A ternary choice cannot simply be considered as a binary choice plus one. - Abstract: Several recent contributions formalize and analyze binary choices games with externalities as those described by Schelling. Nevertheless, in the real world choices are not always binary, and players have often to decide among more than two alternatives. These kinds of interactions are examined in game theory where, starting from the well known rock-paper-scissor game, several other kinds of strategic interactions involving more than two choices are examined. In this paper we investigate how the dynamics evolve introducing one more option in binary choice games with externalities. The dynamics we obtain are always in a stable regime, that is, the structurally stable dynamics are only attracting cycles, but of any possible positive integer as period. We show that, depending on the structure of the game, the dynamics can be quite different from those existing when considering binary choices. The bifurcation structure, due to border collisions, is explained, showing the existence of so-called big-bang bifurcation points.
Discretization analysis of bifurcation based nonlinear amplifiers
Feldkord, Sven; Reit, Marco; Mathis, Wolfgang
2017-09-01
Recently, for modeling biological amplification processes, nonlinear amplifiers based on the supercritical Andronov-Hopf bifurcation have been widely analyzed analytically. For technical realizations, digital systems have become the most relevant systems in signal processing applications. The underlying continuous-time systems are transferred to the discrete-time domain using numerical integration methods. Within this contribution, effects on the qualitative behavior of the Andronov-Hopf bifurcation based systems concerning numerical integration methods are analyzed. It is shown exemplarily that explicit Runge-Kutta methods transform the truncated normalform equation of the Andronov-Hopf bifurcation into the normalform equation of the Neimark-Sacker bifurcation. Dependent on the order of the integration method, higher order terms are added during this transformation.A rescaled normalform equation of the Neimark-Sacker bifurcation is introduced that allows a parametric design of a discrete-time system which corresponds to the rescaled Andronov-Hopf system. This system approximates the characteristics of the rescaled Hopf-type amplifier for a large range of parameters. The natural frequency and the peak amplitude are preserved for every set of parameters. The Neimark-Sacker bifurcation based systems avoid large computational effort that would be caused by applying higher order integration methods to the continuous-time normalform equations.
International Nuclear Information System (INIS)
Agliari, Anna
2006-01-01
In this paper we study some global bifurcations arising in the Puu's oligopoly model when we assume that the producers do not adjust to the best reply but use an adaptive process to obtain at each step the new production. Such bifurcations cause the appearance of a pair of closed invariant curves, one attracting and one repelling, this latter being involved in the subcritical Neimark bifurcation of the Cournot equilibrium point. The aim of the paper is to highlight the relationship between the global bifurcations causing the appearance/disappearance of two invariant closed curves and the homoclinic connections of some saddle cycle, already conjectured in [Agliari A, Gardini L, Puu T. Some global bifurcations related to the appearance of closed invariant curves. Comput Math Simul 2005;68:201-19]. We refine the results obtained in such a paper, showing that the appearance/disappearance of closed invariant curves is not necessarily related to the existence of an attracting cycle. The characterization of the periodicity tongues (i.e. a region of the parameter space in which an attracting cycle exists) associated with a subcritical Neimark bifurcation is also discussed
Detection of bifurcations in noisy coupled systems from multiple time series
Williamson, Mark S.; Lenton, Timothy M.
2015-03-01
We generalize a method of detecting an approaching bifurcation in a time series of a noisy system from the special case of one dynamical variable to multiple dynamical variables. For a system described by a stochastic differential equation consisting of an autonomous deterministic part with one dynamical variable and an additive white noise term, small perturbations away from the system's fixed point will decay slower the closer the system is to a bifurcation. This phenomenon is known as critical slowing down and all such systems exhibit this decay-type behaviour. However, when the deterministic part has multiple coupled dynamical variables, the possible dynamics can be much richer, exhibiting oscillatory and chaotic behaviour. In our generalization to the multi-variable case, we find additional indicators to decay rate, such as frequency of oscillation. In the case of approaching a homoclinic bifurcation, there is no change in decay rate but there is a decrease in frequency of oscillations. The expanded method therefore adds extra tools to help detect and classify approaching bifurcations given multiple time series, where the underlying dynamics are not fully known. Our generalisation also allows bifurcation detection to be applied spatially if one treats each spatial location as a new dynamical variable. One may then determine the unstable spatial mode(s). This is also something that has not been possible with the single variable method. The method is applicable to any set of time series regardless of its origin, but may be particularly useful when anticipating abrupt changes in the multi-dimensional climate system.
Detection of bifurcations in noisy coupled systems from multiple time series
International Nuclear Information System (INIS)
Williamson, Mark S.; Lenton, Timothy M.
2015-01-01
We generalize a method of detecting an approaching bifurcation in a time series of a noisy system from the special case of one dynamical variable to multiple dynamical variables. For a system described by a stochastic differential equation consisting of an autonomous deterministic part with one dynamical variable and an additive white noise term, small perturbations away from the system's fixed point will decay slower the closer the system is to a bifurcation. This phenomenon is known as critical slowing down and all such systems exhibit this decay-type behaviour. However, when the deterministic part has multiple coupled dynamical variables, the possible dynamics can be much richer, exhibiting oscillatory and chaotic behaviour. In our generalization to the multi-variable case, we find additional indicators to decay rate, such as frequency of oscillation. In the case of approaching a homoclinic bifurcation, there is no change in decay rate but there is a decrease in frequency of oscillations. The expanded method therefore adds extra tools to help detect and classify approaching bifurcations given multiple time series, where the underlying dynamics are not fully known. Our generalisation also allows bifurcation detection to be applied spatially if one treats each spatial location as a new dynamical variable. One may then determine the unstable spatial mode(s). This is also something that has not been possible with the single variable method. The method is applicable to any set of time series regardless of its origin, but may be particularly useful when anticipating abrupt changes in the multi-dimensional climate system
Detection of bifurcations in noisy coupled systems from multiple time series
Energy Technology Data Exchange (ETDEWEB)
Williamson, Mark S., E-mail: m.s.williamson@exeter.ac.uk; Lenton, Timothy M. [Earth System Science Group, College of Life and Environmental Sciences, University of Exeter, Laver Building, North Park Road, Exeter EX4 4QE (United Kingdom)
2015-03-15
We generalize a method of detecting an approaching bifurcation in a time series of a noisy system from the special case of one dynamical variable to multiple dynamical variables. For a system described by a stochastic differential equation consisting of an autonomous deterministic part with one dynamical variable and an additive white noise term, small perturbations away from the system's fixed point will decay slower the closer the system is to a bifurcation. This phenomenon is known as critical slowing down and all such systems exhibit this decay-type behaviour. However, when the deterministic part has multiple coupled dynamical variables, the possible dynamics can be much richer, exhibiting oscillatory and chaotic behaviour. In our generalization to the multi-variable case, we find additional indicators to decay rate, such as frequency of oscillation. In the case of approaching a homoclinic bifurcation, there is no change in decay rate but there is a decrease in frequency of oscillations. The expanded method therefore adds extra tools to help detect and classify approaching bifurcations given multiple time series, where the underlying dynamics are not fully known. Our generalisation also allows bifurcation detection to be applied spatially if one treats each spatial location as a new dynamical variable. One may then determine the unstable spatial mode(s). This is also something that has not been possible with the single variable method. The method is applicable to any set of time series regardless of its origin, but may be particularly useful when anticipating abrupt changes in the multi-dimensional climate system.
