Time-periodic solutions of the Benjamin-Ono equation
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Ambrose , D.M.; Wilkening, Jon
2008-04-01
We present a spectrally accurate numerical method for finding non-trivial time-periodic solutions of non-linear partial differential equations. The method is based on minimizing a functional (of the initial condition and the period) that is positive unless the solution is periodic, in which case it is zero. We solve an adjoint PDE to compute the gradient of this functional with respect to the initial condition. We include additional terms in the functional to specify the free parameters, which, in the case of the Benjamin-Ono equation, are the mean, a spatial phase, a temporal phase and the real part of one of the Fourier modes at t = 0. We use our method to study global paths of non-trivial time-periodic solutions connecting stationary and traveling waves of the Benjamin-Ono equation. As a starting guess for each path, we compute periodic solutions of the linearized problem by solving an infinite dimensional eigenvalue problem in closed form. We then use our numerical method to continue these solutions beyond the realm of linear theory until another traveling wave is reached (or until the solution blows up). By experimentation with data fitting, we identify the analytical form of the solutions on the path connecting the one-hump stationary solution to the two-hump traveling wave. We then derive exact formulas for these solutions by explicitly solving the system of ODE's governing the evolution of solitons using the ansatz suggested by the numerical simulations.
Time-periodic solutions of the Benjamin-Ono equation
International Nuclear Information System (INIS)
Ambrose, D.M.; Wilkening, Jon
2008-01-01
We present a spectrally accurate numerical method for finding non-trivial time-periodic solutions of non-linear partial differential equations. The method is based on minimizing a functional (of the initial condition and the period) that is positive unless the solution is periodic, in which case it is zero. We solve an adjoint PDE to compute the gradient of this functional with respect to the initial condition. We include additional terms in the functional to specify the free parameters, which, in the case of the Benjamin-Ono equation, are the mean, a spatial phase, a temporal phase and the real part of one of the Fourier modes at t = 0. We use our method to study global paths of non-trivial time-periodic solutions connecting stationary and traveling waves of the Benjamin-Ono equation. As a starting guess for each path, we compute periodic solutions of the linearized problem by solving an infinite dimensional eigenvalue problem in closed form. We then use our numerical method to continue these solutions beyond the realm of linear theory until another traveling wave is reached (or until the solution blows up). By experimentation with data fitting, we identify the analytical form of the solutions on the path connecting the one-hump stationary solution to the two-hump traveling wave. We then derive exact formulas for these solutions by explicitly solving the system of ODE's governing the evolution of solitons using the ansatz suggested by the numerical simulations
Energy Technology Data Exchange (ETDEWEB)
Ambrose, David M.; Wilkening, Jon
2008-12-11
We classify all bifurcations from traveling waves to non-trivial time-periodic solutions of the Benjamin-Ono equation that are predicted by linearization. We use a spectrally accurate numerical continuation method to study several paths of non-trivial solutions beyond the realm of linear theory. These paths are found to either re-connect with a different traveling wave or to blow up. In the latter case, as the bifurcation parameter approaches a critical value, the amplitude of the initial condition grows without bound and the period approaches zero. We propose a conjecture that gives the mapping from one bifurcation to its counterpart on the other side of the path of non-trivial solutions. By experimentation with data fitting, we identify the form of the exact solutions on the path connecting two traveling waves, which represents the Fourier coefficients of the solution as power sums of a finite number of particle positions whose elementary symmetric functions execute simple orbits in the complex plane (circles or epicycles). We then solve a system of algebraic equations to express the unknown constants in the new representation in terms of the mean, a spatial phase, a temporal phase, four integers (enumerating the bifurcation at each end of the path) and one additional bifurcation parameter. We also find examples of interior bifurcations from these paths of already non-trivial solutions, but we do not attempt to analyze their algebraic structure.
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....
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
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.
Fully developed turbulence via Feigenbaum's period-doubling bifurcations
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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
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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.
Integrable Hierarchy of the Quantum Benjamin-Ono Equation
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Maxim Nazarov
2013-12-01
Full Text Available A hierarchy of pairwise commuting Hamiltonians for the quantum periodic Benjamin-Ono equation is constructed by using the Lax matrix. The eigenvectors of these Hamiltonians are Jack symmetric functions of infinitely many variables x_1,x_2,…. This construction provides explicit expressions for the Hamiltonians in terms of the power sum symmetric functions p_n=x^n_1+x^n_2+⋯ and is based on our recent results from [Comm. Math. Phys. 324 (2013, 831-849].
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.
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
Period-doubling bifurcation and chaos control in a discrete-time mosquito model
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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)
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.
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.
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 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
Limit cycles bifurcating from the periodic annulus of cubic homogeneous polynomial centers
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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....
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
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.
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
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.
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
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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.
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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.
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.
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.
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.
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...
Integrable hydrodynamics of Calogero-Sutherland model: bidirectional Benjamin-Ono equation
International Nuclear Information System (INIS)
Abanov, Alexander G; Bettelheim, Eldad; Wiegmann, Paul
2009-01-01
We develop a hydrodynamic description of the classical Calogero-Sutherland liquid: a Calogero-Sutherland model with an infinite number of particles and a non-vanishing density of particles. The hydrodynamic equations, being written for the density and velocity fields of the liquid, are shown to be a bidirectional analog of the Benjamin-Ono equation. The latter is known to describe internal waves of deep stratified fluids. We show that the bidirectional Benjamin-Ono equation appears as a real reduction of the modified KP hierarchy. We derive the chiral nonlinear equation which appears as a chiral reduction of the bidirectional equation. The conventional Benjamin-Ono equation is a degeneration of the chiral nonlinear equation at large density. We construct multi-phase solutions of the bidirectional Benjamin-Ono equations and of the chiral nonlinear equations
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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.
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.
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
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.
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.
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)
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
Whitham modulation theory for the two-dimensional Benjamin-Ono equation.
Ablowitz, Mark; Biondini, Gino; Wang, Qiao
2017-09-01
Whitham modulation theory for the two-dimensional Benjamin-Ono (2DBO) equation is presented. A system of five quasilinear first-order partial differential equations is derived. The system describes modulations of the traveling wave solutions of the 2DBO equation. These equations are transformed to a singularity-free hydrodynamic-like system referred to here as the 2DBO-Whitham system. Exact reductions of this system are discussed, the formulation of initial value problems is considered, and the system is used to study the transverse stability of traveling wave solutions of the 2DBO equation.
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)
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...
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.
Control and Stabilization of the Benjamin-Ono Equation in {L^2({{T})}}
Laurent, Camille; Linares, Felipe; Rosier, Lionel
2015-12-01
We study the control and stabilization of the Benjamin-Ono equation in {L^2({T})}, the lowest regularity where the initial value problem is well-posed. This problem was already initiated in Linares and Rosier (Trans Am Math Soc 367:4595-4626, 2015) where a stronger stabilization term was used (that makes the equation of parabolic type in the control zone). Here we employ a more natural stabilization term related to the L 2-norm. Moreover, by proving a theorem of controllability in L 2, we manage to prove the global controllability in large time. Our analysis relies strongly on the bilinear estimates proved in Molinet and Pilod (Anal PDE 5:365-395, 2012) and some new extension of these estimates established here.
Structural stability and chaotic solutions of perturbed Benjamin-Ono equations
International Nuclear Information System (INIS)
Birnir, B.; Morrison, P.J.
1986-11-01
A method for proving chaos in partial differential equations is discussed and applied to the Benjamin-Ono equation subject to perturbations. The perturbations are of two types: one that corresponds to viscous dissipation, the so-called Burger's term, and one that involves the Hilbert transform and has been used to model Landau damping. The method proves chaos in the PDE by proving temporal chaos in its pole solutions. The spatial structure of the pole solutions remains intact, but their positions are chaotic in time. Melnikov's method is invoked to show this temporal chaos. It is discovered that the pole behavior is very sensitive to the Burger's perturbation, but is quite insensitive to the perturbation involving the Hilbert transform
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.
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
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
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
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)
Dispersive shock waves in systems with nonlocal dispersion of Benjamin-Ono type
El, G. A.; Nguyen, L. T. K.; Smyth, N. F.
2018-04-01
We develop a general approach to the description of dispersive shock waves (DSWs) for a class of nonlinear wave equations with a nonlocal Benjamin-Ono type dispersion term involving the Hilbert transform. Integrability of the governing equation is not a pre-requisite for the application of this method which represents a modification of the DSW fitting method previously developed for dispersive-hydrodynamic systems of Korteweg-de Vries (KdV) type (i.e. reducible to the KdV equation in the weakly nonlinear, long wave, unidirectional approximation). The developed method is applied to the Calogero-Sutherland dispersive hydrodynamics for which the classification of all solution types arising from the Riemann step problem is constructed and the key physical parameters (DSW edge speeds, lead soliton amplitude, intermediate shelf level) of all but one solution type are obtained in terms of the initial step data. The analytical results are shown to be in excellent agreement with results of direct numerical simulations.
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...
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
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-.
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.
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)
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.
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...
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....
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
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
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.
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...
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
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
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.
Bifurcations of transition states: Morse bifurcations
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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)
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
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...
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.
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 → ∞.
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
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
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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
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
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.
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.
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.
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.
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
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
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
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.)
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
Directory of Open Access Journals (Sweden)
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.
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
Double Hopf bifurcation in delay differential equations
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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...
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
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.
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 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 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
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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
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
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.
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.
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
Bifurcation analysis on a delayed SIS epidemic model with stage structure
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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.
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...
Bifurcations and Crises in a Shape Memory Oscillator
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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.
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
Heteroclinic Bifurcation Behaviors of a Duffing Oscillator with Delayed Feedback
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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.
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.
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.
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.
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
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.
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...
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.
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.
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.
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
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.
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.
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
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.
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
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.
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 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.
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.
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.
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
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.
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.
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.
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 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....
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.
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.
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....
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.
Global Hopf bifurcation analysis on a BAM neural network with delays
International Nuclear Information System (INIS)
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
Stability and Hopf Bifurcation Analysis on a Nonlinear Business Cycle Model
Directory of Open Access Journals (Sweden)
Liming Zhao
2016-01-01
Full Text Available This study begins with the establishment of a three-dimension business cycle model based on the condition of a fixed exchange rate. Using the established model, the reported study proceeds to describe and discuss the existence of the equilibrium and stability of the economic system near the equilibrium point as a function of the speed of market regulation and the degree of capital liquidity and a stable region is defined. In addition, the condition of Hopf bifurcation is discussed and the stability of a periodic solution, which is generated by the Hopf bifurcation and the direction of the Hopf bifurcation, is provided. Finally, a numerical simulation is provided to confirm the theoretical results. This study plays an important role in theoretical understanding of business cycle models and it is crucial for decision makers in formulating macroeconomic policies as detailed in the conclusions of this report.
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.
Simplest bifurcation diagrams for monotone families of vector fields on a torus
Baesens, C.; MacKay, R. S.
2018-06-01
In part 1, we prove that the bifurcation diagram for a monotone two-parameter family of vector fields on a torus has to be at least as complicated as the conjectured simplest one proposed in Baesens et al (1991 Physica D 49 387–475). To achieve this, we define ‘simplest’ by sequentially minimising the numbers of equilibria, Bogdanov–Takens points, closed curves of centre and of neutral saddle, intersections of curves of centre and neutral saddle, Reeb components, other invariant annuli, arcs of rotational homoclinic bifurcation of horizontal homotopy type, necklace points, contractible periodic orbits, points of neutral horizontal homoclinic bifurcation and half-plane fan points. We obtain two types of simplest case, including that initially proposed. In part 2, we analyse the bifurcation diagram for an explicit monotone family of vector fields on a torus and prove that it has at most two equilibria, precisely four Bogdanov–Takens points, no closed curves of centre nor closed curves of neutral saddle, at most two Reeb components, precisely four arcs of rotational homoclinic connection of ‘horizontal’ homotopy type, eight horizontal saddle-node loop points, two necklace points, four points of neutral horizontal homoclinic connection, and two half-plane fan points, and there is no simultaneous existence of centre and neutral saddle, nor contractible homoclinic connection to a neutral saddle. Furthermore, we prove that all saddle-nodes, Bogdanov–Takens points, non-neutral and neutral horizontal homoclinic bifurcations are non-degenerate and the Hopf condition is satisfied for all centres. We also find it has four points of degenerate Hopf bifurcation. It thus provides an example of a family satisfying all the assumptions of part 1 except the one of at most one contractible periodic orbit.
International Nuclear Information System (INIS)
Han, Renji; Dai, Binxiang
2017-01-01
Highlights: • We model general two-dimensional reaction-diffusion with nonlocal delay. • The existence of unique positive steady state is studied. • The bilinear form for the proposed system is given. • The existence, direction of Hopf bifurcation are given by symmetry method. - Abstract: A nonlocal delayed reaction-diffusive two-species model with Dirichlet boundary condition and general functional response is investigated in this paper. Based on the Lyapunov–Schmidt reduction, the existence, bifurcation direction and stability of Hopf bifurcating periodic orbits near the positive spatially nonhomogeneous steady-state solution are obtained, where the time delay is taken as the bifurcation parameter. Moreover, the general results are applied to a diffusive Lotka–Volterra type food-limited population model with nonlocal delay effect, and it is found that diffusion and nonlocal delay can also affect the other dynamic behavior of the system by numerical experiments.
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.
Impact adding bifurcation in an autonomous hybrid dynamical model of church bell
Brzeski, P.; Chong, A. S. E.; Wiercigroch, M.; Perlikowski, P.
2018-05-01
In this paper we present the bifurcation analysis of the yoke-bell-clapper system which corresponds to the biggest bell "Serce Lodzi" mounted in the Cathedral Basilica of St Stanislaus Kostka, Lodz, Poland. The mathematical model of the system considered in this work has been derived and verified based on measurements of dynamics of the real bell. We perform numerical analysis both by direct numerical integration and path-following method using toolbox ABESPOL (Chong, 2016). By introducing the active yoke the position of the bell-clapper system with respect to the yoke axis of rotation can be easily changed and it can be used to probe the system dynamics. We found a wide variety of periodic and non-periodic solutions, and examined the ranges of coexistence of solutions and transitions between them via different types of bifurcations. Finally, a new type of bifurcation induced by a grazing event - an "impact adding bifurcation" has been proposed. When it occurs, the number of impacts between the bell and the clapper is increasing while the period of the system's motion stays the same.
Bifurcation and chaos in high-frequency peak current mode Buck converter
Chang-Yuan, Chang; Xin, Zhao; Fan, Yang; Cheng-En, Wu
2016-07-01
Bifurcation and chaos in high-frequency peak current mode Buck converter working in continuous conduction mode (CCM) are studied in this paper. First of all, the two-dimensional discrete mapping model is established. Next, reference current at the period-doubling point and the border of inductor current are derived. Then, the bifurcation diagrams are drawn with the aid of MATLAB. Meanwhile, circuit simulations are executed with PSIM, and time domain waveforms as well as phase portraits in i L-v C plane are plotted with MATLAB on the basis of simulation data. After that, we construct the Jacobian matrix and analyze the stability of the system based on the roots of characteristic equations. Finally, the validity of theoretical analysis has been verified by circuit testing. The simulation and experimental results show that, with the increase of reference current I ref, the corresponding switching frequency f is approaching to low-frequency stage continuously when the period-doubling bifurcation happens, leading to the converter tending to be unstable. With the increase of f, the corresponding I ref decreases when the period-doubling bifurcation occurs, indicating the stable working range of the system becomes smaller. Project supported by the National Natural Science Foundation of China (Grant No. 61376029), the Fundamental Research Funds for the Central Universities, China, and the College Graduate Research and Innovation Program of Jiangsu Province, China (Grant No. SJLX15_0092).
Stochastic bifurcation in a model of love with colored noise
Yue, Xiaokui; Dai, Honghua; Yuan, Jianping
2015-07-01
In this paper, we wish to examine the stochastic bifurcation induced by multiplicative Gaussian colored noise in a dynamical model of love where the random factor is used to describe the complexity and unpredictability of psychological systems. First, the dynamics in deterministic love-triangle model are considered briefly including equilibrium points and their stability, chaotic behaviors and chaotic attractors. Then, the influences of Gaussian colored noise with different parameters are explored such as the phase plots, top Lyapunov exponents, stationary probability density function (PDF) and stochastic bifurcation. The stochastic P-bifurcation through a qualitative change of the stationary PDF will be observed and bifurcation diagram on parameter plane of correlation time and noise intensity is presented to find the bifurcation behaviors in detail. Finally, the top Lyapunov exponent is computed to determine the D-bifurcation when the noise intensity achieves to a critical value. By comparison, we find there is no connection between two kinds of stochastic bifurcation.
Bifurcation Behavior Analysis in a Predator-Prey Model
Directory of Open Access Journals (Sweden)
Nan Wang
2016-01-01
Full Text Available A predator-prey model is studied mathematically and numerically. The aim is to explore how some key factors influence dynamic evolutionary mechanism of steady conversion and bifurcation behavior in predator-prey model. The theoretical works have been pursuing the investigation of the existence and stability of the equilibria, as well as the occurrence of bifurcation behaviors (transcritical bifurcation, saddle-node bifurcation, and Hopf bifurcation, which can deduce a standard parameter controlled relationship and in turn provide a theoretical basis for the numerical simulation. Numerical analysis ensures reliability of the theoretical results and illustrates that three stable equilibria will arise simultaneously in the model. It testifies the existence of Bogdanov-Takens bifurcation, too. It should also be stressed that the dynamic evolutionary mechanism of steady conversion and bifurcation behavior mainly depend on a specific key parameter. In a word, all these results are expected to be of use in the study of the dynamic complexity of ecosystems.
Directory of Open Access Journals (Sweden)
He Lin
2016-01-01
Full Text Available This study considers the bifurcation evolutions for a combining spiral gear transmission through parameter domain structure analysis. The system nonlinear vibration equations are created with piecewise backlash and general errors. Gill’s numerical integration algorithm is implemented in calculating the vibration equation sets. Based on cell-mapping method (CMM, two-dimensional dynamic domain planes have been developed and primarily focused on the parameters of backlash, transmission error, mesh frequency and damping ratio, and so forth. Solution demonstrates that Period-doubling bifurcation happens as the mesh frequency increases; moreover nonlinear discontinuous jump breaks the periodic orbit and also turns the periodic state into chaos suddenly. In transmission error planes, three cell groups which are Period-1, Period-4, and Chaos have been observed, and the boundary cells are the sensitive areas to dynamic response. Considering the parameter planes which consist of damping ratio associated with backlash, transmission error, mesh stiffness, and external load, the solution domain structure reveals that the system step into chaos undergoes Period-doubling cascade with Period-2m (m: integer periodic regions. Direct simulations to obtain the bifurcation diagram and largest Lyapunov exponent (LE match satisfactorily with the parameter domain solutions.
Gritli, Hassène; Belghith, Safya
2017-06-01
An analysis of the passive dynamic walking of a compass-gait biped model under the OGY-based control approach using the impulsive hybrid nonlinear dynamics is presented in this paper. We describe our strategy for the development of a simplified analytical expression of a controlled hybrid Poincaré map and then for the design of a state-feedback control. Our control methodology is based mainly on the linearization of the impulsive hybrid nonlinear dynamics around a desired nominal one-periodic hybrid limit cycle. Our analysis of the controlled walking dynamics is achieved by means of bifurcation diagrams. Some interesting nonlinear phenomena are displayed, such as the period-doubling bifurcation, the cyclic-fold bifurcation, the period remerging, the period bubbling and chaos. A comparison between the raised phenomena in the impulsive hybrid nonlinear dynamics and the hybrid Poincaré map under control was also presented.