Kashyap, Rahul; Westley, Alexandra; Sen, Surajit
The Duffing oscillator, a nonlinear oscillator with a potential energy with both quadratic and cubic terms, is known to show highly chaotic solutions in certain regions of its parameter space. Here, we examine the behaviors of small chains of harmonically and anharmonically coupled Duffing oscillators and show that these chains exhibit localized nonlinear excitations (LNEs) similar to the ones seen in the Fermi-Pasta-Ulam-Tsingou (FPUT) system. These LNEs demonstrate properties such as long-time energy localization, high periodicity, and slow energy leaking which rapidly accelerates upon frequency matching with the adjacent particles all of which have been observed in the FPUT system. Furthermore, by examining bifurcation diagrams, we will show that many qualitative properties of this system during the transition from weakly to strongly nonlinear behavior depend directly upon the frequencies associated with the individual Duffing oscillators.
Stability and Bifurcation in Magnetic Flux Feedback Maglev Control System
Directory of Open Access Journals (Sweden)
Wen-Qing Zhang
2013-01-01
Full Text Available Nonlinear properties of magnetic flux feedback control system have been investigated mainly in this paper. We analyzed the influence of magnetic flux feedback control system on control property by time delay and interfering signal of acceleration. First of all, we have established maglev nonlinear model based on magnetic flux feedback and then discussed hopf bifurcation’s condition caused by the acceleration’s time delay. The critical value of delayed time is obtained. It is proved that the period solution exists in maglev control system and the stable condition has been got. We obtained the characteristic values by employing center manifold reduction theory and normal form method, which represent separately the direction of hopf bifurcation, the stability of the period solution, and the period of the period motion. Subsequently, we discussed the influence maglev system on stability of by acceleration’s interfering signal and obtained the stable domain of interfering signal. Some experiments have been done on CMS04 maglev vehicle of National University of Defense Technology (NUDT in Tangshan city. The results of experiments demonstrate that viewpoints of this paper are correct and scientific. When time lag reaches the critical value, maglev system will produce a supercritical hopf bifurcation which may cause unstable period motion.
Chaos in generically coupled phase oscillator networks with nonpairwise interactions
Energy Technology Data Exchange (ETDEWEB)
Bick, Christian; Ashwin, Peter; Rodrigues, Ana [Centre for Systems, Dynamics and Control and Department of Mathematics, University of Exeter, Exeter EX4 4QF (United Kingdom)
2016-09-15
The Kuramoto–Sakaguchi system of coupled phase oscillators, where interaction between oscillators is determined by a single harmonic of phase differences of pairs of oscillators, has very simple emergent dynamics in the case of identical oscillators that are globally coupled: there is a variational structure that means the only attractors are full synchrony (in-phase) or splay phase (rotating wave/full asynchrony) oscillations and the bifurcation between these states is highly degenerate. Here we show that nonpairwise coupling—including three and four-way interactions of the oscillator phases—that appears generically at the next order in normal-form based calculations can give rise to complex emergent dynamics in symmetric phase oscillator networks. In particular, we show that chaos can appear in the smallest possible dimension of four coupled phase oscillators for a range of parameter values.
Chaos in generically coupled phase oscillator networks with nonpairwise interactions.
Bick, Christian; Ashwin, Peter; Rodrigues, Ana
2016-09-01
The Kuramoto-Sakaguchi system of coupled phase oscillators, where interaction between oscillators is determined by a single harmonic of phase differences of pairs of oscillators, has very simple emergent dynamics in the case of identical oscillators that are globally coupled: there is a variational structure that means the only attractors are full synchrony (in-phase) or splay phase (rotating wave/full asynchrony) oscillations and the bifurcation between these states is highly degenerate. Here we show that nonpairwise coupling-including three and four-way interactions of the oscillator phases-that appears generically at the next order in normal-form based calculations can give rise to complex emergent dynamics in symmetric phase oscillator networks. In particular, we show that chaos can appear in the smallest possible dimension of four coupled phase oscillators for a range of parameter values.
DEFF Research Database (Denmark)
Behan, Miles W; Holm, Niels Ramsing; Curzen, Nicholas P
2011-01-01
Background— Controversy persists regarding the correct strategy for bifurcation lesions. Therefore, we combined the patient-level data from 2 large trials with similar methodology: the NORDIC Bifurcation Study (NORDIC I) and the British Bifurcation Coronary Study (BBC ONE). Methods and Results— B...
Bifurcation and chaos response of a cracked rotor with random disturbance
Leng, Xiaolei; Meng, Guang; Zhang, Tao; Fang, Tong
2007-01-01
The Monte-Carlo method is used to investigate the bifurcation and chaos characteristics of a cracked rotor with a white noise process as its random disturbance. Special attention is paid to the influence of the stiffness change ratio and the rotating speed ratio on the bifurcation and chaos response of the system. Numerical simulations show that the affect of the random disturbance is significant as the undisturbed response of the cracked rotor system is a quasi-periodic or chaos one, and such affect is smaller as the undisturbed response is a periodic one.