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).
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.
Experimental Study of Flow in a Bifurcation
Fresconi, Frank; Prasad, Ajay
2003-11-01
An instability known as the Dean vortex occurs in curved pipes with a longitudinal pressure gradient. A similar effect is manifest in the flow in a converging or diverging bifurcation, such as those found in the human respiratory airways. The goal of this study is to characterize secondary flows in a bifurcation. Particle image velocimetry (PIV) and laser-induced fluorescence (LIF) experiments were performed in a clear, plastic model. Results show the strength and migration of secondary vortices. Primary velocity features are also presented along with dispersion patterns from dye visualization. Unsteadiness, associated with a hairpin vortex, was also found at higher Re. This work can be used to assess the dispersion of particles in the lung. Medical delivery systems and pollution effect studies would profit from such an understanding.
Bifurcations and chaos of DNA solitonic dynamics
International Nuclear Information System (INIS)
Gonzalez, J.A.; Martin-Landrove, M.; Carbo, J.R.; Chacon, M.
1994-09-01
We investigated the nonlinear DNA torsional equations proposed by Yakushevich in the presence of damping and external torques. Analytical expressions for some solutions are obtained in the case of the isolated chain. Special attention is paid to the stability of the solutions and the range of soliton interaction in the general case. The bifurcation analysis is performed and prediction of chaos is obtained for some set of parameters. Some biological implications are suggested. (author). 11 refs, 13 figs
Torus bifurcations in multilevel converter systems
DEFF Research Database (Denmark)
Zhusubaliyev, Zhanybai T.; Mosekilde, Erik; Yanochkina, Olga O.
2011-01-01
embedded one into the other and with their basins of attraction delineated by intervening repelling tori. The paper illustrates the coexistence of three stable tori with different resonance behaviors and shows how reconstruction of these tori takes place across the borders of different dynamical regimes....... The paper also demonstrates how pairs of attracting and repelling tori emerge through border-collision torus-birth and border-collision torus-fold bifurcations. © 2011 World Scientific Publishing Company....
Sex differences in intracranial arterial bifurcations
DEFF Research Database (Denmark)
Lindekleiv, Haakon M; Valen-Sendstad, Kristian; Morgan, Michael K
2010-01-01
Subarachnoid hemorrhage (SAH) is a serious condition, occurring more frequently in females than in males. SAH is mainly caused by rupture of an intracranial aneurysm, which is formed by localized dilation of the intracranial arterial vessel wall, usually at the apex of the arterial bifurcation. T....... The female preponderance is usually explained by systemic factors (hormonal influences and intrinsic wall weakness); however, the uneven sex distribution of intracranial aneurysms suggests a possible physiologic factor-a local sex difference in the intracranial arteries....
Drift bifurcation detection for dissipative solitons
International Nuclear Information System (INIS)
Liehr, A W; Boedeker, H U; Roettger, M C; Frank, T D; Friedrich, R; Purwins, H-G
2003-01-01
We report on the experimental detection of a drift bifurcation for dissipative solitons, which we observe in the form of current filaments in a planar semiconductor-gas-discharge system. By introducing a new stochastic data analysis technique we find that due to a change of system parameters the dissipative solitons undergo a transition from purely noise-driven objects with Brownian motion to particles with a dynamically stabilized finite velocity
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.
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.
Discontinuous bifurcation and coexistence of attractors in a piecewise linear map with a gap
International Nuclear Information System (INIS)
Qu Shixian; Lu Yongzhi; Zhang Lin; He Daren
2008-01-01
Coexistence of attractors with striking characteristics is observed in this work, where a stable period-5 attractor coexists successively with chaotic band-11, period-6, chaotic band-12 and band-6 attractors. They are induced by different mechanisms due to the interaction between the discontinuity and the non-invertibility. A characteristic boundary collision bifurcation, is observed. The critical conditions are obtained both analytically and numerically. (general)
Energized Oxygen : Speiser Current Sheet Bifurcation
George, D. E.; Jahn, J. M.
2017-12-01
A single population of energized Oxygen (O+) is shown to produce a cross-tail bifurcated current sheet in 2.5D PIC simulations of the magnetotail without the influence of magnetic reconnection. Treatment of oxygen in simulations of space plasmas, specifically a magnetotail current sheet, has been limited to thermal energies despite observations of and mechanisms which explain energized ions. We performed simulations of a homogeneous oxygen background, that has been energized in a physically appropriate manner, to study the behavior of current sheets and magnetic reconnection, specifically their bifurcation. This work uses a 2.5D explicit Particle-In-a-Cell (PIC) code to investigate the dynamics of energized heavy ions as they stream Dawn-to-Dusk in the magnetotail current sheet. We present a simulation study dealing with the response of a current sheet system to energized oxygen ions. We establish a, well known and studied, 2-species GEM Challenge Harris current sheet as a starting point. This system is known to eventually evolve and produce magnetic reconnection upon thinning of the current sheet. We added a uniform distribution of thermal O+ to the background. This 3-species system is also known to eventually evolve and produce magnetic reconnection. We add one additional variable to the system by providing an initial duskward velocity to energize the O+. We also traced individual particle motion within the PIC simulation. Three main results are shown. First, energized dawn- dusk streaming ions are clearly seen to exhibit sustained Speiser motion. Second, a single population of heavy ions clearly produces a stable bifurcated current sheet. Third, magnetic reconnection is not required to produce the bifurcated current sheet. Finally a bifurcated current sheet is compatible with the Harris current sheet model. This work is the first step in a series of investigations aimed at studying the effects of energized heavy ions on magnetic reconnection. This work differs
Experimental observation of parametric effects near period doubling in a loss-modulated CO2 laser
Chizhevsky, V. N.
1996-01-01
A number of parametric effects, such as suppression of period doubling, shift of the bifurcation point, scaling law relating the shift and the perturbation amplitude, influence of the detuning on the suppression, reaching of the maximum gain between the original and shifted bifurcation points, and scaling law for idler power are experimentally observed near period doubling bifurcation in a loss-driven CO2 laser that is subjected to periodic loss perturbations at a frequency that is close to a...
Passive band-gap reconfiguration born from bifurcation asymmetry.
Bernard, Brian P; Mann, Brian P
2013-11-01
Current periodic structures are constrained to have fixed energy transmission behavior unless active control or component replacement is used to alter their wave propagation characteristics. The introduction of nonlinearity to generate multiple stable equilibria is an alternative strategy for realizing distinct energy propagation behaviors. We investigate the creation of a reconfigurable band-gap system by implementing passive switching between multiple stable states of equilibrium, to alter the level of energy attenuation in response to environmental stimuli. The ability to avoid potentially catastrophic loads is demonstrated by tailoring the bandpass and band-gap regions to coalesce for two stable equilibria and varying an external load parameter to trigger a bifurcation. The proposed phenomenon could be utilized in remote or autonomous applications where component modifications and active control are impractical.
Global Bifurcation of a Novel Computer Virus Propagation Model
Directory of Open Access Journals (Sweden)
Jianguo Ren
2014-01-01
Full Text Available In a recent paper by J. Ren et al. (2012, a novel computer virus propagation model under the effect of the antivirus ability in a real network is established. The analysis there only partially uncovers the dynamics behaviors of virus spread over the network in the case where around bifurcation is local. In the present paper, by mathematical analysis, it is further shown that, under appropriate parameter values, the model may undergo a global B-T bifurcation, and the curves of saddle-node bifurcation, Hopf bifurcation, and homoclinic bifurcation are obtained to illustrate the qualitative behaviors of virus propagation. On this basis, a collection of policies is recommended to prohibit the virus prevalence. To our knowledge, this is the first time the global bifurcation has been explored for the computer virus propagation. Theoretical results and corresponding suggestions may help us suppress or eliminate virus propagation in the network.
Nonlinear physical systems spectral analysis, stability and bifurcations
Kirillov, Oleg N
2013-01-01
Bringing together 18 chapters written by leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics, this book presents state-of-the-art approaches to a wide spectrum of new and challenging stability problems.Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations focuses on problems of spectral analysis, stability and bifurcations arising in the nonlinear partial differential equations of modern physics. Bifurcations and stability of solitary waves, geometrical optics stability analysis in hydro- and magnetohydrodynam
Bifurcation of rupture path by linear and cubic damping force
Dennis L. C., C.; Chew X., Y.; Lee Y., C.
2014-06-01
Bifurcation of rupture path is studied for the effect of linear and cubic damping. Momentum equation with Rayleigh factor was transformed into ordinary differential form. Bernoulli differential equation was obtained and solved by the separation of variables. Analytical or exact solutions yielded the bifurcation was visible at imaginary part when the wave was non dispersive. For the dispersive wave, bifurcation of rupture path was invisible.
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...
Predicting bifurcation angle effect on blood flow in the microvasculature.
Yang, Jiho; Pak, Y Eugene; Lee, Tae-Rin
2016-11-01
Since blood viscosity is a basic parameter for understanding hemodynamics in human physiology, great amount of research has been done in order to accurately predict this highly non-Newtonian flow property. However, previous works lacked in consideration of hemodynamic changes induced by heterogeneous vessel networks. In this paper, the effect of bifurcation on hemodynamics in a microvasculature is quantitatively predicted. The flow resistance in a single bifurcation microvessel was calculated by combining a new simple mathematical model with 3-dimensional flow simulation for varying bifurcation angles under physiological flow conditions. Interestingly, the results indicate that flow resistance induced by vessel bifurcation holds a constant value of approximately 0.44 over the whole single bifurcation model below diameter of 60μm regardless of geometric parameters including bifurcation angle. Flow solutions computed from this new model showed substantial decrement in flow velocity relative to other mathematical models, which do not include vessel bifurcation effects, while pressure remained the same. Furthermore, when applying the bifurcation angle effect to the entire microvascular network, the simulation results gave better agreements with recent in vivo experimental measurements. This finding suggests a new paradigm in microvascular blood flow properties, that vessel bifurcation itself, regardless of its angle, holds considerable influence on blood viscosity, and this phenomenon will help to develop new predictive tools in microvascular research. Copyright © 2016 Elsevier Inc. All rights reserved.
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.
Bifurcation theory for toroidal MHD instabilities
International Nuclear Information System (INIS)
Maschke, E.K.; Morros Tosas, J.; Urquijo, G.
1992-01-01
Using a general representation of magneto-hydrodynamics in terms of stream functions and potentials, proposed earlier, a set of reduced MHD equations for the case of toroidal geometry had been derived by an appropriate ordering with respect to the inverse aspect ratio. When all dissipative terms are neglected in this reduced system, it has the same linear stability limits as the full ideal MHD equations, to the order considered. When including resistivity, thermal conductivity and viscosity, we can apply bifurcation theory to investigate nonlinear stationary solution branches related to various instabilities. In particular, we show that a stationary solution of the internal kink type can be found
Spijkerboer, T.P.
2017-01-01
The externalization of European migration policy has resulted in a bifurcation of global human mobility, which is divided along a North/South axis. In two judgments, the EU Court of Justice was confronted with cases challenging the exclusion of Syrian refugees from Europe. These cases concern core
Study of intermittent bifurcations and chaos in boost PFC converters by nonlinear discrete models
International Nuclear Information System (INIS)
Zhang Hao; Ma Xikui; Xue Bianling; Liu Weizeng
2005-01-01
This paper mainly deals with nonlinear phenomena like intermittent bifurcations and chaos in boost PFC converters under peak-current control mode. Two nonlinear models in the form of discrete maps are derived to describe precisely the nonlinear dynamics of boost PFC converters from two points of view, i.e., low- and high-frequency regimes. Based on the presented discrete models, both the evolution of intermittent behavior and the periodicity of intermittency are investigated in detail from the fast and slow-scale aspects, respectively. Numerical results show that the occurrence of intermittent bifurcations and chaos with half one line period is one of the most distinguished dynamical characteristics. Finally, we make some instructive conclusions, which prove to be helpful in improving the performances of practical circuits
Bifurcation into functional niches in adaptation.
White, Justin S; Adami, Christoph
2004-01-01
One of the central questions in evolutionary biology concerns the dynamics of adaptation and diversification. This issue can be addressed experimentally if replicate populations adapting to identical environments can be investigated in detail. We have studied 501 such replicas using digital organisms adapting to at least two fundamentally different functional niches (survival strategies) present in the same environment: one in which fast replication is the way to live, and another where exploitation of the environment's complexity leads to complex organisms with longer life spans and smaller replication rates. While these two modes of survival are closely analogous to those expected to emerge in so-called r and K selection scenarios respectively, the bifurcation of evolutionary histories according to these functional niches occurs in identical environments, under identical selective pressures. We find that the branching occurs early, and leads to drastic phenotypic differences (in fitness, sequence length, and gestation time) that are permanent and irreversible. This study confirms an earlier experimental effort using microorganisms, in that diversification can be understood at least in part in terms of bifurcations on saddle points leading to peak shifts, as in the picture drawn by Sewall Wright.
Bifurcations and chaos of classical trajectories in a deformed nuclear potential
International Nuclear Information System (INIS)
Carbonell, J.; Arvieu, R.
1983-01-01
The organization of the phase space of a classical nucleon in an axially symmetric deformed potential with the restriction Lsub(z)=0 is studied by drawing the Poincare surfaces of section. In the limit of small deformations three simple limits help to understand this organization. Moreover important bifurcations of periodic trajectories occur. At higher deformations multifurcations and chaos are observed. Chaos is developed to a larger extent in the heavier nuclei. (author)
Analysis of Vehicle Steering and Driving Bifurcation Characteristics
Directory of Open Access Journals (Sweden)
Xianbin Wang
2015-01-01
Full Text Available The typical method of vehicle steering bifurcation analysis is based on the nonlinear autonomous vehicle model deriving from the classic two degrees of freedom (2DOF linear vehicle model. This method usually neglects the driving effect on steering bifurcation characteristics. However, in the steering and driving combined conditions, the tyre under different driving conditions can provide different lateral force. The steering bifurcation mechanism without the driving effect is not able to fully reveal the vehicle steering and driving bifurcation characteristics. Aiming at the aforementioned problem, this paper analyzed the vehicle steering and driving bifurcation characteristics with the consideration of driving effect. Based on the 5DOF vehicle system dynamics model with the consideration of driving effect, the 7DOF autonomous system model was established. The vehicle steering and driving bifurcation dynamic characteristics were analyzed with different driving mode and driving torque. Taking the front-wheel-drive system as an example, the dynamic evolution process of steering and driving bifurcation was analyzed by phase space, system state variables, power spectral density, and Lyapunov index. The numerical recognition results of chaos were also provided. The research results show that the driving mode and driving torque have the obvious effect on steering and driving bifurcation characteristics.
Sediment discharge division at two tidally influenced river bifurcations
Sassi, M.G.; Hoitink, A.J.F.; Vermeulen, B.; Hidayat, H.
2013-01-01
[1] We characterize and quantify the sediment discharge division at two tidally influenced river bifurcations in response to mean flow and secondary circulation by employing a boat-mounted acoustic Doppler current profiler (ADCP), to survey transects at bifurcating branches during a semidiurnal
Views on the Hopf bifurcation with respect to voltage instabilities
Energy Technology Data Exchange (ETDEWEB)
Roa-Sepulveda, C A [Universidad de Concepcion, Concepcion (Chile). Dept. de Ingenieria Electrica; Knight, U G [Imperial Coll. of Science and Technology, London (United Kingdom). Dept. of Electrical and Electronic Engineering
1994-12-31
This paper presents a sensitivity study of the Hopf bifurcation phenomenon which can in theory appear in power systems, with reference to the dynamics of the process and the impact of demand characteristics. Conclusions are drawn regarding power levels at which these bifurcations could appear and concern the concept of the imaginary axis as a `hard` limit eigenvalue analyses. (author) 20 refs., 31 figs.
Numerical bifurcation analysis of a class of nonlinear renewal equations
Breda, Dimitri; Diekmann, Odo; Liessi, Davide; Scarabel, Francesca
2016-01-01
We show, by way of an example, that numerical bifurcation tools for ODE yield reliable bifurcation diagrams when applied to the pseudospectral approximation of a one-parameter family of nonlinear renewal equations. The example resembles logistic-and Ricker-type population equations and exhibits
Li, Chengxian; Liu, Haihong; Zhang, Tonghua; Yan, Fang
2017-12-01
In this paper, a gene regulatory network mediated by small noncoding RNA involving two time delays and diffusion under the Neumann boundary conditions is studied. Choosing the sum of delays as the bifurcation parameter, the stability of the positive equilibrium and the existence of spatially homogeneous and spatially inhomogeneous periodic solutions are investigated by analyzing the corresponding characteristic equation. It is shown that the sum of delays can induce Hopf bifurcation and the diffusion incorporated into the system can effect the amplitude of periodic solutions. Furthermore, the spatially homogeneous periodic solution always exists and the spatially inhomogeneous periodic solution will arise when the diffusion coefficients of protein and mRNA are suitably small. Particularly, the small RNA diffusion coefficient is more robust and its effect on model is much less than protein and mRNA. Finally, the explicit formulae for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by employing the normal form theory and center manifold theorem for partial functional differential equations. Finally, numerical simulations are carried out to illustrate our theoretical analysis.
Bifurcation diagram of a cubic three-parameter autonomous system
Directory of Open Access Journals (Sweden)
Lenka Barakova
2005-07-01
Full Text Available In this paper, we study the cubic three-parameter autonomous planar system $$displaylines{ dot x_1 = k_1 + k_2x_1 - x_1^3 - x_2,cr dot x_2 = k_3 x_1 - x_2, }$$ where $k_2, k_3$ are greater than 0. Our goal is to obtain a bifurcation diagram; i.e., to divide the parameter space into regions within which the system has topologically equivalent phase portraits and to describe how these portraits are transformed at the bifurcation boundaries. Results may be applied to the macroeconomical model IS-LM with Kaldor's assumptions. In this model existence of a stable limit cycles has already been studied (Andronov-Hopf bifurcation. We present the whole bifurcation diagram and among others, we prove existence of more difficult bifurcations and existence of unstable cycles.
Critical bifurcation surfaces of 3D discrete dynamics
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Michael Sonis
2000-01-01
Full Text Available This paper deals with the analytical representation of bifurcations of each 3D discrete dynamics depending on the set of bifurcation parameters. The procedure of bifurcation analysis proposed in this paper represents the 3D elaboration and specification of the general algorithm of the n-dimensional linear bifurcation analysis proposed by the author earlier. It is proven that 3D domain of asymptotic stability (attraction of the fixed point for a given 3D discrete dynamics is bounded by three critical bifurcation surfaces: the divergence, flip and flutter surfaces. The analytical construction of these surfaces is achieved with the help of classical Routh–Hurvitz conditions of asymptotic stability. As an application the adjustment process proposed by T. Puu for the Cournot oligopoly model is considered in detail.
Bifurcation of transition paths induced by coupled bistable systems.
Tian, Chengzhe; Mitarai, Namiko
2016-06-07
We discuss the transition paths in a coupled bistable system consisting of interacting multiple identical bistable motifs. We propose a simple model of coupled bistable gene circuits as an example and show that its transition paths are bifurcating. We then derive a criterion to predict the bifurcation of transition paths in a generalized coupled bistable system. We confirm the validity of the theory for the example system by numerical simulation. We also demonstrate in the example system that, if the steady states of individual gene circuits are not changed by the coupling, the bifurcation pattern is not dependent on the number of gene circuits. We further show that the transition rate exponentially decreases with the number of gene circuits when the transition path does not bifurcate, while a bifurcation facilitates the transition by lowering the quasi-potential energy barrier.
Hopf Bifurcation of Compound Stochastic van der Pol System
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Shaojuan Ma
2016-01-01
Full Text Available Hopf bifurcation analysis for compound stochastic van der Pol system with a bound random parameter and Gaussian white noise is investigated in this paper. By the Karhunen-Loeve (K-L expansion and the orthogonal polynomial approximation, the equivalent deterministic van der Pol system can be deduced. Based on the bifurcation theory of nonlinear deterministic system, the critical value of bifurcation parameter is obtained and the influence of random strength δ and noise intensity σ on stochastic Hopf bifurcation in compound stochastic system is discussed. At last we found that increased δ can relocate the critical value of bifurcation parameter forward while increased σ makes it backward and the influence of δ is more sensitive than σ. The results are verified by numerical simulations.
Bifurcations and chaos of a vibration isolation system with magneto-rheological damper
Energy Technology Data Exchange (ETDEWEB)
Zhang, Hailong [Magneto-electronics Lab, School of Physics and Technology, Nanjing Normal University, Nanjing 210046 (China); Vibration Control Lab, School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210042 (China); Zhang, Ning [Magneto-electronics Lab, School of Physics and Technology, Nanjing Normal University, Nanjing 210046 (China); Min, Fuhong; Yan, Wei; Wang, Enrong, E-mail: erwang@njnu.edu.cn [Vibration Control Lab, School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210042 (China)
2016-03-15
Magneto-rheological (MR) damper possesses inherent hysteretic characteristics. We investigate the resulting nonlinear behaviors of a two degree-of-freedom (2-DoF) MR vibration isolation system under harmonic external excitation. A MR damper is identified by employing the modified Bouc-wen hysteresis model. By numerical simulation, we characterize the nonlinear dynamic evolution of period-doubling, saddle node bifurcating and inverse period-doubling using bifurcation diagrams of variations in frequency with a fixed amplitude of the harmonic excitation. The strength of chaos is determined by the Lyapunov exponent (LE) spectrum. Semi-physical experiment on the 2-DoF MR vibration isolation system is proposed. We trace the time history and phase trajectory under certain values of frequency of the harmonic excitation to verify the nonlinear dynamical evolution of period-doubling bifurcations to chaos. The largest LEs computed with the experimental data are also presented, confirming the chaotic motion in the experiment. We validate the chaotic motion caused by the hysteresis of the MR damper, and show the transitions between distinct regimes of stable motion and chaotic motion of the 2-DoF MR vibration isolation system for variations in frequency of external excitation.
Bifurcations and chaos of a vibration isolation system with magneto-rheological damper
Directory of Open Access Journals (Sweden)
Hailong Zhang
2016-03-01
Full Text Available Magneto-rheological (MR damper possesses inherent hysteretic characteristics. We investigate the resulting nonlinear behaviors of a two degree-of-freedom (2-DoF MR vibration isolation system under harmonic external excitation. A MR damper is identified by employing the modified Bouc-wen hysteresis model. By numerical simulation, we characterize the nonlinear dynamic evolution of period-doubling, saddle node bifurcating and inverse period-doubling using bifurcation diagrams of variations in frequency with a fixed amplitude of the harmonic excitation. The strength of chaos is determined by the Lyapunov exponent (LE spectrum. Semi-physical experiment on the 2-DoF MR vibration isolation system is proposed. We trace the time history and phase trajectory under certain values of frequency of the harmonic excitation to verify the nonlinear dynamical evolution of period-doubling bifurcations to chaos. The largest LEs computed with the experimental data are also presented, confirming the chaotic motion in the experiment. We validate the chaotic motion caused by the hysteresis of the MR damper, and show the transitions between distinct regimes of stable motion and chaotic motion of the 2-DoF MR vibration isolation system for variations in frequency of external excitation.
Topological chaos, braiding and bifurcation of almost-cyclic sets.
Grover, Piyush; Ross, Shane D; Stremler, Mark A; Kumar, Pankaj
2012-12-01
In certain two-dimensional time-dependent flows, the braiding of periodic orbits provides a way to analyze chaos in the system through application of the Thurston-Nielsen classification theorem (TNCT). We expand upon earlier work that introduced the application of the TNCT to braiding of almost-cyclic sets, which are individual components of almost-invariant sets [Stremler et al., "Topological chaos and periodic braiding of almost-cyclic sets," Phys. Rev. Lett. 106, 114101 (2011)]. In this context, almost-cyclic sets are periodic regions in the flow with high local residence time that act as stirrers or "ghost rods" around which the surrounding fluid appears to be stretched and folded. In the present work, we discuss the bifurcation of the almost-cyclic sets as a system parameter is varied, which results in a sequence of topologically distinct braids. We show that, for Stokes' flow in a lid-driven cavity, these various braids give good lower bounds on the topological entropy over the respective parameter regimes in which they exist. We make the case that a topological analysis based on spatiotemporal braiding of almost-cyclic sets can be used for analyzing chaos in fluid flows. Hence, we further develop a connection between set-oriented statistical methods and topological methods, which promises to be an important analysis tool in the study of complex systems.
Climate bifurcation during the last deglaciation?
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T. M. Lenton
2012-07-01
Full Text Available There were two abrupt warming events during the last deglaciation, at the start of the Bølling-Allerød 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 loses its stability and the climate tips into an alternative state, providing an early warning signal in the form of slowing responses to perturbations, which may be accompanied by increasing variability. Alternatively, short-term stochastic variability in the climate system can trigger abrupt climate changes, without early warning. Previous work has found signals consistent with slowing down during the last deglaciation as a whole, and during the Younger Dryas, but with conflicting results in the run-up to the Bølling-Allerød. Based on this, we hypothesise that a bifurcation point was approached at the end of the Younger Dryas, in which the cold climate state, with weak Atlantic overturning circulation, lost its stability, and the climate tipped irreversibly into a warm interglacial state. To test the bifurcation hypothesis, we analysed two different climate proxies in three Greenland ice cores, from the Last Glacial Maximum to the end of the Younger Dryas. Prior to the Bølling warming, there was a robust increase in climate variability but no consistent slowing down signal, suggesting this abrupt change was probably triggered by a stochastic fluctuation. The transition to the warm Bølling-Allerød state was accompanied by a slowing down in climate dynamics and an increase in climate variability. We suggest that the Bølling warming excited an internal mode of variability in Atlantic meridional overturning circulation strength, causing multi-centennial climate fluctuations. However, the return to the Younger Dryas cold state increased climate stability. We find no consistent evidence for slowing down during the Younger Dryas, or in a longer
Raskin, Daniel; Khaitovich, Boris; Balan, Shmuel; Silverberg, Daniel; Halak, Moshe; Rimon, Uri
2018-01-01
To assess the technical success of the Outback reentry device in contralateral versus ipsilateral approaches for femoropopliteal arterial occlusion. A retrospective review of patients treated for critical limb ischemia (CLI) using the Outback between January 2013 and July 2016 was performed. Age, gender, length and site of the occlusion, approach site, aortic bifurcation angle, and reentry site were recorded. Calcification score was assigned at both aortic bifurcation and reentry site. Technical success was assessed. During the study period, a total of 1300 endovascular procedures were performed on 489 patients for CLI. The Outback was applied on 50 femoropopliteal chronic total occlusions. Thirty-nine contralateral and 11 ipsilateral antegrade femoral were accessed. The device was used successfully in 41 patients (82%). There were nine failures, all in the contralateral approach group. Six due to inability to deliver the device due to acute aortic bifurcation angle and three due to failure to achieve luminal reentry. Procedural success was significantly affected by the aortic bifurcation angle (p = 0.013). The Outback has high technical success rates in treatment of femoropopliteal occlusion, when applied from either an ipsi- or contralateral approach. When applied in contralateral access, acute aortic bifurcation angle predicts procedural failure.
Bifurcations and Patterns in Nonlinear Dissipative Systems
Energy Technology Data Exchange (ETDEWEB)
Guenter Ahlers
2005-05-27
This project consists of experimental investigations of heat transport, pattern formation, and bifurcation phenomena in non-linear non-equilibrium fluid-mechanical systems. These issues are studies in Rayleigh-B\\'enard convection, using both pure and multicomponent fluids. They are of fundamental scientific interest, but also play an important role in engineering, materials science, ecology, meteorology, geophysics, and astrophysics. For instance, various forms of convection are important in such diverse phenomena as crystal growth from a melt with or without impurities, energy production in solar ponds, flow in the earth's mantle and outer core, geo-thermal stratifications, and various oceanographic and atmospheric phenomena. Our work utilizes computer-enhanced shadowgraph imaging of flow patterns, sophisticated digital image analysis, and high-resolution heat transport measurements.
The bifurcations of nearly flat origami
Santangelo, Christian
Self-folding origami structures provide one means of fabricating complex, three-dimensional structures from a flat, two-dimensional sheet. Self-folding origami structures have been fabricated on scales ranging from macroscopic to microscopic and can have quite complicated structures with hundreds of folds arranged in complex patterns. I will describe our efforts to understand the mechanics and energetics of self-folding origami structures. Though the dimension of the configuration space of an origami structure scales with the size of the boundary and not with the number of vertices in the interior of the structure, a typical origami structure is also floppy in the sense that there are many possible ways to assign fold angles consistently. I will discuss our theoretical progress in understanding the geometry of the configuration space of origami. For random origami, the number of possible bifurcations grows surprisingly quickly even when the dimension of the configuration space is small. EFRI ODISSEI-1240441, DMR-0846582.
Transport Bifurcation in a Rotating Tokamak Plasma
International Nuclear Information System (INIS)
Highcock, E. G.; Barnes, M.; Schekochihin, A. A.; Parra, F. I.; Roach, C. M.; Cowley, S. C.
2010-01-01
The effect of flow shear on turbulent transport in tokamaks is studied numerically in the experimentally relevant limit of zero magnetic shear. It is found that the plasma is linearly stable for all nonzero flow shear values, but that subcritical turbulence can be sustained nonlinearly at a wide range of temperature gradients. Flow shear increases the nonlinear temperature gradient threshold for turbulence but also increases the sensitivity of the heat flux to changes in the temperature gradient, except over a small range near the threshold where the sensitivity is decreased. A bifurcation in the equilibrium gradients is found: for a given input of heat, it is possible, by varying the applied torque, to trigger a transition to significantly higher temperature and flow gradients.
Bifurcated SEN with Fluid Flow Conditioners
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F. Rivera-Perez
2014-01-01
Full Text Available This work evaluates the performance of a novel design for a bifurcated submerged entry nozzle (SEN used for the continuous casting of steel slabs. The proposed design incorporates fluid flow conditioners attached on SEN external wall. The fluid flow conditioners impose a pseudosymmetric pattern in the upper zone of the mold by inhibiting the fluid exchange between the zones created by conditioners. The performance of the SEN with fluid flow conditioners is analyzed through numerical simulations using the CFD technique. Numerical results were validated by means of physical simulations conducted on a scaled cold water model. Numerical and physical simulations confirmed that the performance of the proposed SEN is superior to a traditional one. Fluid flow conditioners reduce the liquid free surface fluctuations and minimize the occurrence of vortexes at the free surface.
Oscillatory bifurcation for semilinear ordinary differential equations
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Tetsutaro Shibata
2016-06-01
\\] where $f(u = u + (1/2\\sin^k u$ ($k \\ge 2$ and $\\lambda > 0$ is a bifurcation parameter. It is known that $\\lambda$ is parameterized by the maximum norm $\\alpha = \\Vert u_\\lambda\\Vert_\\infty$ of the solution $u_\\lambda$ associated with $\\lambda$ and is written as $\\lambda = \\lambda(k,\\alpha$. When we focus on the asymptotic behavior of $\\lambda(k,\\alpha$ as $\\alpha \\to \\infty$, it is natural to expect that $\\lambda(k, \\alpha \\to \\pi^2/4$, and its convergence rate is common to $k$. Contrary to this expectation, we show that $\\lambda(2n_1+1,\\alpha$ tends to $\\pi^2/4$ faster than $\\lambda(2n_2,\\alpha$ as $\\alpha \\to \\infty$, where $n_1\\ge 1,\\ n_2 \\ge 1$ are arbitrary given integers.
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available We consider a simplified bidirectional associated memory (BAM neural network model with four neurons and multiple time delays. The global existence of periodic solutions bifurcating from Hopf bifurcations is investigated by applying the global Hopf bifurcation theorem due to Wu and Bendixson's criterion for high-dimensional ordinary differential equations due to Li and Muldowney. It is shown that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of the sum of two delays. Numerical simulations supporting the theoretical analysis are also included.
Clausius entropy for arbitrary bifurcate null surfaces
International Nuclear Information System (INIS)
Baccetti, Valentina; Visser, Matt
2014-01-01
Jacobson’s thermodynamic derivation of the Einstein equations was originally applied only to local Rindler horizons. But at least some parts of that construction can usefully be extended to give meaningful results for arbitrary bifurcate null surfaces. As presaged in Jacobson’s original article, this more general construction sharply brings into focus the questions: is entropy objectively ‘real’? Or is entropy in some sense subjective and observer-dependent? These innocent questions open a Pandora’s box of often inconclusive debate. A consensus opinion, though certainly not universally held, seems to be that Clausius entropy (thermodynamic entropy, defined via a Clausius relation dS=đQ/T) should be objectively real, but that the ontological status of statistical entropy (Shannon or von Neumann entropy) is much more ambiguous, and much more likely to be observer-dependent. This question is particularly pressing when it comes to understanding Bekenstein entropy (black hole entropy). To perhaps further add to the confusion, we shall argue that even the Clausius entropy can often be observer-dependent. In the current article we shall conclusively demonstrate that one can meaningfully assign a notion of Clausius entropy to arbitrary bifurcate null surfaces—effectively defining a ‘virtual Clausius entropy’ for arbitrary ‘virtual (local) causal horizons’. As an application, we see that we can implement a version of the generalized second law (GSL) for this virtual Clausius entropy. This version of GSL can be related to certain (nonstandard) integral variants of the null energy condition. Because the concepts involved are rather subtle, we take some effort in being careful and explicit in developing our framework. In future work we will apply this construction to generalize Jacobson’s derivation of the Einstein equations. (paper)
Local and global Hopf bifurcation analysis in a neutral-type neuron system with two delays
Lv, Qiuyu; Liao, Xiaofeng
2018-03-01
In recent years, neutral-type differential-difference equations have been applied extensively in the field of engineering, and their dynamical behaviors are more complex than that of the delay differential-difference equations. In this paper, the equations used to describe a neutral-type neural network system of differential difference equation with two delays are studied (i.e. neutral-type differential equations). Firstly, by selecting τ1, τ2 respectively as a parameter, we provide an analysis about the local stability of the zero equilibrium point of the equations, and sufficient conditions of asymptotic stability for the system are derived. Secondly, by using the theory of normal form and applying the theorem of center manifold introduced by Hassard et al., the Hopf bifurcation is found and some formulas for deciding the stability of periodic solutions and the direction of Hopf bifurcation are given. Moreover, by applying the theorem of global Hopf bifurcation, the existence of global periodic solution of the system is studied. Finally, an example is given, and some computer numerical simulations are taken to demonstrate and certify the correctness of the presented results.
Stability switches, Hopf bifurcation and chaos of a neuron model with delay-dependent parameters
International Nuclear Information System (INIS)
Xu, X.; Hu, H.Y.; Wang, H.L.
2006-01-01
It is very common that neural network systems usually involve time delays since the transmission of information between neurons is not instantaneous. Because memory intensity of the biological neuron usually depends on time history, some of the parameters may be delay dependent. Yet, little attention has been paid to the dynamics of such systems. In this Letter, a detailed analysis on the stability switches, Hopf bifurcation and chaos of a neuron model with delay-dependent parameters is given. Moreover, the direction and the stability of the bifurcating periodic solutions are obtained by the normal form theory and the center manifold theorem. It shows that the dynamics of the neuron model with delay-dependent parameters is quite different from that of systems with delay-independent parameters only
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...
Pitchfork bifurcation and circuit implementation of a novel Chen hyper-chaotic system
International Nuclear Information System (INIS)
Dong En-Zeng; Chen Zeng-Qiang; Chen Zai-Ping; Ni Jian-Yun
2012-01-01
In this paper, a novel four dimensional hyper-chaotic system is coined based on the Chen system, which contains two quadratic terms and five system parameters. The proposed system can generate a hyper-chaotic attractor in wide parameters regions. By using the center manifold theorem and the local bifurcation theory, a pitchfork bifurcation is demonstrated to arise at the zero equilibrium point. Numerical analysis demonstrates that the hyper-chaotic system can generate complex dynamical behaviors, e.g., a direct transition from quasi-periodic behavior to hyper-chaotic behavior. Finally, an electronic circuit is designed to implement the hyper-chaotic system, the experimental results are consist with the numerical simulations, which verifies the existence of the hyper-chaotic attractor. Due to the complex dynamic behaviors, this new hyper-chaotic system is useful in the secure communication. (general)
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.
International Nuclear Information System (INIS)
Wang, C.-C.; Jang, M.-J.; Yeh, Y.-L.
2007-01-01
This paper studies the bifurcation and nonlinear behaviors of a flexible rotor supported by relative short gas film bearings. A time-dependent mathematical model for gas journal bearings is presented. The finite difference method with successive over relation method is employed to solve the Reynolds' equation. The system state trajectory, Poincare maps, power spectra, and bifurcation diagrams are used to analyze the dynamic behavior of the rotor and journal center in the horizontal and vertical directions under different operating conditions. The analysis reveals a complex dynamic behavior comprising periodic and subharmonic response of the rotor and journal center. This paper shows how the dynamic behavior of this type of system varies with changes in rotor mass and rotational velocity. The results of this study contribute to a further understanding of the nonlinear dynamics of gas film rotor-bearing systems
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.
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).