Symmetry-breaking analysis for the general Helmholtz-Duffing oscillator
International Nuclear Information System (INIS)
Cao Hongjun; Seoane, Jesus M.; Sanjuan, Miguel A.F.
2007-01-01
The symmetry breaking phenomenon for a general Helmholtz-Duffing oscillator as a function of a symmetric parameter in the nonlinear force is investigated. Different values of this parameter convert the general oscillator into either the Helmholtz or the Duffing oscillator. Due to the variation of the symmetric parameter, the phase space patterns of the unperturbed Helmholtz-Duffing oscillator will cause a huge difference between the left-hand homoclinic orbit and the right-hand one. In particular, the area of the left-hand homoclinic orbits is a strictly monotonously decreasing function, while the area of the right-hand homoclinic orbit varies only in a very small range. There exist distinct local supercritical and subcritical saddle-node bifurcations at two different centers. The left-hand and the right-hand existing regions of the harmonic solutions of the Helmholtz-Duffing oscillator created by the left-hand and the right-hand saddle-node bifurcation curves will lead to different transition in the amplitude-frequency plane. There exists also a critical frequency which has the effect that the left-hand homoclinic bifurcation value is equal to the right-hand homoclinic bifurcation value. And, if the amplitude coefficient of the Helmholtz-Duffing oscillator is used as the control parameter, and it is larger than the same left-hand and right-hand homoclinic bifurcation, then the global stability of the system will be destroyed at a lowest cost. Besides this critical frequency, the left-hand and the right-hand homoclinic bifurcations are not only unequal, but also their effects for the system's stability are different. Among them, the effect resulting from the small homoclinic bifurcation for the system's stability is local and negligible, while the effect from the large homoclinic bifurcation is global but this is accomplished at a quite larger cost
Complex behavior in chains of nonlinear oscillators.
Alonso, Leandro M
2017-06-01
This article outlines sufficient conditions under which a one-dimensional chain of identical nonlinear oscillators can display complex spatio-temporal behavior. The units are described by phase equations and consist of excitable oscillators. The interactions are local and the network is poised to a critical state by balancing excitation and inhibition locally. The results presented here suggest that in networks composed of many oscillatory units with local interactions, excitability together with balanced interactions is sufficient to give rise to complex emergent features. For values of the parameters where complex behavior occurs, the system also displays a high-dimensional bifurcation where an exponentially large number of equilibria are borne in pairs out of multiple saddle-node bifurcations.
Bifurcation analysis of a three dimensional system
Directory of Open Access Journals (Sweden)
Yongwen WANG
2018-04-01
Full Text Available In order to enrich the stability and bifurcation theory of the three dimensional chaotic systems, taking a quadratic truncate unfolding system with the triple singularity equilibrium as the research subject, the existence of the equilibrium, the stability and the bifurcation of the system near the equilibrium under different parametric conditions are studied. Using the method of mathematical analysis, the existence of the real roots of the corresponding characteristic equation under the different parametric conditions is analyzed, and the local manifolds of the equilibrium are gotten, then the possible bifurcations are guessed. The parametric conditions under which the equilibrium is saddle-focus are analyzed carefully by the Cardan formula. Moreover, the conditions of codimension-one Hopf bifucation and the prerequisites of the supercritical and subcritical Hopf bifurcation are found by computation. The results show that the system has abundant stability and bifurcation, and can also supply theorical support for the proof of the existence of the homoclinic or heteroclinic loop connecting saddle-focus and the Silnikov's chaos. This method can be extended to study the other higher nonlinear systems.
Directory of Open Access Journals (Sweden)
Huitao Zhao
2013-01-01
Full Text Available A ratio-dependent predator-prey model with two time delays is studied. By means of an iteration technique, sufficient conditions are obtained for the global attractiveness of the positive equilibrium. By comparison arguments, the global stability of the semitrivial equilibrium is addressed. By using the theory of functional equation and Hopf bifurcation, the conditions on which positive equilibrium exists and the quality of Hopf bifurcation are given. Using a global Hopf bifurcation result of Wu (1998 for functional differential equations, the global existence of the periodic solutions is obtained. Finally, an example for numerical simulations is also included.
The genesis of period-adding bursting without bursting-chaos in the Chay model
International Nuclear Information System (INIS)
Yang Zhuoqin; Lu Qishao; Li Li
2006-01-01
According to the period-adding firing patterns without chaos observed in neuronal experiments, the genesis of the period-adding 'fold/homoclinic' bursting sequence without bursting-chaos is explored by numerical simulation, fast/slow dynamics and bifurcation analysis of limit cycle in the neuronal Chay model. It is found that each periodic bursting, from period-1 to period-7, is separately generated by the corresponding periodic spiking pattern through two period-doubling bifurcations, except for the period-1 bursting occurring via a Hopf bifurcation. Consequently, it can be revealed that this period-adding bursting bifurcation without chaos has a compound bifurcation structure with transitions from spiking to bursting, which is closely related to period-doubling bifurcations of periodic spiking in essence
Bifurcations in a discrete time model composed of Beverton-Holt function and Ricker function.
Shang, Jin; Li, Bingtuan; Barnard, Michael R
2015-05-01
We provide rigorous analysis for a discrete-time model composed of the Ricker function and Beverton-Holt function. This model was proposed by Lewis and Li [Bull. Math. Biol. 74 (2012) 2383-2402] in the study of a population in which reproduction occurs at a discrete instant of time whereas death and competition take place continuously during the season. We show analytically that there exists a period-doubling bifurcation curve in the model. The bifurcation curve divides the parameter space into the region of stability and the region of instability. We demonstrate through numerical bifurcation diagrams that the regions of periodic cycles are intermixed with the regions of chaos. We also study the global stability of the model. Copyright © 2015 Elsevier Inc. All rights reserved.
Periodicity, chaos, and multiple attractors in a memristor-based Shinriki's circuit
Energy Technology Data Exchange (ETDEWEB)
Kengne, J. [Laboratory of Automation and Applied Computer (LAIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, Dschang (Cameroon); Njitacke Tabekoueng, Z.; Kamdoum Tamba, V.; Nguomkam Negou, A. [Laboratory of Automation and Applied Computer (LAIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, Dschang (Cameroon); Department of Physics, Laboratory of Electronics and Signal Processing (LETS), Faculty of Science, University of Dschang, Dschang (Cameroon)
2015-10-15
In this contribution, a novel memristor-based oscillator, obtained from Shinriki's circuit by substituting the nonlinear positive conductance with a first order memristive diode bridge, is introduced. The model is described by a continuous time four-dimensional autonomous system with smooth nonlinearities. The basic dynamical properties of the system are investigated including equilibria and stability, phase portraits, frequency spectra, bifurcation diagrams, and Lyapunov exponents' spectrum. It is found that in addition to the classical period-doubling and symmetry restoring crisis scenarios reported in the original circuit, the memristor-based oscillator experiences the unusual and striking feature of multiple attractors (i.e., coexistence of a pair of asymmetric periodic attractors with a pair of asymmetric chaotic ones) over a broad range of circuit parameters. Results of theoretical analyses are verified by laboratory experimental measurements.
Chenciner bubbles and torus break-up in a periodically forced delay differential equation
Keane, A.; Krauskopf, B.
2018-06-01
We study a generic model for the interaction of negative delayed feedback and periodic forcing that was first introduced by Ghil et al (2008 Nonlinear Process. Geophys. 15 417–33) in the context of the El Niño Southern Oscillation climate system. This model takes the form of a delay differential equation and has been shown in previous work to be capable of producing complicated dynamics, which is organised by resonances between the external forcing and dynamics induced by feedback. For certain parameter values, we observe in simulations the sudden disappearance of (two-frequency dynamics on) tori. This can be explained by the folding of invariant tori and their associated resonance tongues. It is known that two smooth tori cannot simply meet and merge; they must actually break up in complicated bifurcation scenarios that are organised within so-called resonance bubbles first studied by Chenciner. We identify and analyse such a Chenciner bubble in order to understand the dynamics at folds of tori. We conduct a bifurcation analysis of the Chenciner bubble by means of continuation software and dedicated simulations, whereby some bifurcations involve tori and are detected in appropriate two-dimensional projections associated with Poincaré sections. We find close agreement between the observed bifurcation structure in the Chenciner bubble and a previously suggested theoretical picture. As far as we are aware, this is the first time the bifurcation structure associated with a Chenciner bubble has been analysed in a delay differential equation and, in fact, for a flow rather than an explicit map. Following our analysis, we briefly discuss the possible role of folding tori and Chenciner bubbles in the context of tipping.
Directory of Open Access Journals (Sweden)
A. Rouillard
2004-12-01
Full Text Available An understanding of how the heliosphere modulates galactic cosmic ray (GCR fluxes and spectra is important, not only for studies of their origin, acceleration and propagation in our galaxy, but also for predicting their effects (on technology and on the Earth's environment and organisms and for interpreting abundances of cosmogenic isotopes in meteorites and terrestrial reservoirs. In contrast to the early interplanetary measurements, there is growing evidence for a dominant role in GCR shielding of the total open magnetic flux, which emerges from the solar atmosphere and enters the heliosphere. In this paper, we relate a strong 1.68-year oscillation in GCR fluxes to a corresponding oscillation in the open solar magnetic flux and infer cosmic-ray propagation paths confirming the predictions of theories in which drift is important in modulating the cosmic ray flux. Key words. Interplanetary physics (Cosmic rays, Interplanetary magnetic fields
International Nuclear Information System (INIS)
Sushko, Iryna; Agliari, Anna; Gardini, Laura
2006-01-01
We study the structure of the 2D bifurcation diagram for a two-parameter family of piecewise smooth unimodal maps f with one break point. Analysing the parameters of the normal form for the border-collision bifurcation of an attracting n-cycle of the map f, we describe the possible kinds of dynamics associated with such a bifurcation. Emergence and role of border-collision bifurcation curves in the 2D bifurcation plane are studied. Particular attention is paid also to the curves of homoclinic bifurcations giving rise to the band merging of pieces of cyclic chaotic intervals
The genesis of period-adding bursting without bursting-chaos in the Chay model
International Nuclear Information System (INIS)
Yang Zhuoqin; Lu Qishao; Li Li
2006-01-01
According to the period-adding firing patterns without chaos observed in neuronal experiments, the genesis of the period-adding 'fold/homoclinic' bursting sequence without bursting-chaos is explored by numerical simulation, fast/slow dynamics and bifurcation analysis of limit cycle in the neuronal Chay model. It is found that each periodic bursting, from period-1 to 7, is separately generated by the corresponding periodic spiking pattern through two period-doubling bifurcations, except for the period-1 bursting occurring via a Hopf bifurcation. Consequently, it can be revealed that this period-adding bursting bifurcation without chaos has a compound bifurcation structure with transitions from spiking to bursting, which is closely related to period-doubling bifurcations of periodic spiking in essence
Bifurcation of Jovian magnetotail current sheet
Directory of Open Access Journals (Sweden)
P. L. Israelevich
2006-07-01
Full Text Available Multiple crossings of the magnetotail current sheet by a single spacecraft give the possibility to distinguish between two types of electric current density distribution: single-peaked (Harris type current layer and double-peaked (bifurcated current sheet. Magnetic field measurements in the Jovian magnetic tail by Voyager-2 reveal bifurcation of the tail current sheet. The electric current density possesses a minimum at the point of the Bx-component reversal and two maxima at the distance where the magnetic field strength reaches 50% of its value in the tail lobe.
Bifurcation of Jovian magnetotail current sheet
Directory of Open Access Journals (Sweden)
P. L. Israelevich
2006-07-01
Full Text Available Multiple crossings of the magnetotail current sheet by a single spacecraft give the possibility to distinguish between two types of electric current density distribution: single-peaked (Harris type current layer and double-peaked (bifurcated current sheet. Magnetic field measurements in the Jovian magnetic tail by Voyager-2 reveal bifurcation of the tail current sheet. The electric current density possesses a minimum at the point of the B_{x}-component reversal and two maxima at the distance where the magnetic field strength reaches 50% of its value in the tail lobe.