International Nuclear Information System (INIS)
Xing Ming; Yang Pengfei; Huang Qinghai; Zhao Wenyuan; Hong Bo; Xu Yi; Liu Jianmin
2012-01-01
Objective: To preliminarily evaluate the feasibility, safety and efficacy of stent placement for the treatment of wide-necked aneurysms located at internal carotid artery bifurcation. Methods: Eleven patients with wide-necked aneurysms located at internal carotid artery bifurcation, who were encountered during the period from Jan. 2004 to Dec. 2010 in hospital, were collected. A total of 16 intracranial aneurysms were detected, of which 11 were wide-necked and were located at internal carotid artery bifurcation. The diameters of the aneurysms ranged from 2.5 mm to 18 mm. Individual stent type and stenting technique was employed for each patient. Follow-up at 1, 3, 6 and 12 months after the procedure was conducted. Results: A total of 11 different stents were successfully deployed in the eleven patients. The stents included balloon expandable stent (n=1) and self-expanding stent (n=10). According to Raymond grading for the immediate occlusion of the aneurysm, grade Ⅰ (complete obliteration) was obtained in 4, grade Ⅱ (residual neck) in 2 and grade Ⅲ (residual aneurysm) in 5 cases. No procedure-related complications occurred. At the time of discharge, the modified Rankin score was 0-1 in the eleven patients. During the follow-up period lasting for 1-108 months, all the patients were in stable condition and no newly-developed neurological dysfunction or bleeding observed. Follow-up examination with angiography (1-48 months) showed that the aneurysms were cured (no visualization) in 4 cases, improved in 2 cases and in stable condition in one case. Conclusion: For the treatment of wide-necked aneurysms located at internal carotid artery bifurcation, stent implantation is clinically feasible, safe and effective. Further studies are required to evaluate its long-term efficacy. (authors)
Fractional noise destroys or induces a stochastic bifurcation
Energy Technology Data Exchange (ETDEWEB)
Yang, Qigui, E-mail: qgyang@scut.edu.cn [School of Sciences, South China University of Technology, Guangzhou 510640 (China); Zeng, Caibin, E-mail: zeng.cb@mail.scut.edu.cn [School of Sciences, South China University of Technology, Guangzhou 510640 (China); School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640 (China); Wang, Cong, E-mail: wangcong@scut.edu.cn [School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640 (China)
2013-12-15
Little seems to be known about the stochastic bifurcation phenomena of non-Markovian systems. Our intention in this paper is to understand such complex dynamics by a simple system, namely, the Black-Scholes model driven by a mixed fractional Brownian motion. The most interesting finding is that the multiplicative fractional noise not only destroys but also induces a stochastic bifurcation under some suitable conditions. So it opens a possible way to explore the theory of stochastic bifurcation in the non-Markovian framework.
Optimization Design and Application of Underground Reinforced Concrete Bifurcation Pipe
Directory of Open Access Journals (Sweden)
Chao Su
2015-01-01
Full Text Available Underground reinforced concrete bifurcation pipe is an important part of conveyance structure. During construction, the workload of excavation and concrete pouring can be significantly decreased according to optimized pipe structure, and the engineering quality can be improved. This paper presents an optimization mathematical model of underground reinforced concrete bifurcation pipe structure according to real working status of several common pipe structures from real cases. Then, an optimization design system was developed based on Particle Swarm Optimization algorithm. Furthermore, take the bifurcation pipe of one hydropower station as an example: optimization analysis was conducted, and accuracy and stability of the optimization design system were verified successfully.
Arctic melt ponds and bifurcations in the climate system
Sudakov, I.; Vakulenko, S. A.; Golden, K. M.
2015-05-01
Understanding how sea ice melts is critical to climate projections. In the Arctic, melt ponds that develop on the surface of sea ice floes during the late spring and summer largely determine their albedo - a key parameter in climate modeling. Here we explore the possibility of a conceptual sea ice climate model passing through a bifurcation point - an irreversible critical threshold as the system warms, by incorporating geometric information about melt pond evolution. This study is based on a bifurcation analysis of the energy balance climate model with ice-albedo feedback as the key mechanism driving the system to bifurcation points.
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.
Bifurcation of learning and structure formation in neuronal maps
DEFF Research Database (Denmark)
Marschler, Christian; Faust-Ellsässer, Carmen; Starke, Jens
2014-01-01
to map formation in the laminar nucleus of the barn owl's auditory system. Using equation-free methods, we perform a bifurcation analysis of spatio-temporal structure formation in the associated synaptic-weight matrix. This enables us to analyze learning as a bifurcation process and follow the unstable...... states as well. A simple time translation of the learning window function shifts the bifurcation point of structure formation and goes along with traveling waves in the map, without changing the animal's sound localization performance....
Bifurcations in the response of a flexible rotor in squeeze-film dampers with retainer springs
International Nuclear Information System (INIS)
Inayat-Hussain, Jawaid I.
2009-01-01
Squeeze-film dampers are commonly used in conjunction with rolling-element or hydrodynamic bearings in rotating machinery. Although these dampers serve to provide additional damping to the rotor-bearing system, there have however been some cases of rotors mounted in these dampers exhibiting non-linear behaviour. In this paper a numerical study is undertaken to determine the effects of design parameters, i.e., gravity parameter, W, mass ratio, α, and stiffness ratio, K, on the bifurcations in the response of a flexible rotor mounted in squeeze-film dampers with retainer springs. The numerical simulations were undertaken for a range of speed parameter, Ω, between 0.1 and 5.0. Numerical results showed that increasing K causes the onset speed of bifurcation to increase, whilst an increase of α reduces the onset speed of bifurcation. For a specific combination of K and α values, the onset speed of bifurcation appeared to be independent of W. The instability of the rotor response at this onset speed was due to a saddle-node bifurcation for all the parameter values investigated in this work with the exception of the combination of α = 0.1 and K = 0.5, where a secondary Hopf bifurcation was observed. The speed range of non-synchronous response was seen to decrease with the increase of α; in fact non-synchronous rotor response was totally absent for α=0.4. With the exception of the case α = 0.1, the speed range of non-synchronous response was also seen to decrease with the increase of K. Multiple responses of the rotor were observed at certain values of Ω for various combinations of parameters W, α and K, where, depending on the values of the initial conditions the rotor response could be either synchronous or quasi-periodic. The numerical results presented in this work were obtained for an unbalance parameter, U, value of 0.1, which is considered as the upper end of the normal unbalance range of most practical rotor systems. These results provide some insights
Eckhaus and Benjamin-Feir instabilities near a weakly inverted bifurcation
International Nuclear Information System (INIS)
Brand, H.R.; Deissler, R.J.
1992-01-01
We investigate how the criteria for two prototype instabilities in one-dimensional pattern-forming systems, namely for the Eckhaus instability and for the Benjamin-Feir instability, change as one goes from a continuous bifurcation to a spatially periodic or spatially and/or time-periodic state to the corresponding weakly inverted, i.e., hysteretic, cases. We also give the generalization to two-dimensional patterns in systems with anisotropy as they arise, for example, for hydrodynamic instabilities in nematic liquid crystals
International Nuclear Information System (INIS)
Wang, C.-C.
2007-01-01
This paper investigates the bifurcation and nonlinear behavior of an aerodynamic journal bearing system taking into account the effect of stationary herringbone grooves. A finite difference method based on the successive over relation approach is employed to solve the Reynolds' equation. The analysis reveals a complex dynamical behavior comprising periodic and quasi-periodic responses of the rotor center. The dynamic behavior of the bearing system varies with changes in the bearing number and rotor mass. The results of this study provide a better understanding of the nonlinear dynamics of aerodynamic grooved journal bearing systems
Regularizations of two-fold bifurcations in planar piecewise smooth systems using blowup
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall; Hogan, S. J.
2015-01-01
type of limit cycle that does not appear to be present in the original PWS system. For both types of limit cycle, we show that the criticality of the Hopf bifurcation that gives rise to periodic orbits is strongly dependent on the precise form of the regularization. Finally, we analyse the limit cycles...... as locally unique families of periodic orbits of the regularization and connect them, when possible, to limit cycles of the PWS system. We illustrate our analysis with numerical simulations and show how the regularized system can undergo a canard explosion phenomenon...
CISM Session on Bifurcation and Stability of Dissipative Systems
1993-01-01
The first theme concerns the plastic buckling of structures in the spirit of Hill’s classical approach. Non-bifurcation and stability criteria are introduced and post-bifurcation analysis performed by asymptotic development method in relation with Hutchinson’s work. Some recent results on the generalized standard model are given and their connection to Hill’s general formulation is presented. Instability phenomena of inelastic flow processes such as strain localization and necking are discussed. The second theme concerns stability and bifurcation problems in internally damaged or cracked colids. In brittle fracture or brittle damage, the evolution law of crack lengths or damage parameters is time-independent like in plasticity and leads to a similar mathematical description of the quasi-static evolution. Stability and non-bifurcation criteria in the sense of Hill can be again obtained from the discussion of the rate response.
Bifurcation dynamics of the tempered fractional Langevin equation
Energy Technology Data Exchange (ETDEWEB)
Zeng, Caibin, E-mail: macbzeng@scut.edu.cn; Yang, Qigui, E-mail: qgyang@scut.edu.cn [School of Mathematics, South China University of Technology, Guangzhou 510640 (China); Chen, YangQuan, E-mail: ychen53@ucmerced.edu [MESA LAB, School of Engineering, University of California, Merced, 5200 N. Lake Road, Merced, California 95343 (United States)
2016-08-15
Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings.
Deformable 4DCT lung registration with vessel bifurcations
International Nuclear Information System (INIS)
Hilsmann, A.; Vik, T.; Kaus, M.; Franks, K.; Bissonette, J.P.; Purdie, T.; Beziak, A.; Aach, T.
2007-01-01
In radiotherapy planning of lung cancer, breathing motion causes uncertainty in the determination of the target volume. Image registration makes it possible to get information about the deformation of the lung and the tumor movement in the respiratory cycle from a few images. A dedicated, automatic, landmark-based technique was developed that finds corresponding vessel bifurcations. Hereby, we developed criteria to characterize pronounced bifurcations for which correspondence finding was more stable and accurate. The bifurcations were extracted from automatically segmented vessel trees in maximum inhale and maximum exhale CT thorax data sets. To find corresponding bifurcations in both data sets we used the shape context approach of Belongie et al. Finally, a volumetric lung deformation was obtained using thin-plate spline interpolation and affine registration. The method is evaluated on 10 4D-CT data sets of patients with lung cancer. (orig.)
Bifurcation theory for hexagonal agglomeration in economic geography
Ikeda, Kiyohiro
2014-01-01
This book contributes to an understanding of how bifurcation theory adapts to the analysis of economic geography. It is easily accessible not only to mathematicians and economists, but also to upper-level undergraduate and graduate students who are interested in nonlinear mathematics. The self-organization of hexagonal agglomeration patterns of industrial regions was first predicted by the central place theory in economic geography based on investigations of southern Germany. The emergence of hexagonal agglomeration in economic geography models was envisaged by Krugman. In this book, after a brief introduction of central place theory and new economic geography, the missing link between them is discovered by elucidating the mechanism of the evolution of bifurcating hexagonal patterns. Pattern formation by such bifurcation is a well-studied topic in nonlinear mathematics, and group-theoretic bifurcation analysis is a well-developed theoretical tool. A finite hexagonal lattice is used to express uniformly distri...
Defining Electron Bifurcation in the Electron-Transferring Flavoprotein Family.
Garcia Costas, Amaya M; Poudel, Saroj; Miller, Anne-Frances; Schut, Gerrit J; Ledbetter, Rhesa N; Fixen, Kathryn R; Seefeldt, Lance C; Adams, Michael W W; Harwood, Caroline S; Boyd, Eric S; Peters, John W
2017-11-01
Electron bifurcation is the coupling of exergonic and endergonic redox reactions to simultaneously generate (or utilize) low- and high-potential electrons. It is the third recognized form of energy conservation in biology and was recently described for select electron-transferring flavoproteins (Etfs). Etfs are flavin-containing heterodimers best known for donating electrons derived from fatty acid and amino acid oxidation to an electron transfer respiratory chain via Etf-quinone oxidoreductase. Canonical examples contain a flavin adenine dinucleotide (FAD) that is involved in electron transfer, as well as a non-redox-active AMP. However, Etfs demonstrated to bifurcate electrons contain a second FAD in place of the AMP. To expand our understanding of the functional variety and metabolic significance of Etfs and to identify amino acid sequence motifs that potentially enable electron bifurcation, we compiled 1,314 Etf protein sequences from genome sequence databases and subjected them to informatic and structural analyses. Etfs were identified in diverse archaea and bacteria, and they clustered into five distinct well-supported groups, based on their amino acid sequences. Gene neighborhood analyses indicated that these Etf group designations largely correspond to putative differences in functionality. Etfs with the demonstrated ability to bifurcate were found to form one group, suggesting that distinct conserved amino acid sequence motifs enable this capability. Indeed, structural modeling and sequence alignments revealed that identifying residues occur in the NADH- and FAD-binding regions of bifurcating Etfs. Collectively, a new classification scheme for Etf proteins that delineates putative bifurcating versus nonbifurcating members is presented and suggests that Etf-mediated bifurcation is associated with surprisingly diverse enzymes. IMPORTANCE Electron bifurcation has recently been recognized as an electron transfer mechanism used by microorganisms to maximize
Ergodicity-breaking bifurcations and tunneling in hyperbolic transport models
Giona, M.; Brasiello, A.; Crescitelli, S.
2015-11-01
One of the main differences between parabolic transport, associated with Langevin equations driven by Wiener processes, and hyperbolic models related to generalized Kac equations driven by Poisson processes, is the occurrence in the latter of multiple stable invariant densities (Frobenius multiplicity) in certain regions of the parameter space. This phenomenon is associated with the occurrence in linear hyperbolic balance equations of a typical bifurcation, referred to as the ergodicity-breaking bifurcation, the properties of which are thoroughly analyzed.
Hopf bifurcation of the stochastic model on business cycle
International Nuclear Information System (INIS)
Xu, J; Wang, H; Ge, G
2008-01-01
A stochastic model on business cycle was presented in thas paper. Simplifying the model through the quasi Hamiltonian theory, the Ito diffusion process was obtained. According to Oseledec multiplicative ergodic theory and singular boundary theory, the conditions of local and global stability were acquired. Solving the stationary FPK equation and analyzing the stationary probability density, the stochastic Hopf bifurcation was explained. The result indicated that the change of parameter awas the key factor to the appearance of the stochastic Hopf bifurcation
Iterative Controller Tuning for Process with Fold Bifurcations
DEFF Research Database (Denmark)
Huusom, Jakob Kjøbsted; Poulsen, Niels Kjølstad; Jørgensen, Sten Bay
2007-01-01
Processes involving fold bifurcation are notoriously difficult to control in the vicinity of the fold where most often optimal productivity is achieved . In cases with limited process insight a model based control synthesis is not possible. This paper uses a data driven approach with an improved...... version of iterative feedback tuning to optimizing a closed loop performance criterion, as a systematic tool for tuning process with fold bifurcations....
Bifurcated states of the error-field-induced magnetic islands
International Nuclear Information System (INIS)
Zheng, L.-J.; Li, B.; Hazeltine, R.D.
2008-01-01
We find that the formation of the magnetic islands due to error fields shows bifurcation when neoclassical effects are included. The bifurcation, which follows from including bootstrap current terms in a description of island growth in the presence of error fields, provides a path to avoid the island-width pole in the classical description. The theory offers possible theoretical explanations for the recent DIII-D and JT-60 experimental observations concerning confinement deterioration with increasing error field
Attractors, bifurcations, & chaos nonlinear phenomena in economics
Puu, Tönu
2003-01-01
The present book relies on various editions of my earlier book "Nonlinear Economic Dynamics", first published in 1989 in the Springer series "Lecture Notes in Economics and Mathematical Systems", and republished in three more, successively revised and expanded editions, as a Springer monograph, in 1991, 1993, and 1997, and in a Russian translation as "Nelineynaia Economicheskaia Dinamica". The first three editions were focused on applications. The last was differ ent, as it also included some chapters with mathematical background mate rial -ordinary differential equations and iterated maps -so as to make the book self-contained and suitable as a textbook for economics students of dynamical systems. To the same pedagogical purpose, the number of illus trations were expanded. The book published in 2000, with the title "A ttractors, Bifurcations, and Chaos -Nonlinear Phenomena in Economics", was so much changed, that the author felt it reasonable to give it a new title. There were two new math ematics ch...
Bifurcated equilibria in centrifugally confined plasma
International Nuclear Information System (INIS)
Shamim, I.; Teodorescu, C.; Guzdar, P. N.; Hassam, A. B.; Clary, R.; Ellis, R.; Lunsford, R.
2008-01-01
A bifurcation theory and associated computational model are developed to account for abrupt transitions observed recently on the Maryland Centrifugal eXperiment (MCX) [R. F. Ellis et al. Phys. Plasmas 8, 2057 (2001)], a supersonically rotating magnetized plasma that relies on centrifugal forces to prevent thermal expansion of plasma along the magnetic field. The observed transitions are from a well-confined, high-rotation state (HR-mode) to a lower-rotation, lesser-confined state (O-mode). A two-dimensional time-dependent magnetohydrodynamics code is used to simulate the dynamical equilibrium states of the MCX configuration. In addition to the expected viscous drag on the core plasma rotation, a momentum loss term is added that models the friction of plasma on the enhanced level of neutrals expected in the vicinity of the insulators at the throats of the magnetic mirror geometry. At small values of the external rotation drive, the plasma is not well-centrifugally confined and hence experiences the drag from near the insulators. Beyond a critical value of the external drive, the system makes an abrupt transition to a well-centrifugally confined state in which the plasma has pulled away from the end insulator plates; more effective centrifugal confinement lowers the plasma mass near the insulators allowing runaway increases in the rotation speed. The well-confined steady state is reached when the external drive is balanced by only the viscosity of the core plasma. A clear hysteresis phenomenon is shown.
Dansgaard–Oeschger events: bifurcation points in the climate system
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A. A. Cimatoribus
2013-02-01
Full Text Available Dansgaard–Oeschger events are a prominent mode of variability in the records of the last glacial cycle. Various prototype models have been proposed to explain these rapid climate fluctuations, and no agreement has emerged on which may be the more correct for describing the palaeoclimatic signal. In this work, we assess the bimodality of the system, reconstructing the topology of the multi-dimensional attractor over which the climate system evolves. We use high-resolution ice core isotope data to investigate the statistical properties of the climate fluctuations in the period before the onset of the abrupt change. We show that Dansgaard–Oeschger events have weak early warning signals if the ensemble of events is considered. We find that the statistics are consistent with the switches between two different climate equilibrium states in response to a changing external forcing (e.g. solar, ice sheets, either forcing directly the transition or pacing it through stochastic resonance. These findings are most consistent with a model that associates Dansgaard–Oeschger with changing boundary conditions, and with the presence of a bifurcation point.
Freeform inkjet printing of cellular structures with bifurcations.
Christensen, Kyle; Xu, Changxue; Chai, Wenxuan; Zhang, Zhengyi; Fu, Jianzhong; Huang, Yong
2015-05-01
Organ printing offers a great potential for the freeform layer-by-layer fabrication of three-dimensional (3D) living organs using cellular spheroids or bioinks as building blocks. Vascularization is often identified as a main technological barrier for building 3D organs. As such, the fabrication of 3D biological vascular trees is of great importance for the overall feasibility of the envisioned organ printing approach. In this study, vascular-like cellular structures are fabricated using a liquid support-based inkjet printing approach, which utilizes a calcium chloride solution as both a cross-linking agent and support material. This solution enables the freeform printing of spanning and overhang features by providing a buoyant force. A heuristic approach is implemented to compensate for the axially-varying deformation of horizontal tubular structures to achieve a uniform diameter along their axial directions. Vascular-like structures with both horizontal and vertical bifurcations have been successfully printed from sodium alginate only as well as mouse fibroblast-based alginate bioinks. The post-printing fibroblast cell viability of printed cellular tubes was found to be above 90% even after a 24 h incubation, considering the control effect. © 2014 Wiley Periodicals, Inc.
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.