Wang, S.; Pogue, R.; Morre, D. M.; Morre, D. J.
2001-01-01
NOX proteins are cell surface-associated and growth-related hydroquinone (NADH) oxidases with protein disulfide-thiol interchange activity. A defining characteristic of NOX proteins is that the two enzymatic activities alternate to generate a regular period length of about 24 min. HeLa cells exhibit at least two forms of NOX. One is tumor-associated (tNOX) and is inhibited by putative quinone site inhibitors (e.g., capsaicin or the antitumor sulfonylurea, LY181984). Another is constitutive (CNOX) and refractory to inhibition. The periodic alternation of activities and drug sensitivity of the NADH oxidase activity observed with intact HeLa cells was retained in isolated plasma membranes and with the solubilized and partially purified enzyme. At least two activities were present. One had a period length of 24 min and the other had a period length of 22 min. The lengths of both the 22 and the 24 min periods were temperature compensated (approximately the same when measured at 17, 27 or 37 degrees C) whereas the rate of NADH oxidation approximately doubled with each 10 degrees C rise in temperature. The rate of increase in cell area of HeLa cells when measured by video-enhanced light microscopy also exhibited a complex period of oscillations reflective of both 22 and 24 min period lengths. The findings demonstrate the presence of a novel oscillating NOX activity at the surface of cancer cells with a period length of 22 min in addition to the constitutive NOX of non-cancer cells and tissues with a period length of 24 min.
Zhao, Huitao; Lu, Mengxia; Zuo, Junmei
2014-01-01
A controlled model for a financial system through washout-filter-aided dynamical feedback control laws is developed, the problem of anticontrol of Hopf bifurcation from the steady state is studied, and the existence, stability, and direction of bifurcated periodic solutions are discussed in detail. The obtained results show that the delay on price index has great influences on the financial system, which can be applied to suppress or avoid the chaos phenomenon appearing in the financial system.
International Nuclear Information System (INIS)
Quazzani, T.H.A.; Dekkaki, S.; Kharbach, J.; Quazzani-Ja, M.
2000-01-01
In this paper, the topology of Hamiltonian flows is described on the real phase space for the Goryatchev-Tchaplygin top. By making use of Fomenko's theory of surgery on Liouville tori, it is given a complete description of the generic bifurcations of the common level sets of the first integrals. It is also given a numerical investigation of these bifurcations. Explicit periodic solutions for singular common level sets of the first integrals were determined
Discretizing the transcritical and pitchfork bifurcations – conjugacy results
Ló czi, Lajos
2015-01-01
© 2015 Taylor & Francis. We present two case studies in one-dimensional dynamics concerning the discretization of transcritical (TC) and pitchfork (PF) bifurcations. In the vicinity of a TC or PF bifurcation point and under some natural assumptions
Codimension-2 bifurcations of the Kaldor model of business cycle
International Nuclear Information System (INIS)
Wu, Xiaoqin P.
2011-01-01
Research highlights: → The conditions are given such that the characteristic equation may have purely imaginary roots and double zero roots. → Purely imaginary roots lead us to study Hopf and Bautin bifurcations and to calculate the first and second Lyapunov coefficients. → Double zero roots lead us to study Bogdanov-Takens (BT) bifurcation. → Bifurcation diagrams for Bautin and BT bifurcations are obtained by using the normal form theory. - Abstract: In this paper, complete analysis is presented to study codimension-2 bifurcations for the nonlinear Kaldor model of business cycle. Sufficient conditions are given for the model to demonstrate Bautin and Bogdanov-Takens (BT) bifurcations. By computing the first and second Lyapunov coefficients and performing nonlinear transformation, the normal forms are derived to obtain the bifurcation diagrams such as Hopf, homoclinic and double limit cycle bifurcations. Some examples are given to confirm the theoretical results.
Nonlinear Analysis of Ring Oscillator and Cross-Coupled Oscillator Circuits
Ge, Xiaoqing
2010-12-01
Hassan Khalil’s research results and beautifully written textbook on nonlinear systems have influenced generations of researchers, including the authors of this paper. Using nonlinear systems techniques, this paper analyzes ring oscillator and cross-coupled oscillator circuits, which are essential building blocks in digital systems. The paper first investigates local and global stability properties of an n-stage ring oscillator by making use of its cyclic structure. It next studies global stability properties of a class of cross-coupled oscillators which admit the representation of a dynamic system in feedback with a static nonlinearity, and presents su cient conditions for almost global convergence of the solutions to a limit cycle when the feedback gain is in the vicinity of a bifurcation point. The result are also extended to the synchronization of interconnected identical oscillator circuits.
Nonlinear Analysis of Ring Oscillator and Cross-Coupled Oscillator Circuits
Ge, Xiaoqing; Arcak, Murat; Salama, Khaled N.
2010-01-01
Hassan Khalil’s research results and beautifully written textbook on nonlinear systems have influenced generations of researchers, including the authors of this paper. Using nonlinear systems techniques, this paper analyzes ring oscillator and cross-coupled oscillator circuits, which are essential building blocks in digital systems. The paper first investigates local and global stability properties of an n-stage ring oscillator by making use of its cyclic structure. It next studies global stability properties of a class of cross-coupled oscillators which admit the representation of a dynamic system in feedback with a static nonlinearity, and presents su cient conditions for almost global convergence of the solutions to a limit cycle when the feedback gain is in the vicinity of a bifurcation point. The result are also extended to the synchronization of interconnected identical oscillator circuits.
Oscillations in the bistable regime of neuronal networks.
Roxin, Alex; Compte, Albert
2016-07-01
Bistability between attracting fixed points in neuronal networks has been hypothesized to underlie persistent activity observed in several cortical areas during working memory tasks. In network models this kind of bistability arises due to strong recurrent excitation, sufficient to generate a state of high activity created in a saddle-node (SN) bifurcation. On the other hand, canonical network models of excitatory and inhibitory neurons (E-I networks) robustly produce oscillatory states via a Hopf (H) bifurcation due to the E-I loop. This mechanism for generating oscillations has been invoked to explain the emergence of brain rhythms in the β to γ bands. Although both bistability and oscillatory activity have been intensively studied in network models, there has not been much focus on the coincidence of the two. Here we show that when oscillations emerge in E-I networks in the bistable regime, their phenomenology can be explained to a large extent by considering coincident SN and H bifurcations, known as a codimension two Takens-Bogdanov bifurcation. In particular, we find that such oscillations are not composed of a stable limit cycle, but rather are due to noise-driven oscillatory fluctuations. Furthermore, oscillations in the bistable regime can, in principle, have arbitrarily low frequency.
Spiral intensity patterns in the internally pumped optical parametric oscillator
DEFF Research Database (Denmark)
Lodahl, Peter; Bache, Morten; Saffman, Mark
2001-01-01
We describe a nonlinear optical system that supports spiral pattern solutions in the field intensity. This new spatial structure is found to bifurcate above a secondary instability in the internally pumped optical parametric oscillator. The analytical predictions of threshold and spatial scale...
Experimental bifurcation analysis—Continuation for noise-contaminated zero problems
DEFF Research Database (Denmark)
Schilder, Frank; Bureau, Emil; Santos, Ilmar Ferreira
2015-01-01
Noise contaminated zero problems involve functions that cannot be evaluated directly, but only indirectly via observations. In addition, such observations are affected by a non-deterministic observation error (noise). We investigate the application of numerical bifurcation analysis for studying...... the solution set of such noise contaminated zero problems, which is highly relevant in the context of equation-free analysis (coarse grained analysis) and bifurcation analysis in experiments, and develop specialized algorithms to address challenges that arise due to the presence of noise. As a working example......, we demonstrate and test our algorithms on a mechanical nonlinear oscillator experiment using control based continuation, which we used as a main application and test case for development of the Coco compatible Matlab toolbox Continex that implements our algorithms....
Basin stability measure of different steady states in coupled oscillators
Rakshit, Sarbendu; Bera, Bidesh K.; Majhi, Soumen; Hens, Chittaranjan; Ghosh, Dibakar
2017-04-01
In this report, we investigate the stabilization of saddle fixed points in coupled oscillators where individual oscillators exhibit the saddle fixed points. The coupled oscillators may have two structurally different types of suppressed states, namely amplitude death and oscillation death. The stabilization of saddle equilibrium point refers to the amplitude death state where oscillations are ceased and all the oscillators converge to the single stable steady state via inverse pitchfork bifurcation. Due to multistability features of oscillation death states, linear stability theory fails to analyze the stability of such states analytically, so we quantify all the states by basin stability measurement which is an universal nonlocal nonlinear concept and it interplays with the volume of basins of attractions. We also observe multi-clustered oscillation death states in a random network and measure them using basin stability framework. To explore such phenomena we choose a network of coupled Duffing-Holmes and Lorenz oscillators which are interacting through mean-field coupling. We investigate how basin stability for different steady states depends on mean-field density and coupling strength. We also analytically derive stability conditions for different steady states and confirm by rigorous bifurcation analysis.
International Nuclear Information System (INIS)
McNeill, G.A.
1981-01-01
Present high-speed data acquisition systems in nuclear diagnostics use high-frequency oscillators to provide timing references for signals recorded on fast, traveling-wave oscilloscopes. An oscillator's sinusoidal wave shape is superimposed on the recorded signal with each cycle representing a fixed time increment. During data analysis the sinusoid is stripped from the signal, leaving a clean signal shape with known timing. Since all signal/time relationships are totally dependant upon working oscillators, these critical devices must have remote verification of proper operation. This manual presents the newly-developed oscillator monitor which will provide the required verification
Suppression of period-doubling and nonlinear parametric effects in periodically perturbed systems
International Nuclear Information System (INIS)
Bryant, P.; Wiesenfeld, K.
1986-01-01
We consider the effect on a generic period-doubling bifurcation of a periodic perturbation, whose frequency ω 1 is near the period-doubled frequency ω 0 /2. The perturbation is shown to always suppress the bifurcation, shifting the bifurcation point and stabilizing the behavior at the original bifurcation point. We derive an equation characterizing the response of the system to the perturbation, analysis of which reveals many interesting features of the perturbed bifurcation, including (1) the scaling law relating the shift of the bifurcation point and the amplitude of the perturbation, (2) the characteristics of the system's response as a function of bifurcation parameter, (3) parametric amplification of the perturbation signal including nonlinear effects such as gain saturation and a discontinuity in the response at a critical perturbation amplitude, (4) the effect of the detuning (ω 1 -ω 0 /2) on the bifurcation, and (5) the emergence of a closely spaced set of peaks in the response spectrum. An important application is the use of period-doubling systems as small-signal amplifiers, e.g., the superconducting Josephson parametric amplifier
Neimark-Sacker bifurcations and evidence of chaos in a discrete dynamical model of walkers
International Nuclear Information System (INIS)
Rahman, Aminur; Blackmore, Denis
2016-01-01
Bouncing droplets on a vibrating fluid bath can exhibit wave-particle behavior, such as being propelled by interacting with its own wave field. These droplets seem to walk across the bath, and thus are dubbed walkers. Experiments have shown that walkers can exhibit exotic dynamical behavior indicative of chaos. While the integro-differential models developed for these systems agree well with the experiments, they are difficult to analyze mathematically. In recent years, simpler discrete dynamical models have been derived and studied numerically. The numerical simulations of these models show evidence of exotic dynamics such as period doubling bifurcations, Neimark–Sacker (N–S) bifurcations, and even chaos. For example, in [1], based on simulations Gilet conjectured the existence of a supercritical N-S bifurcation as the damping factor in his one- dimensional path model. We prove Gilet’s conjecture and more; in fact, both supercritical and subcritical (N-S) bifurcations are produced by separately varying the damping factor and wave-particle coupling for all eigenmode shapes. Then we compare our theoretical results with some previous and new numerical simulations, and find complete qualitative agreement. Furthermore, evidence of chaos is shown by numerically studying a global bifurcation.