Bifurcation magnetic resonance in films magnetized along hard magnetization axis
Energy Technology Data Exchange (ETDEWEB)
Vasilevskaya, Tatiana M., E-mail: t_vasilevs@mail.ru [Ulyanovsk State University, Leo Tolstoy 42, 432017 Ulyanovsk (Russian Federation); Sementsov, Dmitriy I.; Shutyi, Anatoliy M. [Ulyanovsk State University, Leo Tolstoy 42, 432017 Ulyanovsk (Russian Federation)
2012-09-15
We study low-frequency ferromagnetic resonance in a thin film magnetized along the hard magnetization axis performing an analysis of magnetization precession dynamics equations and numerical simulation. Two types of films are considered: polycrystalline uniaxial films and single-crystal films with cubic magnetic anisotropy. An additional (bifurcation) resonance initiated by the bistability, i.e. appearance of two closely spaced equilibrium magnetization states is registered. The modification of dynamic modes provoked by variation of the frequency, amplitude, and magnetic bias value of the ac field is studied. Both steady and chaotic magnetization precession modes are registered in the bifurcation resonance range. - Highlights: Black-Right-Pointing-Pointer An additional bifurcation resonance arises in a case of a thin film magnetized along HMA. Black-Right-Pointing-Pointer Bifurcation resonance occurs due to the presence of two closely spaced equilibrium magnetization states. Black-Right-Pointing-Pointer Both regular and chaotic precession modes are realized within bifurcation resonance range. Black-Right-Pointing-Pointer Appearance of dynamic bistability is typical for bifurcation resonance.
Bifurcation magnetic resonance in films magnetized along hard magnetization axis
International Nuclear Information System (INIS)
Vasilevskaya, Tatiana M.; Sementsov, Dmitriy I.; Shutyi, Anatoliy M.
2012-01-01
We study low-frequency ferromagnetic resonance in a thin film magnetized along the hard magnetization axis performing an analysis of magnetization precession dynamics equations and numerical simulation. Two types of films are considered: polycrystalline uniaxial films and single-crystal films with cubic magnetic anisotropy. An additional (bifurcation) resonance initiated by the bistability, i.e. appearance of two closely spaced equilibrium magnetization states is registered. The modification of dynamic modes provoked by variation of the frequency, amplitude, and magnetic bias value of the ac field is studied. Both steady and chaotic magnetization precession modes are registered in the bifurcation resonance range. - Highlights: ► An additional bifurcation resonance arises in a case of a thin film magnetized along HMA. ► Bifurcation resonance occurs due to the presence of two closely spaced equilibrium magnetization states. ► Both regular and chaotic precession modes are realized within bifurcation resonance range. ► Appearance of dynamic bistability is typical for bifurcation resonance.
Periodic precursors of nonlinear dynamical transitions
International Nuclear Information System (INIS)
Jiang Yu; Dong Shihai; Lozada-Cassou, M.
2004-01-01
We study the resonant response of a nonlinear system to external periodic perturbations. We show by numerical simulation that the periodic resonance curve may anticipate the dynamical instability of the unperturbed nonlinear periodic system, at parameter values far away from the bifurcation points. In the presence of noise, the buried intrinsic periodic dynamics can be picked out by analyzing the system's response to periodic modulation of appropriate intensity
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.
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.
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.
Complexity and Hopf Bifurcation Analysis on a Kind of Fractional-Order IS-LM Macroeconomic System
Ma, Junhai; Ren, Wenbo
On the basis of our previous research, we deepen and complete a kind of macroeconomics IS-LM model with fractional-order calculus theory, which is a good reflection on the memory characteristics of economic variables, we also focus on the influence of the variables on the real system, and improve the analysis capabilities of the traditional economic models to suit the actual macroeconomic environment. The conditions of Hopf bifurcation in fractional-order system models are briefly demonstrated, and the fractional order when Hopf bifurcation occurs is calculated, showing the inherent complex dynamic characteristics of the system. With numerical simulation, bifurcation, strange attractor, limit cycle, waveform and other complex dynamic characteristics are given; and the order condition is obtained with respect to time. We find that the system order has an important influence on the running state of the system. The system has a periodic motion when the order meets the conditions of Hopf bifurcation; the fractional-order system gradually stabilizes with the change of the order and parameters while the corresponding integer-order system diverges. This study has certain significance to policy-making about macroeconomic regulation and control.
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.
Inverse bifurcation analysis: application to simple gene systems
Directory of Open Access Journals (Sweden)
Schuster Peter
2006-07-01
Full Text Available Abstract Background Bifurcation analysis has proven to be a powerful method for understanding the qualitative behavior of gene regulatory networks. In addition to the more traditional forward problem of determining the mapping from parameter space to the space of model behavior, the inverse problem of determining model parameters to result in certain desired properties of the bifurcation diagram provides an attractive methodology for addressing important biological problems. These include understanding how the robustness of qualitative behavior arises from system design as well as providing a way to engineer biological networks with qualitative properties. Results We demonstrate that certain inverse bifurcation problems of biological interest may be cast as optimization problems involving minimal distances of reference parameter sets to bifurcation manifolds. This formulation allows for an iterative solution procedure based on performing a sequence of eigen-system computations and one-parameter continuations of solutions, the latter being a standard capability in existing numerical bifurcation software. As applications of the proposed method, we show that the problem of maximizing regions of a given qualitative behavior as well as the reverse engineering of bistable gene switches can be modelled and efficiently solved.
Stochastic Bifurcation Analysis of an Elastically Mounted Flapping Airfoil
Directory of Open Access Journals (Sweden)
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.
Steady-state bifurcations of the three-dimensional Kolmogorov problem
Directory of Open Access Journals (Sweden)
Zhi-Min Chen
2000-08-01
Full Text Available This paper studies the spatially periodic incompressible fluid motion in $mathbb R^3$ excited by the external force $k^2(sin kz, 0,0$ with $kgeq 2$ an integer. This driving force gives rise to the existence of the unidirectional basic steady flow $u_0=(sin kz,0, 0$ for any Reynolds number. It is shown in Theorem 1.1 that there exist a number of critical Reynolds numbers such that $u_0$ bifurcates into either 4 or 8 or 16 different steady states, when the Reynolds number increases across each of such numbers.
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.
International Nuclear Information System (INIS)
Zhao Yiguang
1991-01-01
The method of obtaining self-consistent solutions of the field equation and the rate equations of photon density and carrier concentration has been used to study frequecny locking, quasiperiodicity, subharmonic bifurcations and chaos in high frequency modulated stripe geometry DH semiconductor lasers. The results show that the chaotic behavior arises in self-pulsing stripe geometry semiconductor lasers. The route to chaos is not period-double, but quasiperiodicity to chaos. All of the results agree with the experiments. Some obscure points in previous theory about chaos have been cleared up
Stability and Bifurcation Analysis in a Maglev System with Multiple Delays
Zhang, Lingling; Huang, Jianhua; Huang, Lihong; Zhang, Zhizhou
This paper considers the time-delayed feedback control for Maglev system with two discrete time delays. We determine constraints on the feedback time delays which ensure the stability of the Maglev system. An algorithm is developed for drawing a two-parametric bifurcation diagram with respect to two delays τ1 and τ2. Direction and stability of periodic solutions are also determined using the normal form method and center manifold theory by Hassard. The complex dynamical behavior of the Maglev system near the domain of stability is confirmed by exhaustive numerical simulation.
Sediment sorting at a side channel bifurcation
van Denderen, Pepijn; Schielen, Ralph; Hulscher, Suzanne
2017-04-01
Side channels have been constructed to reduce the flood risk and to increase the ecological value of the river. In various Dutch side channels large aggradation in these channels occurred after construction. Measurements show that the grain size of the deposited sediment in the side channel is smaller than the grain size found on the bed of the main channel. This suggest that sorting occurs at the bifurcation of the side channel. The objective is to reproduce with a 2D morphological model the fining of the bed in the side channel and to study the effect of the sediment sorting on morphodynamic development of the side channel. We use a 2D Delft3D model with two sediment fractions. The first fraction corresponds with the grain size that can be found on the bed of the main channel and the second fraction corresponds with the grain size found in the side channel. With the numerical model we compute several side channel configurations in which we vary the length and the width of the side channel, and the curvature of the upstream channel. From these computations we can derive the equilibrium state and the time scale of the morphodynamic development of the side channel. Preliminary results show that even when a simple sediment transport relation is used, like Engelund & Hansen, more fine sediment enters the side channel than coarse sediment. This is as expected, and is probably related to the bed slope effects which are a function of the Shields parameter. It is expected that by adding a sill at the entrance of the side channel the slope effect increases. This might reduce the amount of coarse sediment which enters the side channel even more. It is unclear whether the model used is able to reproduce the effect of such a sill correctly as modelling a sill and reproducing the correct hydrodynamic and morphodynamic behaviour is not straightforward in a 2D model. Acknowledgements: This research is funded by STW, part of the Dutch Organization for Scientific Research under
Bifurcation and chaos in the simple passive dynamic walking model with upper body.
Li, Qingdu; Guo, Jianli; Yang, Xiao-Song
2014-09-01
We present some rich new complex gaits in the simple walking model with upper body by Wisse et al. in [Robotica 22, 681 (2004)]. We first show that the stable gait found by Wisse et al. may become chaotic via period-doubling bifurcations. Such period-doubling routes to chaos exist for all parameters, such as foot mass, upper body mass, body length, hip spring stiffness, and slope angle. Then, we report three new gaits with period 3, 4, and 6; for each gait, there is also a period-doubling route to chaos. Finally, we show a practical method for finding a topological horseshoe in 3D Poincaré map, and present a rigorous verification of chaos from these gaits.
Bifurcation and chaos in the simple passive dynamic walking model with upper body
Energy Technology Data Exchange (ETDEWEB)
Li, Qingdu; Guo, Jianli [Key Laboratory of Industrial Internet of Things and Networked Control, Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing 400065 (China); Yang, Xiao-Song, E-mail: yangxs@hust.edu.cn [Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074 (China)
2014-09-01
We present some rich new complex gaits in the simple walking model with upper body by Wisse et al. in [Robotica 22, 681 (2004)]. We first show that the stable gait found by Wisse et al. may become chaotic via period-doubling bifurcations. Such period-doubling routes to chaos exist for all parameters, such as foot mass, upper body mass, body length, hip spring stiffness, and slope angle. Then, we report three new gaits with period 3, 4, and 6; for each gait, there is also a period-doubling route to chaos. Finally, we show a practical method for finding a topological horseshoe in 3D Poincaré map, and present a rigorous verification of chaos from these gaits.
Bifurcation and chaos in the simple passive dynamic walking model with upper body
International Nuclear Information System (INIS)
Li, Qingdu; Guo, Jianli; Yang, Xiao-Song
2014-01-01
We present some rich new complex gaits in the simple walking model with upper body by Wisse et al. in [Robotica 22, 681 (2004)]. We first show that the stable gait found by Wisse et al. may become chaotic via period-doubling bifurcations. Such period-doubling routes to chaos exist for all parameters, such as foot mass, upper body mass, body length, hip spring stiffness, and slope angle. Then, we report three new gaits with period 3, 4, and 6; for each gait, there is also a period-doubling route to chaos. Finally, we show a practical method for finding a topological horseshoe in 3D Poincaré map, and present a rigorous verification of chaos from these gaits
EXPERIMENTAL STUDY ON SEDIMENT DISTRIBUTION AT CHANNEL BIFURCATION
Institute of Scientific and Technical Information of China (English)
G.M. Tarekul ISLAM; M.R. KABIR; Ainun NISHAT
2002-01-01
This paper presents the experimental results on the distribution of sediments at channel bifurcation.The experiments have been conducted in a physical model of channel bifurcation. It consists of a straight main channel which bifurcates into two branch channels of different widths. The test rig is a mobile bed with fixed bank. Four different noses have been used to study the phenomenon. For each nose, three upstream discharges viz. 20 l/s, 30 l/s and 40 l/s have been employed. From the measured data, discharges and sediment transport ratios per unit width are calculated in the downstream branches.These data have been set to the general nodal point relation and a set of equations has been developed to describe the distribution of sediments to the downstream branches for different nose angles.
Adaptive Control of Electromagnetic Suspension System by HOPF Bifurcation
Directory of Open Access Journals (Sweden)
Aming Hao
2013-01-01
Full Text Available EMS-type maglev system is essentially nonlinear and unstable. It is complicated to design a stable controller for maglev system which is under large-scale disturbance and parameter variance. Theory analysis expresses that this phenomenon corresponds to a HOPF bifurcation in mathematical model. An adaptive control law which adjusts the PID control parameters is given in this paper according to HOPF bifurcation theory. Through identification of the levitated mass, the controller adjusts the feedback coefficient to make the system far from the HOPF bifurcation point and maintain the stability of the maglev system. Simulation result indicates that adjusting proportion gain parameter using this method can extend the state stability range of maglev system and avoid the self-excited vibration efficiently.
Bifurcated equilibria in two-dimensional MHD with diamagnetic effects
International Nuclear Information System (INIS)
Ottaviani, M.; Tebaldi, C.
1998-12-01
In this work we analyzed the sequence of bifurcated equilibria in two-dimensional reduced magnetohydrodynamics. Diamagnetic effects are studied under the assumption of a constant equilibrium pressure gradient, not altered by the formation of the magnetic island. The formation of an island when the symmetric equilibrium becomes unstable is studied as a function of the tearing mode stability parameter Δ' and of the diamagnetic frequency, by employing fixed-points numerical techniques and an initial value code. At larger values of Δ' a tangent bifurcation takes place, above which no small island solutions exist. This bifurcation persists up to fairly large values of the diamagnetic frequency (of the order of one tenth of the Alfven frequency). The implications of this phenomenology for the intermittent MHD dynamics observed in tokamaks is discussed. (authors)
Stochastic stability and bifurcation in a macroeconomic model
International Nuclear Information System (INIS)
Li Wei; Xu Wei; Zhao Junfeng; Jin Yanfei
2007-01-01
On the basis of the work of Goodwin and Puu, a new business cycle model subject to a stochastically parametric excitation is derived in this paper. At first, we reduce the model to a one-dimensional diffusion process by applying the stochastic averaging method of quasi-nonintegrable Hamiltonian system. Secondly, we utilize the methods of Lyapunov exponent and boundary classification associated with diffusion process respectively to analyze the stochastic stability of the trivial solution of system. The numerical results obtained illustrate that the trivial solution of system must be globally stable if it is locally stable in the state space. Thirdly, we explore the stochastic Hopf bifurcation of the business cycle model according to the qualitative changes in stationary probability density of system response. It is concluded that the stochastic Hopf bifurcation occurs at two critical parametric values. Finally, some explanations are given in a simply way on the potential applications of stochastic stability and bifurcation analysis
Dynamical systems V bifurcation theory and catastrophe theory
1994-01-01
Bifurcation theory and catastrophe theory are two of the best known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Moreover, understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, the first printing of w...
Bifurcations in the optimal elastic foundation for a buckling column
International Nuclear Information System (INIS)
Rayneau-Kirkhope, Daniel; Farr, Robert; Ding, K.; Mao, Yong
2010-01-01
We investigate the buckling under compression of a slender beam with a distributed lateral elastic support, for which there is an associated cost. For a given cost, we study the optimal choice of support to protect against Euler buckling. We show that with only weak lateral support, the optimum distribution is a delta-function at the centre of the beam. When more support is allowed, we find numerically that the optimal distribution undergoes a series of bifurcations. We obtain analytical expressions for the buckling load around the first bifurcation point and corresponding expansions for the optimal position of support. Our theoretical predictions, including the critical exponent of the bifurcation, are confirmed by computer simulations.
Bifurcations in the optimal elastic foundation for a buckling column
Energy Technology Data Exchange (ETDEWEB)
Rayneau-Kirkhope, Daniel, E-mail: ppxdr@nottingham.ac.u [School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD (United Kingdom); Farr, Robert [Unilever R and D, Olivier van Noortlaan 120, AT3133, Vlaardingen (Netherlands); London Institute for Mathematical Sciences, 22 South Audley Street, Mayfair, London (United Kingdom); Ding, K. [Department of Physics, Fudan University, Shanghai, 200433 (China); Mao, Yong [School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD (United Kingdom)
2010-12-01
We investigate the buckling under compression of a slender beam with a distributed lateral elastic support, for which there is an associated cost. For a given cost, we study the optimal choice of support to protect against Euler buckling. We show that with only weak lateral support, the optimum distribution is a delta-function at the centre of the beam. When more support is allowed, we find numerically that the optimal distribution undergoes a series of bifurcations. We obtain analytical expressions for the buckling load around the first bifurcation point and corresponding expansions for the optimal position of support. Our theoretical predictions, including the critical exponent of the bifurcation, are confirmed by computer simulations.
Bifurcation-free design method of pulse energy converter controllers
International Nuclear Information System (INIS)
Kolokolov, Yury; Ustinov, Pavel; Essounbouli, Najib; Hamzaoui, Abdelaziz
2009-01-01
In this paper, a design method of pulse energy converter (PEC) controllers is proposed. This method develops a classical frequency domain design, based on the small signal modeling, by means of an addition of a nonlinear dynamics analysis stage. The main idea of the proposed method consists in fact that the PEC controller, designed with an application of the small signal modeling, is tuned after with taking into the consideration an essentially nonlinear nature of the PEC that makes it possible to avoid bifurcation phenomena in the PEC dynamics at the design stage (bifurcation-free design). Also application of the proposed method allows an improvement of the designed controller performance. The application of this bifurcation-free design method is demonstrated on an example of the controller design of direct current-direct current (DC-DC) buck converter with an input electromagnetic interference filter.
International Nuclear Information System (INIS)
Zhang Jiangang; Li Xianfeng; Chu Yandong; Yu Jianning; Chang Yingxiang
2009-01-01
In this paper, complex dynamical behavior of a class of centrifugal flywheel governor system is studied. These systems have a rich variety of nonlinear behavior, which are investigated here by numerically integrating the Lagrangian equations of motion. A tiny change in parameters can lead to an enormous difference in the long-term behavior of the system. Bubbles of periodic orbits may also occur within the bifurcation sequence. Hyperchaotic behavior is also observed in cases where two of the Lyapunov exponents are positive, one is zero, and one is negative. The routes to chaos are analyzed using Poincare maps, which are found to be more complicated than those of nonlinear rotational machines. Periodic and chaotic motions can be clearly distinguished by all of the analytical tools applied here, namely Poincare sections, bifurcation diagrams, Lyapunov exponents, and Lyapunov dimensions. This paper proposes a parametric open-plus-closed-loop approach to controlling chaos, which is capable of switching from chaotic motion to any desired periodic orbit. The theoretical work and numerical simulations of this paper can be extended to other systems. Finally, the results of this paper are of practical utility to designers of rotational machines.
Longitudinal traveling waves bifurcating from Vlasov plasma equilibria
International Nuclear Information System (INIS)
Holloway, J.P.