Invariants, Attractors and Bifurcation in Two Dimensional Maps with Polynomial Interaction
Hacinliyan, Avadis Simon; Aybar, Orhan Ozgur; Aybar, Ilknur Kusbeyzi
This work will present an extended discrete-time analysis on maps and their generalizations including iteration in order to better understand the resulting enrichment of the bifurcation properties. The standard concepts of stability analysis and bifurcation theory for maps will be used. Both iterated maps and flows are used as models for chaotic behavior. It is well known that when flows are converted to maps by discretization, the equilibrium points remain the same but a richer bifurcation scheme is observed. For example, the logistic map has a very simple behavior as a differential equation but as a map fold and period doubling bifurcations are observed. A way to gain information about the global structure of the state space of a dynamical system is investigating invariant manifolds of saddle equilibrium points. Studying the intersections of the stable and unstable manifolds are essential for understanding the structure of a dynamical system. It has been known that the Lotka-Volterra map and systems that can be reduced to it or its generalizations in special cases involving local and polynomial interactions admit invariant manifolds. Bifurcation analysis of this map and its higher iterates can be done to understand the global structure of the system and the artifacts of the discretization by comparing with the corresponding results from the differential equation on which they are based.
Comments on the Bifurcation Structure of 1D Maps
DEFF Research Database (Denmark)
Belykh, V.N.; Mosekilde, Erik
1997-01-01
-within-a-box structure of the total bifurcation set. This presents a picture in which the homoclinic orbit bifurcations act as a skeleton for the bifurcational set. At the same time, experimental results on continued subharmonic generation for piezoelectrically amplified sound waves, predating the Feigenbaum theory......, are called into attention....
NUMERICAL HOPF BIFURCATION OF DELAY-DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper we consider the numerical solution of some delay differential equations undergoing a Hopf bifurcation. We prove that if the delay differential equations have a Hopf bifurcation point atλ=λ*, then the numerical solution of the equation also has a Hopf bifurcation point atλh =λ* + O(h).
Turing instability and bifurcation analysis in a diffusive bimolecular system with delayed feedback
Wei, Xin; Wei, Junjie
2017-09-01
A diffusive autocatalytic bimolecular model with delayed feedback subject to Neumann boundary conditions is considered. We mainly study the stability of the unique positive equilibrium and the existence of periodic solutions. Our study shows that diffusion can give rise to Turing instability, and the time delay can affect the stability of the positive equilibrium and result in the occurrence of Hopf bifurcations. By applying the normal form theory and center manifold reduction for partial functional differential equations, we investigate the stability and direction of the bifurcations. Finally, we give some simulations to illustrate our theoretical results.
Bifurcation of elastic solids with sliding interfaces
Bigoni, D.; Bordignon, N.; Piccolroaz, A.; Stupkiewicz, S.
2018-01-01
Lubricated sliding contact between soft solids is an interesting topic in biomechanics and for the design of small-scale engineering devices. As a model of this mechanical set-up, two elastic nonlinear solids are considered jointed through a frictionless and bilateral surface, so that continuity of the normal component of the Cauchy traction holds across the surface, but the tangential component is null. Moreover, the displacement can develop only in a way that the bodies in contact do neither detach, nor overlap. Surprisingly, this finite strain problem has not been correctly formulated until now, so this formulation is the objective of the present paper. The incremental equations are shown to be non-trivial and different from previously (and erroneously) employed conditions. In particular, an exclusion condition for bifurcation is derived to show that previous formulations based on frictionless contact or `spring-type' interfacial conditions are not able to predict bifurcations in tension, while experiments-one of which, ad hoc designed, is reported-show that these bifurcations are a reality and become possible when the correct sliding interface model is used. The presented results introduce a methodology for the determination of bifurcations and instabilities occurring during lubricated sliding between soft bodies in contact.
Climate bifurcation during the last deglaciation?
Lenton, T.M.; Livina, V.N.; Dakos, V.; Scheffer, M.
2012-01-01
There were two abrupt warming events during the last deglaciation, at the start of the Bolling-Allerod and at the end of the Younger Dryas, but their underlying dynamics are unclear. Some abrupt climate changes may involve gradual forcing past a bifurcation point, in which a prevailing climate state
Resource competition: a bifurcation theory approach.
Kooi, B.W.; Dutta, P.S.; Feudel, U.
2013-01-01
We develop a framework for analysing the outcome of resource competition based on bifurcation theory. We elaborate our methodology by readdressing the problem of competition of two species for two resources in a chemostat environment. In the case of perfect-essential resources it has been
Digital subtraction angiography of carotid bifurcation
International Nuclear Information System (INIS)
Vries, A.R. de.
1984-01-01
This study demonstrates the reliability of digital subtraction angiography (DSA) by means of intra- and interobserver investigations as well as indicating the possibility of substituting catheterangiography by DSA in the diagnosis of carotid bifurcation. Whenever insufficient information is obtained from the combination of non-invasive investigation and DSA, a catheterangiogram will be necessary. (Auth.)
Percutaneous coronary intervention for coronary bifurcation disease
DEFF Research Database (Denmark)
Lassen, Jens Flensted; Holm, Niels Ramsing; Banning, Adrian
2016-01-01
of combining the opinions of interventional cardiologists with the opinions of a large variety of other scientists on bifurcation management. The present 11th EBC consensus document represents the summary of the up-to-date EBC consensus and recommendations. It points to the fact that there is a multitude...
Bifurcation of self-folded polygonal bilayers
Abdullah, Arif M.; Braun, Paul V.; Hsia, K. Jimmy
2017-09-01
Motivated by the self-assembly of natural systems, researchers have investigated the stimulus-responsive curving of thin-shell structures, which is also known as self-folding. Self-folding strategies not only offer possibilities to realize complicated shapes but also promise actuation at small length scales. Biaxial mismatch strain driven self-folding bilayers demonstrate bifurcation of equilibrium shapes (from quasi-axisymmetric doubly curved to approximately singly curved) during their stimulus-responsive morphing behavior. Being a structurally instable, bifurcation could be used to tune the self-folding behavior, and hence, a detailed understanding of this phenomenon is appealing from both fundamental and practical perspectives. In this work, we investigated the bifurcation behavior of self-folding bilayer polygons. For the mechanistic understanding, we developed finite element models of planar bilayers (consisting of a stimulus-responsive and a passive layer of material) that transform into 3D curved configurations. Our experiments with cross-linked Polydimethylsiloxane samples that change shapes in organic solvents confirmed our model predictions. Finally, we explored a design scheme to generate gripper-like architectures by avoiding the bifurcation of stimulus-responsive bilayers. Our research contributes to the broad field of self-assembly as the findings could motivate functional devices across multiple disciplines such as robotics, artificial muscles, therapeutic cargos, and reconfigurable biomedical devices.