1989-01-01
The kinetic equations governing longitudinal motion along a straight magnetic field in a multi-species collisionless plasma are investigated. A necessary condition for the existence of small amplitude spatially periodic equilibria and traveling waves near a given spatially uniform background equilibrium is derived, and the wavelengths which such solutions must approach as their amplitude decreases to zero are discussed. A sufficient condition for the existence of these small amplitude waves is also established. This is accomplished by studying the nonlinear ODE for the potential which arises when the distribution functions are represented in a BGK form; the arbitrary functions of energy that describe the BGK representation are tested as an infinite dimensional set of parameters in a bifurcation theory for the ODE. The positivity and zero current condition in the wave frame of the BGK distribution functions are maintained. The undamped small amplitude nonlinear waves so constructed can be made to satisfy the Vlasov dispersion relation exactly, but in general they need only satisfy it approximately. Numerical calculations reveal that even a thermal equilibrium electron-proton plasma with equal ion and electron temperatures will support undamped traveling waves with phase speeds greater than 1.3 times the electron velocity; the dispersion relation for this case exhibits both Langmuir and ion-acoustic branches as long wavelength limits, and shows how these branches are in fact connected by short wavelength waves of intermediate frequency. In apparent contradiction to the linear theory of Landau, these exact solutions of the kinetic equations do not damp; this contradiction is explained by observing that the linear theory is, in general, fundamentally incapable of describing undamped traveling waves
An Approach to Robust Control of the Hopf Bifurcation
Directory of Open Access Journals (Sweden)
Giacomo Innocenti
2011-01-01
Full Text Available The paper illustrates a novel approach to modify the Hopf bifurcation nature via a nonlinear state feedback control, which leaves the equilibrium properties unchanged. This result is achieved by recurring to linear and nonlinear transformations, which lead the system to locally assume the ordinary differential equation representation. Third-order models are considered, since they can be seen as proper representatives of a larger class of systems. The explicit relationship between the control input and the Hopf bifurcation nature is obtained via a frequency approach, that does not need the computation of the center manifold.
Three dimensional nilpotent singularity and Sil'nikov bifurcation
International Nuclear Information System (INIS)
Li Xindan; Liu Haifei
2007-01-01
In this paper, by using the normal form, blow-up theory and the technique of global bifurcations, we study the singularity at the origin with threefold zero eigenvalue for nonsymmetric vector fields with nilpotent linear part and 4-jet C ∼ -equivalent toy-bar -bar x+z-bar -bar y+ax 3 y-bar -bar z,with a 0, and analytically prove the existence of Sil'nikov bifurcation, and then of the strange attractor for certain subfamilies of the nonsymmetric versal unfoldings of this singularity under some conditions
Transportation and concentration inequalities for bifurcating Markov chains
DEFF Research Database (Denmark)
Penda, S. Valère Bitseki; Escobar-Bach, Mikael; Guillin, Arnaud
2017-01-01
We investigate the transportation inequality for bifurcating Markov chains which are a class of processes indexed by a regular binary tree. Fitting well models like cell growth when each individual gives birth to exactly two offsprings, we use transportation inequalities to provide useful...... concentration inequalities.We also study deviation inequalities for the empirical means under relaxed assumptions on the Wasserstein contraction for the Markov kernels. Applications to bifurcating nonlinear autoregressive processes are considered for point-wise estimates of the non-linear autoregressive...
Bifurcated transition of radial transport in the HIEI tandem mirror
International Nuclear Information System (INIS)
Sakai, O.; Yasaka, Y.
1995-01-01
Transition to a high radial confinement mode in a mirror plasma is triggered by limiter biasing. Sheared plasma rotation is induced in the high confinement phase which is characterized by reduction of edge turbulence and a confinement enhancement factor of 2-4. Edge plasma parameters related to radial confinement show a hysteresis phenomenon as a function of bias voltage or bias current, leading to the fact that transition from low to high confinement mode occurs between the bifurcated states. A transition model based on azimuthal momentum balance is employed to clarify physics of the observed bifurcation. copyright 1995 American Institute of Physics
Flow Topology Transition via Global Bifurcation in Thermally Driven Turbulence
Xie, Yi-Chao; Ding, Guang-Yu; Xia, Ke-Qing
2018-05-01
We report an experimental observation of a flow topology transition via global bifurcation in a turbulent Rayleigh-Bénard convection. This transition corresponds to a spontaneous symmetry breaking with the flow becomes more turbulent. Simultaneous measurements of the large-scale flow (LSF) structure and the heat transport show that the LSF bifurcates from a high heat transport efficiency quadrupole state to a less symmetric dipole state with a lower heat transport efficiency. In the transition zone, the system switches spontaneously and stochastically between the two long-lived metastable states.
Discretizing the transcritical and pitchfork bifurcations – conjugacy results
Lóczi, Lajos
2015-01-07
© 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 on the one-step discretization method of order (Formula presented.) , we show that the time- (Formula presented.) exact and the step-size- (Formula presented.) discretized dynamics are topologically equivalent by constructing a two-parameter family of conjugacies in each case. As a main result, we prove that the constructed conjugacy maps are (Formula presented.) -close to the identity and these estimates are optimal.
International Nuclear Information System (INIS)
Fefferman, C L; Lee-Thorp, J P; Weinstein, M I
2016-01-01
Edge states are time-harmonic solutions to energy-conserving wave equations, which are propagating parallel to a line-defect or ‘edge’ and are localized transverse to it. This paper summarizes and extends the authors’ work on the bifurcation of topologically protected edge states in continuous two-dimensional (2D) honeycomb structures. We consider a family of Schrödinger Hamiltonians consisting of a bulk honeycomb potential and a perturbing edge potential. The edge potential interpolates between two different periodic structures via a domain wall. We begin by reviewing our recent bifurcation theory of edge states for continuous 2D honeycomb structures (http://arxiv.org/abs/1506.06111). The topologically protected edge state bifurcation is seeded by the zero-energy eigenstate of a one-dimensional Dirac operator. We contrast these protected bifurcations with (more common) non-protected bifurcations from spectral band edges, which are induced by bound states of an effective Schrödinger operator. Numerical simulations for honeycomb structures of varying contrasts and ‘rational edges’ (zigzag, armchair and others), support the following scenario: (a) for low contrast, under a sign condition on a distinguished Fourier coefficient of the bulk honeycomb potential, there exist topologically protected edge states localized transverse to zigzag edges. Otherwise, and for general edges, we expect long lived edge quasi-modes which slowly leak energy into the bulk. (b) For an arbitrary rational edge, there is a threshold in the medium-contrast (depending on the choice of edge) above which there exist topologically protected edge states. In the special case of the armchair edge, there are two families of protected edge states; for each parallel quasimomentum (the quantum number associated with translation invariance) there are edge states which propagate in opposite directions along the armchair edge. (paper)
Fefferman, C. L.; Lee-Thorp, J. P.; Weinstein, M. I.
2016-03-01
Edge states are time-harmonic solutions to energy-conserving wave equations, which are propagating parallel to a line-defect or ‘edge’ and are localized transverse to it. This paper summarizes and extends the authors’ work on the bifurcation of topologically protected edge states in continuous two-dimensional (2D) honeycomb structures. We consider a family of Schrödinger Hamiltonians consisting of a bulk honeycomb potential and a perturbing edge potential. The edge potential interpolates between two different periodic structures via a domain wall. We begin by reviewing our recent bifurcation theory of edge states for continuous 2D honeycomb structures (http://arxiv.org/abs/1506.06111). The topologically protected edge state bifurcation is seeded by the zero-energy eigenstate of a one-dimensional Dirac operator. We contrast these protected bifurcations with (more common) non-protected bifurcations from spectral band edges, which are induced by bound states of an effective Schrödinger operator. Numerical simulations for honeycomb structures of varying contrasts and ‘rational edges’ (zigzag, armchair and others), support the following scenario: (a) for low contrast, under a sign condition on a distinguished Fourier coefficient of the bulk honeycomb potential, there exist topologically protected edge states localized transverse to zigzag edges. Otherwise, and for general edges, we expect long lived edge quasi-modes which slowly leak energy into the bulk. (b) For an arbitrary rational edge, there is a threshold in the medium-contrast (depending on the choice of edge) above which there exist topologically protected edge states. In the special case of the armchair edge, there are two families of protected edge states; for each parallel quasimomentum (the quantum number associated with translation invariance) there are edge states which propagate in opposite directions along the armchair edge.
Kan-On, Yukio
2007-04-01
This paper is concerned with the bifurcation structure of positive stationary solutions for a generalized Lotka-Volterra competition model with diffusion. To establish the structure, the bifurcation theory and the interval arithmetic are employed.
Bifurcations and chaos in convection taking non-Fourier heat-flux
Layek, G. C.; Pati, N. C.
2017-11-01
In this Letter, we report the influences of thermal time-lag on the onset of convection, its bifurcations and chaos of a horizontal layer of Boussinesq fluid heated underneath taking non-Fourier Cattaneo-Christov hyperbolic model for heat propagation. A five-dimensional nonlinear system is obtained for a low-order Galerkin expansion, and it reduces to Lorenz system for Cattaneo number tending to zero. The linear stability agreed with existing results that depend on Cattaneo number C. It also gives a threshold Cattaneo number, CT, above which only oscillatory solutions can persist. The oscillatory solutions branch terminates at the subcritical steady branch with a heteroclinic loop connecting a pair of saddle points for subcritical steady-state solutions. For subcritical onset of convection two stable solutions coexist, that is, hysteresis phenomenon occurs at this stage. The steady solution undergoes a Hopf bifurcation and is of subcritical type for small value of C, while it becomes supercritical for moderate Cattaneo number. The system goes through period-doubling/noisy period-doubling transition to chaos depending on the control parameters. There after the system exhibits Shil'nikov chaos via homoclinic explosion. The complexity of spiral strange attractor is analyzed using fractal dimension and return map.
Necessary and sufficient conditions for Hopf bifurcation in tri-neuron equation with a delay
International Nuclear Information System (INIS)
Liu Xiaoming; Liao Xiaofeng
2009-01-01
In this paper, we consider the delayed differential equations modeling three-neuron equations with only a time delay. Using the time delay as a bifurcation parameter, necessary and sufficient conditions for Hopf bifurcation to occur are derived. Numerical results indicate that for this model, Hopf bifurcation is likely to occur at suitable delay parameter values.
Local bifurcation analysis in nuclear reactor dynamics by Sotomayor’s theorem
International Nuclear Information System (INIS)
Pirayesh, Behnam; Pazirandeh, Ali; Akbari, Monireh
2016-01-01
Highlights: • When the feedback reactivity is considered as a nonlinear function some complex behaviors may emerge in the system such as local bifurcation phenomenon. • The qualitative behaviors of a typical nuclear reactor near its equilibrium points have been studied analytically. • Comprehensive analytical bifurcation analyses presented in this paper are transcritical bifurcation, saddle- node bifurcation and pitchfork bifurcation. - Abstract: In this paper, a qualitative approach has been used to explore nuclear reactor behaviors with nonlinear feedback. First, a system of four dimensional ordinary differential equations governing the dynamics of a typical nuclear reactor is introduced. These four state variables are the relative power of the reactor, the relative concentration of delayed neutron precursors, the fuel temperature and the coolant temperature. Then, the qualitative behaviors of the dynamical system near its equilibria have been studied analytically by using local bifurcation theory and Sotomayor’s theorem. The results indicated that despite the uncertainty of the reactivity, we can analyze the qualitative behavior changes of the reactor from the bifurcation point of view. Notably, local bifurcations that were considered in this paper include transcritical bifurcation, saddle-node bifurcation and pitchfork bifurcation. The theoretical analysis showed that these three types of local bifurcations may occur in the four dimensional dynamical system. In addition, to confirm the analytical results the numerical simulations are given.
International Nuclear Information System (INIS)
Kumar Samanta, Utpal; Saha, Asit; Chatterjee, Prasanta
2013-01-01
Bifurcations of nonlinear propagation of ion acoustic waves (IAWs) in a magnetized plasma whose constituents are cold ions and kappa distributed electron are investigated using a two component plasma model. The standard reductive perturbation technique is used to derive the Zakharov-Kuznetsov (ZK) equation for IAWs. By using the bifurcation theory of planar dynamical systems to this ZK equation, the existence of solitary wave solutions and periodic travelling wave solutions is established. All exact explicit solutions of these travelling waves are determined. The results may have relevance in dense space plasmas
Coronary bifurcation lesions treated with simple or complex stenting
DEFF Research Database (Denmark)
Behan, Miles W; Holm, Niels R; de Belder, Adam J
2016-01-01
AIMS: Randomized trials of coronary bifurcation stenting have shown better outcomes from a simple (provisional) strategy rather than a complex (planned two-stent) strategy in terms of short-term efficacy and safety. Here, we report the 5-year all-cause mortality based on pooled patient-level data...
The Boundary-Hopf-Fold Bifurcation in Filippov Systems
Efstathiou, Konstantinos; Liu, Xia; Broer, Henk W.
2015-01-01
This paper studies the codimension-3 boundary-Hopf-fold (BHF) bifurcation of planar Filippov systems. Filippov systems consist of at least one discontinuity boundary locally separating the phase space to disjoint components with different dynamics. Such systems find applications in several fields,
Stability and Hopf bifurcation analysis of a new system
International Nuclear Information System (INIS)
Huang Kuifei; Yang Qigui
2009-01-01
In this paper, a new chaotic system is introduced. The system contains special cases as the modified Lorenz system and conjugate Chen system. Some subtle characteristics of stability and Hopf bifurcation of the new chaotic system are thoroughly investigated by rigorous mathematical analysis and symbolic computations. Meanwhile, some numerical simulations for justifying the theoretical analysis are also presented.
Pitchfork bifurcation and vibrational resonance in a fractional-order ...
Indian Academy of Sciences (India)
The fractional-order damping mainly determines the pattern of the vibrational resonance. There is a bifurcation point of the fractional order which, in the case of double-well potential, transforms vibrational resonance pattern from a single resonance to a double resonance, while in the case of single-well potential, transforms ...
Nonintegrability of the unfolding of the fold-Hopf bifurcation
Yagasaki, Kazuyuki
2018-02-01
We consider the unfolding of the codimension-two fold-Hopf bifurcation and prove its meromorphic nonintegrability in the meaning of Bogoyavlenskij for almost all parameter values. Our proof is based on a generalized version of the Morales-Ramis-Simó theory for non-Hamiltonian systems and related variational equations up to second order are used.
Bifurcations and complete chaos for the diamagnetic Kepler problem
Hansen, Kai T.
1995-03-01
We describe the structure of bifurcations in the unbounded classical diamagnetic Kepler problem. We conjecture that this system does not have any stable orbits and that the nonwandering set is described by a complete trinary symbolic dynamics for scaled energies larger than ɛc=0.328 782. . ..
Bifurcations and Complete Chaos for the Diamagnetic Kepler Problem
Hansen, Kai T.
1995-01-01
We describe the structure of bifurcations in the unbounded classical Diamagnetic Kepler problem. We conjecture that this system does not have any stable orbits and that the non-wandering set is described by a complete trinary symbolic dynamics for scaled energies larger then $\\epsilon_c=0.328782\\ldots$.
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.
Stability of Bifurcating Stationary Solutions of the Artificial Compressible System
Teramoto, Yuka
2018-02-01
The artificial compressible system gives a compressible approximation of the incompressible Navier-Stokes system. The latter system is obtained from the former one in the zero limit of the artificial Mach number ɛ which is a singular limit. The sets of stationary solutions of both systems coincide with each other. It is known that if a stationary solution of the incompressible system is asymptotically stable and the velocity field of the stationary solution satisfies an energy-type stability criterion, then it is also stable as a solution of the artificial compressible one for sufficiently small ɛ . In general, the range of ɛ shrinks when the spectrum of the linearized operator for the incompressible system approaches to the imaginary axis. This can happen when a stationary bifurcation occurs. It is proved that when a stationary bifurcation from a simple eigenvalue occurs, the range of ɛ can be taken uniformly near the bifurcation point to conclude the stability of the bifurcating solution as a solution of the artificial compressible system.
Long term results of kissing stents in the aortic bifurcation
Hinnen, J.W.; Konickx, M.A.; Meerwaldt, Robbert; Kolkert, J.L.P.; van der Palen, Jacobus Adrianus Maria; Huisman, A.B.
2015-01-01
BACKGROUND: To evaluate the long-term outcome after aortoiliac kissing stent placement and to analyze variables, which potentially influence the outcome of endovascular reconstruction of the aortic bifurcation. METHODS: All patients treated with aortoiliac kissing stents at our institution between
Femoral bifurcation with ipsilateral tibia hemimelia: Early outcome of ...
African Journals Online (AJOL)
Hereby, we present a case report of a 2-year-old boy who first presented in our orthopedic clinic as a 12-day-old neonate, with a grossly deformed right lower limb from a combination of complete tibia hemimelia and ipsilateral femoral bifurcation. Excision of femoral exostosis, knee disarticulation and prosthetic fitting gives ...
Hopf bifurcation formula for first order differential-delay equations
Rand, Richard; Verdugo, Anael
2007-09-01
This work presents an explicit formula for determining the radius of a limit cycle which is born in a Hopf bifurcation in a class of first order constant coefficient differential-delay equations. The derivation is accomplished using Lindstedt's perturbation method.
Direction and stability of bifurcating solutions for a Signorini problem
Czech Academy of Sciences Publication Activity Database
Eisner, J.; Kučera, Milan; Recke, L.
2015-01-01
Roč. 113, January (2015), s. 357-371 ISSN 0362-546X Institutional support: RVO:67985840 Keywords : Signorini problem * variational inequality * bifurcation direction Subject RIV: BA - General Mathematics Impact factor: 1.125, year: 2015 http://www.sciencedirect.com/science/article/pii/S0362546X14003228
Smooth bifurcation for a Signorini problem on a rectangle
Czech Academy of Sciences Publication Activity Database
Eisner, J.; Kučera, Milan; Recke, L.
2012-01-01
Roč. 137, č. 2 (2012), s. 131-138 ISSN 0862-7959 R&D Projects: GA AV ČR IAA100190805 Institutional research plan: CEZ:AV0Z10190503 Keywords : Signorini problem * smooth bifurcation * variational inequality Subject RIV: BA - General Mathematics http://dml.cz/dmlcz/142859
Bifurcation analysis and the travelling wave solutions of the Klein
Indian Academy of Sciences (India)
In this paper, we investigate the bifurcations and dynamic behaviour of travelling wave solutions of the Klein–Gordon–Zakharov equations given in Shang et al, Comput. Math. Appl. 56, 1441 (2008). Under different parameter conditions, we obtain some exact explicit parametric representations of travelling wave solutions by ...
Epidemic model with vaccinated age that exhibits backward bifurcation
International Nuclear Information System (INIS)
Yang Junyuan; Zhang Fengqin; Li Xuezhi
2009-01-01
Vaccination of susceptibilities is included in a transmission model for a disease that confers immunity. In this paper, interplay of vaccination strategy together with vaccine efficacy and the vaccinated age is studied. In particular, vaccine efficacy can lead to a backward bifurcation. At the same time, we also discuss an abstract formulation of the problem, and establish the well-posedness of the model.
Bifurcation methods of dynamical systems for handling nonlinear ...
Indian Academy of Sciences (India)
physics pp. 863–868. Bifurcation methods of dynamical systems for handling nonlinear wave equations. DAHE FENG and JIBIN LI. Center for Nonlinear Science Studies, School of Science, Kunming University of Science and Technology .... (b) It can be shown from (15) and (18) that the balance between the weak nonlinear.
Bifurcation analysis of wind-driven flows with MOM4
Bernsen, E.; Dijkstra, H.A.; Wubs, F.W.
2009-01-01
In this paper, the methodology of bifurcation analysis is applied to the explicit time-stepping ocean model MOM4 using a Jacobian–Free Newton–Krylov (JFNK) approach. We in detail present the implementation of the JFNK method in MOM4 but restrict the preconditioning technique to the case for which
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
Bifurcation Analysis of Spiral Growth Processes in Plants
DEFF Research Database (Denmark)
Andersen, C.A.; Ernstsen, C.N.; Mosekilde, Erik
1999-01-01
In order to examine the significance of different assumptions about the range of the inhibitory forces, we have performed a series of bifurcation analyses of a simple model that can explain the formation of helical structures in phyllotaxis. Computer simulations are used to illustrate the role...
Smooth bifurcation for variational inequalities based on Lagrange multipliers
Czech Academy of Sciences Publication Activity Database
Eisner, Jan; Kučera, Milan; Recke, L.
2006-01-01
Roč. 19, č. 9 (2006), s. 981-1000 ISSN 0893-4983 R&D Projects: GA AV ČR(CZ) IAA100190506 Institutional research plan: CEZ:AV0Z10190503 Keywords : abstract variational inequality * bifurcation * Lagrange multipliers Subject RIV: BA - General Mathematics
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...
Regularization of the Boundary-Saddle-Node Bifurcation
Directory of Open Access Journals (Sweden)
Xia Liu
2018-01-01
Full Text Available In this paper we treat a particular class of planar Filippov systems which consist of two smooth systems that are separated by a discontinuity boundary. In such systems one vector field undergoes a saddle-node bifurcation while the other vector field is transversal to the boundary. The boundary-saddle-node (BSN bifurcation occurs at a critical value when the saddle-node point is located on the discontinuity boundary. We derive a local topological normal form for the BSN bifurcation and study its local dynamics by applying the classical Filippov’s convex method and a novel regularization approach. In fact, by the regularization approach a given Filippov system is approximated by a piecewise-smooth continuous system. Moreover, the regularization process produces a singular perturbation problem where the original discontinuous set becomes a center manifold. Thus, the regularization enables us to make use of the established theories for continuous systems and slow-fast systems to study the local behavior around the BSN bifurcation.
Topography of Aortic Bifurcation in a Black Kenyan Population ...
African Journals Online (AJOL)
After removal of abdominal viscera, peritoneum, fibrofatty connective tissue, inferior vena cava was removed to expose the termination of abdominal aorta. Vertebral level, angle and asymmetry of bifurcation were recorded. Data were analysed by SPSS version 17.0 for windows and are presented in tables and bar charts.
Numerical bifurcation analysis of conformal formulations of the Einstein constraints
International Nuclear Information System (INIS)
Holst, M.; Kungurtsev, V.
2011-01-01
The Einstein constraint equations have been the subject of study for more than 50 years. The introduction of the conformal method in the 1970s as a parametrization of initial data for the Einstein equations led to increased interest in the development of a complete solution theory for the constraints, with the theory for constant mean curvature (CMC) spatial slices and closed manifolds completely developed by 1995. The first general non-CMC existence result was establish by Holst et al. in 2008, with extensions to rough data by Holst et al. in 2009, and to vacuum spacetimes by Maxwell in 2009. The non-CMC theory remains mostly open; moreover, recent work of Maxwell on specific symmetry models sheds light on fundamental nonuniqueness problems with the conformal method as a parametrization in non-CMC settings. In parallel with these mathematical developments, computational physicists have uncovered surprising behavior in numerical solutions to the extended conformal thin sandwich formulation of the Einstein constraints. In particular, numerical evidence suggests the existence of multiple solutions with a quadratic fold, and a recent analysis of a simplified model supports this conclusion. In this article, we examine this apparent bifurcation phenomena in a methodical way, using modern techniques in bifurcation theory and in numerical homotopy methods. We first review the evidence for the presence of bifurcation in the Hamiltonian constraint in the time-symmetric case. We give a brief introduction to the mathematical framework for analyzing bifurcation phenomena, and then develop the main ideas behind the construction of numerical homotopy, or path-following, methods in the analysis of bifurcation phenomena. We then apply the continuation software package AUTO to this problem, and verify the presence of the fold with homotopy-based numerical methods. We discuss these results and their physical significance, which lead to some interesting remaining questions to
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
Imura, Jun-ichi; Ueta, Tetsushi
2015-01-01
This book is the first to report on theoretical breakthroughs on control of complex dynamical systems developed by collaborative researchers in the two fields of dynamical systems theory and control theory. As well, its basic point of view is of three kinds of complexity: bifurcation phenomena subject to model uncertainty, complex behavior including periodic/quasi-periodic orbits as well as chaotic orbits, and network complexity emerging from dynamical interactions between subsystems. Analysis and Control of Complex Dynamical Systems offers a valuable resource for mathematicians, physicists, and biophysicists, as well as for researchers in nonlinear science and control engineering, allowing them to develop a better fundamental understanding of the analysis and control synthesis of such complex systems.
DEFF Research Database (Denmark)
Bredahl, Kim; Jensen, Leif Panduro; Schroeder, Torben V
2015-01-01
skills, particularly because open surgery is increasingly used in those patients who are unsuitable for endovascular repair and hence technically more demanding. We assessed the early outcome after aortic bifurcated bypass procedures during two decades of growing endovascular activity and identified...... preoperative risk factors. METHODS: Data on patients with chronic limb ischemia were prospectively collected during a 20-year period (1993 to 2012). The data were obtained from the Danish Vascular Registry, assessed, and merged with data from The Danish Civil Registration System. RESULTS: We identified 3623...... aortobifemoral and 144 aortobiiliac bypass procedures. The annual caseload fell from 323 to 106 during the study period, but the 30-day mortality at 3.6% (95% confidence interval [CI], 3.0-4.1) and the 30-day major complication rate remained constant at 20% (95% CI, 18-21). Gangrene (odds ratio [OR], 3.3; 95% CI...
Numerical bifurcation analysis of delay differential equations arising from physiological modeling.
Engelborghs, K; Lemaire, V; Bélair, J; Roose, D
2001-04-01
This paper has a dual purpose. First, we describe numerical methods for continuation and bifurcation analysis of steady state solutions and periodic solutions of systems of delay differential equations with an arbitrary number of fixed, discrete delays. Second, we demonstrate how these methods can be used to obtain insight into complex biological regulatory systems in which interactions occur with time delays: for this, we consider a system of two equations for the plasma glucose and insulin concentrations in a diabetic patient subject to a system of external assistance. The model has two delays: the technological delay of the external system, and the physiological delay of the patient's liver. We compute stability of the steady state solution as a function of two parameters, compare with analytical results and compute several branches of periodic solutions and their stability. These numerical results allow to infer two categories of diabetic patients for which the external system has different efficiency.
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.
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.
Bifurcation, pattern formation and chaos in combustion
International Nuclear Information System (INIS)
Bayliss, A.; Matkowsky, B.J.
1991-01-01
In this paper problems in gaseous combustion and in gasless condensed phase combustion are studied both analytically and numerically. In gaseous combustion we consider the problem of a flame stabilized on a line source of fuel. The authors find both stationary and pulsating axisymmetric solutions as well as stationary and pulsating cellular solutions. The pulsating cellular solutions take the form of either traveling waves or standing waves. Transitions between these patterns occur as parameters related to the curvature of the flame front and the Lewis number are varied. In gasless condensed phase combustion both planar and nonplanar problems are studied. For planar condensed phase combustion we consider two models: accounts for melting and does not. Both models are shown to exhibit a transition from uniformly to pulsating propagating combustion when a parameter related to the activation energy is increased. Upon further increasing this parameter both models undergo a transition to chaos: by intermittency and by a period doubling sequence. In nonplanar condensed phase combustion the nonlinear development of a branch of standing wave solutions is studied and is shown to lead to relaxation oscillations and subsequently to a transition to quasi-periodicity
Directory of Open Access Journals (Sweden)
B. Swathi
2009-01-01
Full Text Available Simulation of the Gyorgyi, Rempe and Field eleven variable chaotic model in CSTR [Continuously Stirred Tank Reactor] is performed with respect to the concentrations of malonic acid and [Ce(III]. These simulation studies show steady state, periodic and non-periodic regions. These studies have been presented as two variable bifurcation phase diagrams. We also have observed the bursting phenomenon under different set of constraints. We have given much importance on computer simulation work but not included the experimental methods in this paper.
Ibrahim, K. M.; Jamal, R. K.; Ali, F. H.
2018-05-01
The behaviour of certain dynamical nonlinear systems are described in term as chaos, i.e., systems’ variables change with the time, displaying very sensitivity to initial conditions of chaotic dynamics. In this paper, we study archetype systems of ordinary differential equations in two-dimensional phase spaces of the Rössler model. A system displays continuous time chaos and is explained by three coupled nonlinear differential equations. We study its characteristics and determine the control parameters that lead to different behavior of the system output, periodic, quasi-periodic and chaos. The time series, attractor, Fast Fourier Transformation and bifurcation diagram for different values have been described.
Efficient algorithm for bifurcation problems of variational inequalities
International Nuclear Information System (INIS)
Mittelmann, H.D.
1983-01-01
For a class of variational inequalities on a Hilbert space H bifurcating solutions exist and may be characterized as critical points of a functional with respect to the intersection of the level surfaces of another functional and a closed convex subset K of H. In a recent paper [13] we have used a gradient-projection type algorithm to obtain the solutions for discretizations of the variational inequalities. A related but Newton-based method is given here. Global and asymptotically quadratic convergence is proved. Numerical results show that it may be used very efficiently in following the bifurcating branches and that is compares favorably with several other algorithms. The method is also attractive for a class of nonlinear eigenvalue problems (K = H) for which it reduces to a generalized Rayleigh-quotient interaction. So some results are included for the path following in turning-point problems
Bifurcation software in Matlab with applications in neuronal modeling.
Govaerts, Willy; Sautois, Bart
2005-02-01
Many biological phenomena, notably in neuroscience, can be modeled by dynamical systems. We describe a recent improvement of a Matlab software package for dynamical systems with applications to modeling single neurons and all-to-all connected networks of neurons. The new software features consist of an object-oriented approach to bifurcation computations and the partial inclusion of C-code to speed up the computation. As an application, we study the origin of the spiking behaviour of neurons when the equilibrium state is destabilized by an incoming current. We show that Class II behaviour, i.e. firing with a finite frequency, is possible even if the destabilization occurs through a saddle-node bifurcation. Furthermore, we show that synchronization of an all-to-all connected network of such neurons with only excitatory connections is also possible in this case.
Hybrid intravenous digital subtraction angiography of the carotid bifurcation
International Nuclear Information System (INIS)
Burbank, F.H.; Enzmann, D.; Keyes, G.S.; Brody, W.R.
1984-01-01
A hybrid digital subtraction angiography technique and noise-reduction algorithm were used to evaluate the carotid bifurcation. Temporal, hybrid, and reduced-noise hybrid images were obtained in right and left anterior oblique projections, and both single- and multiple-frame images were created with each method. The resulting images were graded on a scale of 1 to 5 by three experienced neuroradiologists. Temporal images were preferred over hybrid images. The percentage of nondiagnostic examinations, as agreed upon by two readers, was higher for temporal alone than temporal + hybrid. In addition, also by agreement between two readers, temporal + hybrid images significantly increased the number of bifurcations seen in two views (87%) compared to temporal subtraction alone
Local bifurcations in differential equations with state-dependent delay.
Sieber, Jan
2017-11-01
A common task when analysing dynamical systems is the determination of normal forms near local bifurcations of equilibria. As most of these normal forms have been classified and analysed, finding which particular class of normal form one encounters in a numerical bifurcation study guides follow-up computations. This paper builds on normal form algorithms for equilibria of delay differential equations with constant delay that were developed and implemented in DDE-Biftool recently. We show how one can extend these methods to delay-differential equations with state-dependent delay (sd-DDEs). Since higher degrees of regularity of local center manifolds are still open for sd-DDEs, we give an independent (still only partial) argument which phenomena from the truncated normal must persist in the full sd-DDE. In particular, we show that all invariant manifolds with a sufficient degree of normal hyperbolicity predicted by the normal form exist also in the full sd-DDE.
Local bifurcations in differential equations with state-dependent delay
Sieber, Jan
2017-11-01
A common task when analysing dynamical systems is the determination of normal forms near local bifurcations of equilibria. As most of these normal forms have been classified and analysed, finding which particular class of normal form one encounters in a numerical bifurcation study guides follow-up computations. This paper builds on normal form algorithms for equilibria of delay differential equations with constant delay that were developed and implemented in DDE-Biftool recently. We show how one can extend these methods to delay-differential equations with state-dependent delay (sd-DDEs). Since higher degrees of regularity of local center manifolds are still open for sd-DDEs, we give an independent (still only partial) argument which phenomena from the truncated normal must persist in the full sd-DDE. In particular, we show that all invariant manifolds with a sufficient degree of normal hyperbolicity predicted by the normal form exist also in the full sd-DDE.
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)
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.
Fold points and singularity induced bifurcation in inviscid transonic flow
International Nuclear Information System (INIS)
Marszalek, Wieslaw
2012-01-01
Transonic inviscid flow equation of elliptic–hyperbolic type when written in terms of the velocity components and similarity variable results in a second order nonlinear ODE having several features typical of differential–algebraic equations rather than ODEs. These features include the fold singularities (e.g. folded nodes and saddles, forward and backward impasse points), singularity induced bifurcation behavior and singularity crossing phenomenon. We investigate the above properties and conclude that the quasilinear DAEs of transonic flow have interesting properties that do not occur in other known quasilinear DAEs, for example, in MHD. Several numerical examples are included. -- Highlights: ► A novel analysis of inviscid transonic flow and its similarity solutions. ► Singularity induced bifurcation, singular points of transonic flow. ► Projection method, index of transonic flow DAEs, linearization via matrix pencil.
Bifurcation theory applied to buckling states of a cylindrical shell
Chaskalovic, J.; Naili, S.
1995-01-01
Veins, bronchii, and many other vessels in the human body are flexible enough to be capable of collapse if submitted to suitable applied external and internal loads. One way to describe this phenomenon is to consider an inextensible elastic and infinite tube, with a circular cross section in the reference configuration, subjected to a uniform external pressure. In this paper, we establish that the nonlinear equilibrium equation for this model has nontrivial solutions which appear for critical values of the pressure. To this end, the tools we use are the Liapunov-Schmidt decomposition and the bifurcation theorem for simple multiplicity. We conclude with the bifurcation diagram, showing the dependence between the cross-sectional area and the pressure.
Structural bifurcation of microwave helium jet discharge at atmospheric pressure
International Nuclear Information System (INIS)
Takamura, Shuichi; Kitoh, Masakazu; Soga, Tadasuke
2008-01-01
Structural bifurcation of microwave-sustained jet discharge at atmospheric gas pressure was found to produce a stable helium plasma jet, which may open the possibility of a new type of high-flux test plasma beam for plasma-wall interactions in fusion devices. The fundamental discharge properties are presented including hysteresis characteristics, imaging of discharge emissive structure, and stable ignition parameter area. (author)
Bifurcation analysis of magnetization dynamics driven by spin transfer
International Nuclear Information System (INIS)
Bertotti, G.; Magni, A.; Bonin, R.; Mayergoyz, I.D.; Serpico, C.
2005-01-01
Nonlinear magnetization dynamics under spin-polarized currents is discussed by the methods of the theory of nonlinear dynamical systems. The fixed points of the dynamics are calculated. It is shown that there may exist 2, 4, or 6 fixed points depending on the values of the external field and of the spin-polarized current. The stability of the fixed points is analyzed and the conditions for the occurrence of saddle-node and Hopf bifurcations are determined
Bifurcation analysis of magnetization dynamics driven by spin transfer
Energy Technology Data Exchange (ETDEWEB)
Bertotti, G. [IEN Galileo Ferraris, Strada delle Cacce 91, 10135 Turin (Italy); Magni, A. [IEN Galileo Ferraris, Strada delle Cacce 91, 10135 Turin (Italy); Bonin, R. [Dipartimento di Fisica, Politecnico di Torino, Corso degli Abbruzzi, 10129 Turin (Italy)]. E-mail: bonin@ien.it; Mayergoyz, I.D. [Department of Electrical and Computer Engineering, University of Maryland, College Park, Maryland 20742 (United States); Serpico, C. [Department of Electrical Engineering, University of Napoli Federico II, via Claudio 21, 80125 Naples (Italy)
2005-04-15
Nonlinear magnetization dynamics under spin-polarized currents is discussed by the methods of the theory of nonlinear dynamical systems. The fixed points of the dynamics are calculated. It is shown that there may exist 2, 4, or 6 fixed points depending on the values of the external field and of the spin-polarized current. The stability of the fixed points is analyzed and the conditions for the occurrence of saddle-node and Hopf bifurcations are determined.
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
Stability and bifurcation of an SIS epidemic model with treatment
International Nuclear Information System (INIS)
Li Xuezhi; Li Wensheng; Ghosh, Mini
2009-01-01
An SIS epidemic model with a limited resource for treatment is introduced and analyzed. It is assumed that treatment rate is proportional to the number of infectives below the capacity and is a constant when the number of infectives is greater than the capacity. It is found that a backward bifurcation occurs if the capacity is small. It is also found that there exist bistable endemic equilibria if the capacity is low.
Bifurcation in Z2-symmetry quadratic polynomial systems with delay
International Nuclear Information System (INIS)
Zhang Chunrui; Zheng Baodong
2009-01-01
Z 2 -symmetry systems are considered. Firstly the general forms of Z 2 -symmetry quadratic polynomial system are given, and then a three-dimensional Z 2 equivariant system is considered, which describes the relations of two predator species for a single prey species. Finally, the explicit formulas for determining the Fold and Hopf bifurcations are obtained by using the normal form theory and center manifold argument.
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...
Streamline topology: Patterns in fluid flows and their bifurcations
DEFF Research Database (Denmark)
Brøns, Morten
2007-01-01
Using dynamical systems theory, we consider structures such as vortices and separation in the streamline patterns of fluid flows. Bifurcation of patterns under variation of external parameters is studied using simplifying normal form transformations. Flows away from boundaries, flows close to fix...... walls, and axisymmetric flows are analyzed in detail. We show how to apply the ideas from the theory to analyze numerical simulations of the vortex breakdown in a closed cylindrical container....
Spiral blood flow in aorta-renal bifurcation models.
Javadzadegan, Ashkan; Simmons, Anne; Barber, Tracie
2016-01-01
The presence of a spiral arterial blood flow pattern in humans has been widely accepted. It is believed that this spiral component of the blood flow alters arterial haemodynamics in both positive and negative ways. The purpose of this study was to determine the effect of spiral flow on haemodynamic changes in aorta-renal bifurcations. In this regard, a computational fluid dynamics analysis of pulsatile blood flow was performed in two idealised models of aorta-renal bifurcations with and without flow diverter. The results show that the spirality effect causes a substantial variation in blood velocity distribution, while causing only slight changes in fluid shear stress patterns. The dominant observed effect of spiral flow is on turbulent kinetic energy and flow recirculation zones. As spiral flow intensity increases, the rate of turbulent kinetic energy production decreases, reducing the region of potential damage to red blood cells and endothelial cells. Furthermore, the recirculation zones which form on the cranial sides of the aorta and renal artery shrink in size in the presence of spirality effect; this may lower the rate of atherosclerosis development and progression in the aorta-renal bifurcation. These results indicate that the spiral nature of blood flow has atheroprotective effects in renal arteries and should be taken into consideration in analyses of the aorta and renal arteries.