Electromagnetic flow control of a bifurcated jet in a rectangular cavity
International Nuclear Information System (INIS)
Kalter, R.; Tummers, M.J.; Kenjereš, S.; Righolt, B.W.; Kleijn, C.R.
2014-01-01
Highlights: • Self-sustained oscillations in a thin cavity with submerged nozzle were observed. • The self-sustained oscillations were influenced by applying a Lorentz force. • A POD was applied to study the distribution of kinetic energy. • The large scale fluctuations can be enhanced or suppressed by the Lorentz force. • The turbulence fluctuations are not affected by the Lorentz force. - Abstract: The effect of Lorentz forcing on self-sustained oscillations of turbulent jets (Re = 3.1 × 10 3 ) issuing from a submerged bifurcated nozzle into a thin rectangular liquid filled cavity was investigated using free surface visualization and time-resolved particle image velocimetry (PIV). A Lorentz force is produced by applying an electrical current across the width of the cavity in conjunction with a magnetic field. As a working fluid a saline solution is used. The Lorentz force can be directed downward (F L L >0), to weaken or strengthen the self-sustained jet oscillations. The low frequency self-sustained jet oscillations induce a free surface oscillation. When F L L >0 the free surface oscillation amplitude is enhanced by a factor of 1.5. A large fraction of the turbulence kinetic energy k=1/2 u i ′ u i ′‾ is due to the self-sustained jet oscillations. A triple decomposition of the instantaneous velocity was used to divide the turbulence kinetic energy into a part originating from the self-sustained jet oscillation k osc and a part originating from the higher frequency turbulent fluctuations k turb . It follows that the Lorentz force does not influence k turb in the measurement plane, but the distribution of k osc can be altered significantly. The amount of energy contained in the self-sustained oscillation is three times lower when F L L >0
Complex bifurcation patterns in a discrete predator–prey model with ...
Indian Academy of Sciences (India)
We consider the simplest model in the family of discrete predator–prey system and introduce for the first time an environmental factor in the evolution of the system by periodically modulating the natural death rateof the predator.We show that with the introduction of environmental modulation, the bifurcation structure ...
The bifurcation and peakons for the special C(3,2,2) equation
Indian Academy of Sciences (India)
Keywords. C(3, 2, 2) equation; peakons; bell-shaped solitary waves; periodic cusp waves. .... In other words, the function φ is not well defined on ... Figure 2. The phase portrait bifurcation of system (22). 336. Pramana – J. Phys., Vol. 83, No.
Bifurcation and complex dynamics of a discrete-time predator-prey system
Directory of Open Access Journals (Sweden)
S. M. Sohel Rana
2015-06-01
Full Text Available In this paper, we investigate the dynamics of a discrete-time predator-prey system of Holling-I type in the closed first quadrant R+2. The existence and local stability of positive fixed point of the discrete dynamical system is analyzed algebraically. It is shown that the system undergoes a flip bifurcation and a Neimark-Sacker bifurcation in the interior of R+2 by using bifurcation theory. It has been found that the dynamical behavior of the model is very sensitive to the parameter values and the initial conditions. Numerical simulation results not only show the consistence with the theoretical analysis but also display the new and interesting dynamic behaviors, including phase portraits, period-9, 10, 20-orbits, attracting invariant circle, cascade of period-doubling bifurcation from period-20 leading to chaos, quasi-periodic orbits, and sudden disappearance of the chaotic dynamics and attracting chaotic set. In particular, we observe that when the prey is in chaotic dynamic, the predator can tend to extinction or to a stable equilibrium. The Lyapunov exponents are numerically computed to characterize the complexity of the dynamical behaviors. The analysis and results in this paper are interesting in mathematics and biology.
Explicit Solutions and Bifurcations for a Class of Generalized Boussinesq Wave Equation
International Nuclear Information System (INIS)
Ma Zhi-Min; Sun Yu-Huai; Liu Fu-Sheng
2013-01-01
In this paper, the generalized Boussinesq wave equation u tt — u xx + a(u m ) xx + bu xxxx = 0 is investigated by using the bifurcation theory and the method of phase portraits analysis. Under the different parameter conditions, the exact explicit parametric representations for solitary wave solutions and periodic wave solutions are obtained. (general)
Bifurcation and chaos in a dc-driven long annular Josephson junction
DEFF Research Database (Denmark)
Grnbech-Jensen, N.; Lomdahl, Peter S.; Samuelsen, Mogens Rugholm
1991-01-01
Simulations of long annular Josephson junctions in a static magnetic field show that in large regions of bias current the system can exhibit a period-doubling bifurcation route to chaos. This is in contrast to previously studied Josephson-junction systems where chaotic behavior has primarily been...
Bifurcating Solutions to the Monodomain Model Equipped with FitzHugh-Nagumo Kinetics
Directory of Open Access Journals (Sweden)
Robert Artebrant
2009-01-01
cells surrounded by collections of normal cells. Thus, the cell model features a discontinuous coefficient. Analytical techniques are applied to approximate the time-periodic solution that arises at the Hopf bifurcation point. Accurate numerical experiments are employed to complement our findings.
Global Hopf bifurcation analysis on a BAM neural network with delays
Sun, Chengjun; Han, Maoan; Pang, Xiaoming
2007-01-01
A delayed differential equation that models a bidirectional associative memory (BAM) neural network with four neurons is considered. By using a global Hopf bifurcation theorem for FDE and a Bendixon's criterion for high-dimensional ODE, a group of sufficient conditions for the system to have multiple periodic solutions are obtained when the sum of delays is sufficiently large.