Endodontic-periodontic bifurcation lesions: a novel treatment option.
Lin, Shaul; Tillinger, Gabriel; Zuckerman, Offer
2008-05-01
The purpose of this preliminary clinical report is to suggest a novel treatment modality for periodontal bifurcation lesions of endodontic origin. The study consisted of 11 consecutive patients who presented with periodontal bifurcation lesions of endodontic origin (endo-perio lesions). All patients were followed-up for at least 12 months. Treatment included calcium hydroxide with iodine-potassium iodide placed in the root canals for 90 days followed by canal sealing with gutta-percha and cement during a second stage. Dentin bonding was used to seal the furcation floor to prevent the ingress of bacteria and their by-products to the furcation root area through the accessory canals. A radiographic examination showed complete healing of the periradicular lesion in all patients. Probing periodontal pocket depths decreased to 2 to 4 mm (mean 3.5 mm), and resolution of the furcation involvement was observed in post-operative clinical evaluations. The suggested treatment of endo-perio lesions may result in complete healing. Further studies are warranted. This treatment method improves both the disinfection of the bifurcation area and the healing process in endodontically treated teeth considered to be hopeless.
Bifurcation in autonomous and nonautonomous differential equations with discontinuities
Akhmet, Marat
2017-01-01
This book is devoted to bifurcation theory for autonomous and nonautonomous differential equations with discontinuities of different types. That is, those with jumps present either in the right-hand-side or in trajectories or in the arguments of solutions of equations. The results obtained in this book can be applied to various fields such as neural networks, brain dynamics, mechanical systems, weather phenomena, population dynamics, etc. Without any doubt, bifurcation theory should be further developed to different types of differential equations. In this sense, the present book will be a leading one in this field. The reader will benefit from the recent results of the theory and will learn in the very concrete way how to apply this theory to differential equations with various types of discontinuity. Moreover, the reader will learn new ways to analyze nonautonomous bifurcation scenarios in these equations. The book will be of a big interest both for beginners and experts in the field. For the former group o...
Hopf Bifurcation Control of Subsynchronous Resonance Utilizing UPFC
Directory of Open Access Journals (Sweden)
Μ. Μ. Alomari
2017-06-01
Full Text Available The use of a unified power flow controller (UPFC to control the bifurcations of a subsynchronous resonance (SSR in a multi-machine power system is introduced in this study. UPFC is one of the flexible AC transmission systems (FACTS where a voltage source converter (VSC is used based on gate-turn-off (GTO thyristor valve technology. Furthermore, UPFC can be used as a stabilizer by means of a power system stabilizer (PSS. The considered system is a modified version of the second system of the IEEE second benchmark model of subsynchronous resonance where the UPFC is added to its transmission line. The dynamic effects of the machine components on SSR are considered. Time domain simulations based on the complete nonlinear dynamical mathematical model are used for numerical simulations. The results in case of including UPFC are compared to the case where the transmission line is conventionally compensated (without UPFC where two Hopf bifurcations are predicted with unstable operating point at wide range of compensation levels. For UPFC systems, it is worth to mention that the operating point of the system never loses stability at all realistic compensation degrees and therefore all power system bifurcations have been eliminated.
Nonlinear stability, bifurcation and resonance in granular plane Couette flow
Shukla, Priyanka; Alam, Meheboob
2010-11-01
A weakly nonlinear stability theory is developed to understand the effect of nonlinearities on various linear instability modes as well as to unveil the underlying bifurcation scenario in a two-dimensional granular plane Couette flow. The relevant order parameter equation, the Landau-Stuart equation, for the most unstable two-dimensional disturbance has been derived using the amplitude expansion method of our previous work on the shear-banding instability.ootnotetextShukla and Alam, Phys. Rev. Lett. 103, 068001 (2009). Shukla and Alam, J. Fluid Mech. (2010, accepted). Two types of bifurcations, Hopf and pitchfork, that result from travelling and stationary linear instabilities, respectively, are analysed using the first Landau coefficient. It is shown that the subcritical instability can appear in the linearly stable regime. The present bifurcation theory shows that the flow is subcritically unstable to disturbances of long wave-lengths (kx˜0) in the dilute limit, and both the supercritical and subcritical states are possible at moderate densities for the dominant stationary and traveling instabilities for which kx=O(1). We show that the granular plane Couette flow is prone to a plethora of resonances.ootnotetextShukla and Alam, J. Fluid Mech. (submitted, 2010)
Bifurcation-based approach reveals synergism and optimal combinatorial perturbation.
Liu, Yanwei; Li, Shanshan; Liu, Zengrong; Wang, Ruiqi
2016-06-01
Cells accomplish the process of fate decisions and form terminal lineages through a series of binary choices in which cells switch stable states from one branch to another as the interacting strengths of regulatory factors continuously vary. Various combinatorial effects may occur because almost all regulatory processes are managed in a combinatorial fashion. Combinatorial regulation is crucial for cell fate decisions because it may effectively integrate many different signaling pathways to meet the higher regulation demand during cell development. However, whether the contribution of combinatorial regulation to the state transition is better than that of a single one and if so, what the optimal combination strategy is, seem to be significant issue from the point of view of both biology and mathematics. Using the approaches of combinatorial perturbations and bifurcation analysis, we provide a general framework for the quantitative analysis of synergism in molecular networks. Different from the known methods, the bifurcation-based approach depends only on stable state responses to stimuli because the state transition induced by combinatorial perturbations occurs between stable states. More importantly, an optimal combinatorial perturbation strategy can be determined by investigating the relationship between the bifurcation curve of a synergistic perturbation pair and the level set of a specific objective function. The approach is applied to two models, i.e., a theoretical multistable decision model and a biologically realistic CREB model, to show its validity, although the approach holds for a general class of biological systems.
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 ...
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
Quasi-periodicity and chaos in a differentially heated cavity
Energy Technology Data Exchange (ETDEWEB)
Mercader, Isabel; Batiste, Oriol [Universitat Politecnica de Catalunya, Dep. Fisica Aplicada, Barcelona (Spain); Ruiz, Xavier [Univesitat Rovira i Virgili, Lab. Fisica Aplicada, Facultat de Ciencies Quimiques, Tarragona (Spain)
2004-11-01
Convective flows of a small Prandtl number fluid contained in a two-dimensional vertical cavity subject to a lateral thermal gradient are studied numerically. The chosen geometry and the values of the material parameters are relevant to semiconductor crystal growth experiments in the horizontal configuration of the Bridgman method. For increasing Rayleigh numbers we find a transition from a steady flow to periodic solutions through a supercritical Hopf bifurcation that maintains the centro-symmetry of the basic circulation. For a Rayleigh number of about ten times that of the Hopf bifurcation, the periodic solution loses stability in a subcritical Neimark-Sacker bifurcation, which gives rise to a branch of quasiperiodic states. In this branch, several intervals of frequency locking have been identified. Inside the resonance horns the stable limit cycles lose and gain stability via some typical scenarios in the bifurcation of periodic solutions. After a complicated bifurcation diagram of the stable limit cycle of the 1:10 resonance horn, a soft transition to chaos is obtained. (orig.)
Hegemony and Bifurcation Points in World History
Directory of Open Access Journals (Sweden)
Terry Boswell
1995-08-01
Full Text Available Examination of the rise and fall of hegemons over the last 500 years reveals that each lasts about 100 years, with another 100 year period between hegemons that is characterized by rough balance among shifting powers frequent major wars. Can the future differ from the long and established pattern? Theories that causally link hegemony to uneven development succeed in explaining the perennial rise and fall of world leaders, but fail to explain the persistence of a leader who has become hegemonic. The explanation given here is the establishment of institutional inertia in the world order, which slows the diffusion of innovations, but also restrains the adoption of subsequent changes. An analytic model describes the cycle of hegemony as the historically and politically contingent interaction of long terms trends in the world-system. Recently, hegemony has come into interaction with the cumulative trends of market commodification, decolonization, and democratization. This has produced a rise in independent nations and decline of imperial states worldwide. In the conclusion, we speculate on how these new developments make possible such events as a multi-state hegemony, a shared world polity, and a democratic world government.
Bifurcating Particle Swarms in Smooth-Walled Fractures
Pyrak-Nolte, L. J.; Sun, H.
2010-12-01
Particle swarms can occur naturally or from industrial processes where small liquid drops containing thousands to millions of micron-size to colloidal-size particles are released over time from seepage or leaks into fractured rock. The behavior of these particle swarms as they fall under gravity are affected by particle interactions as well as interactions with the walls of the fractures. In this paper, we present experimental results on the effect of fractures on the cohesiveness of the swarm and the formation of bifurcation structures as they fall under gravity and interact with the fracture walls. A transparent cubic sample (100 mm x 100 mm x 100 mm) containing a synthetic fracture with uniform aperture distributions was optically imaged to quantify the effect of confinement within fractures on particle swarm formation, swarm velocity, and swarm geometry. A fracture with a uniform aperture distribution was fabricated from two polished rectangular prisms of acrylic. A series of experiments were performed to determine how swarm movement and geometry are affected as the walls of the fracture are brought closer together from 50 mm to 1 mm. During the experiments, the fracture was fully saturated with water. We created the swarms using two different particle sizes in dilute suspension (~ 1.0% by mass). The particles were 3 micron diameter fluorescent polymer beads and 25 micron diameter soda-lime glass beads. Experiments were performed using swarms that ranged in size from 5 µl to 60 µl. The swarm behavior was imaged using an optical fluorescent imaging system composed of a CCD camera illuminated by a 100 mW diode-pumped doubled YAG laser. As a swarm falls in an open-tank of water, it forms a torroidal shape that is stable as long as no ambient or background currents exist in the water tank. When a swarm is released into a fracture with an aperture less than 5 mm, the swarm forms the torroidal shape but it is distorted because of the presence of the walls. The
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
Tongues of periodicity in a family of two-dimensional discontinuous maps of real Moebius type
International Nuclear Information System (INIS)
Sushko, Iryna; Gardini, Laura; Puu, Toenu
2004-01-01
In this paper we consider a two-dimensional piecewise-smooth discontinuous map representing the so-called 'relative dynamics' of an Hicksian business cycle model. The main features of the dynamics occur in the parameter region in which no fixed points at finite distance exist, but we may have attracting cycles of any periods. The bifurcations associated with the periodicity tongues of the map are studied making use of the first-return map on a suitable segment of the phase plane. The bifurcation curves bounding the periodicity tongues in the parameter plane are related with saddle-node and border-collision bifurcations of the first-return map. Moreover, the particular 'sausages structure' of the bifurcation tongues is also explained
Barker, Blake; Jung, Soyeun; Zumbrun, Kevin
2018-03-01
Turing patterns on unbounded domains have been widely studied in systems of reaction-diffusion equations. However, up to now, they have not been studied for systems of conservation laws. Here, we (i) derive conditions for Turing instability in conservation laws and (ii) use these conditions to find families of periodic solutions bifurcating from uniform states, numerically continuing these families into the large-amplitude regime. For the examples studied, numerical stability analysis suggests that stable periodic waves can emerge either from supercritical Turing bifurcations or, via secondary bifurcation as amplitude is increased, from subcritical Turing bifurcations. This answers in the affirmative a question of Oh-Zumbrun whether stable periodic solutions of conservation laws can occur. Determination of a full small-amplitude stability diagram - specifically, determination of rigorous Eckhaus-type stability conditions - remains an interesting open problem.
Wang, William S.; Vanapalli, Siva A.
2014-01-01
We report that modular millifluidic networks are simpler, more cost-effective alternatives to traditional microfluidic networks, and they can be rapidly generated and altered to optimize designs. Droplet traffic can also be studied more conveniently and inexpensively at the millimeter scale, as droplets are readily visible to the naked eye. Bifurcated loops, ladder networks, and parking networks were made using only Tygon® tubing and plastic T-junction fittings and visualized using an iPod® camera. As a case study, droplet traffic experiments through a millifluidic bifurcated loop were conducted, and the periodicity of drop spacing at the outlet was mapped over a wide range of inlet drop spacing. We observed periodic, intermittent, and aperiodic behaviors depending on the inlet drop spacing. The experimentally observed periodic behaviors were in good agreement with numerical simulations based on the simple network model. Our experiments further identified three main sources of intermittency between different periodic and/or aperiodic behaviors: (1) simultaneous entering and exiting events, (2) channel defects, and (3) equal or nearly equal hydrodynamic resistances in both sides of the bifurcated loop. In cases of simultaneous events and/or channel defects, the range of input spacings where intermittent behaviors are observed depends on the degree of inherent variation in input spacing. Finally, using a time scale analysis of syringe pump fluctuations and experiment observation times, we find that in most cases, more consistent results can be generated in experiments conducted at the millimeter scale than those conducted at the micrometer scale. Thus, millifluidic networks offer a simple means to probe collective interactions due to drop traffic and optimize network geometry to engineer passive devices for biological and material analysis. PMID:25553188
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
Bifurcations of the normal modes of the Ne...Br{sub 2} complex
Energy Technology Data Exchange (ETDEWEB)
Blesa, Fernando [Departamento de Fisica Aplicada, Universidad de Zaragoza, Zaragoza (Spain); Mahecha, Jorge [Instituto de Fisica, Universidad de Antioquia, Medellin (Colombia); Salas, J. Pablo [Area de Fisica Aplicada, Universidad de La Rioja, Logrono (Spain); Inarrea, Manuel, E-mail: manuel.inarrea@unirioja.e [Area de Fisica Aplicada, Universidad de La Rioja, Logrono (Spain)
2009-12-28
We study the classical dynamics of the rare gas-dihalogen Ne...Br{sub 2} complex in its ground electronic state. By considering the dihalogen bond frozen at its equilibrium distance, the system has two degrees of freedom and its potential energy surface presents linear and T-shape isomers. We find the nonlinear normal modes of both isomers that determine the phase space structure of the system. By means of surfaces of section and applying the numerical continuation of families of periodic orbits, we detect and identify the different bifurcations suffered by the normal modes as a function of the system energy. Finally, using the Orthogonal Fast Lyapunov Indicator (OFLI), we study the evolution of the fraction of the phase space volume occupied by regular motions.
A global qualitative view of bifurcations and dynamics in the Roessler system
International Nuclear Information System (INIS)
Genesio, R.; Innocenti, G.; Gualdani, F.
2008-01-01
The aim of the Letter is a global study of the well-known Roessler system to point out the main complex dynamics that it can exhibit. The structural analysis is based on the periodic solutions of the system investigated by a harmonic balance technique. Simplified expressions of such limit cycles are first derived and characterized, then their local bifurcations are denoted, also giving indications to predict possible homoclinic orbits with the same unifying approach. These analytical results give a general picture of the system behaviours in the parameter space and numerical analysis and simulations confirm the qualitative accuracy of the whole. Such predictions have also an important role in applying efficiently the above numerical procedures
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.
Codimension-two bifurcation analysis on firing activities in Chay neuron model
International Nuclear Information System (INIS)
Duan Lixia; Lu Qishao
2006-01-01
Using codimension-two bifurcation analysis in the Chay neuron model, the relationship between the electric activities and the parameters of neurons is revealed. The whole parameter space is divided into two parts, that is, the firing and silence regions of neurons. It is found that the transition sets between firing and silence regions are composed of the Hopf bifurcation curves of equilibrium states and the saddle-node bifurcation curves of limit cycles, with some codimension-two bifurcation points. The transitions from silence to firing in neurons are due to the Hopf bifurcation or the fold limit cycle bifurcation, but the codimension-two singularities lead to complexity in dynamical behaviour of neuronal firing
Codimension-Two Bifurcation Analysis in DC Microgrids Under Droop Control
Lenz, Eduardo; Pagano, Daniel J.; Tahim, André P. N.
This paper addresses local and global bifurcations that may appear in electrical power systems, such as DC microgrids, which recently has attracted interest from the electrical engineering society. Most sources in these networks are voltage-type and operate in parallel. In such configuration, the basic technique for stabilizing the bus voltage is the so-called droop control. The main contribution of this work is a codimension-two bifurcation analysis of a small DC microgrid considering the droop control gain and the power processed by the load as bifurcation parameters. The codimension-two bifurcation set leads to practical rules for achieving a robust droop control design. Moreover, the bifurcation analysis also offers a better understanding of the dynamics involved in the problem and how to avoid possible instabilities. Simulation results are presented in order to illustrate the bifurcation analysis.
Codimension-two bifurcation analysis on firing activities in Chay neuron model
Energy Technology Data Exchange (ETDEWEB)
Duan Lixia [School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083 (China); Lu Qishao [School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083 (China)]. E-mail: qishaolu@hotmail.com
2006-12-15
Using codimension-two bifurcation analysis in the Chay neuron model, the relationship between the electric activities and the parameters of neurons is revealed. The whole parameter space is divided into two parts, that is, the firing and silence regions of neurons. It is found that the transition sets between firing and silence regions are composed of the Hopf bifurcation curves of equilibrium states and the saddle-node bifurcation curves of limit cycles, with some codimension-two bifurcation points. The transitions from silence to firing in neurons are due to the Hopf bifurcation or the fold limit cycle bifurcation, but the codimension-two singularities lead to complexity in dynamical behaviour of neuronal firing.
Sliding bifurcations and chaos induced by dry friction in a braking system
International Nuclear Information System (INIS)
Yang, F.H.; Zhang, W.; Wang, J.
2009-01-01
In this paper, non-smooth bifurcations and chaotic dynamics are investigated for a braking system. A three-degree-of-freedom model is considered to capture the complicated nonlinear characteristics, in particular, non-smooth bifurcations in the braking system. The stick-slip transition is analyzed for the braking system. From the results of numerical simulation, it is observed that there also exist the grazing-sliding bifurcation and stick-slip chaos in the braking system.
Bifurcation Analysis of the QI 3-D Four-Wing Chaotic System
International Nuclear Information System (INIS)
Sun, Y.; Qi, G.; Wang, Z.; Wyk, B.J. van
2010-01-01
This paper analyzes the pitchfork and Hopf bifurcations of a new 3-D four-wing quadratic autonomous system proposed by Qi et al. The center manifold technique is used to reduce the dimensions of this system. The pitchfork and Hopf bifurcations of the system are theoretically analyzed. The influence of system parameters on other bifurcations are also investigated. The theoretical analysis and simulations demonstrate the rich dynamics of the system. (authors)
Stability and bifurcation of a discrete BAM neural network model with delays
International Nuclear Information System (INIS)
Zheng Baodong; Zhang Yang; Zhang Chunrui
2008-01-01
A map modelling a discrete bidirectional associative memory neural network with delays is investigated. Its dynamics is studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, its linear stability is investigated and Hopf bifurcations are demonstrated. It is found that there exist Hopf bifurcations when the delay passes a sequence of critical values. Numerical simulation is performed to verify the analytical results
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
Bifurcation structure of localized states in the Lugiato-Lefever equation with anomalous dispersion
Parra-Rivas, P.; Gomila, D.; Gelens, L.; Knobloch, E.
2018-04-01
The origin, stability, and bifurcation structure of different types of bright localized structures described by the Lugiato-Lefever equation are studied. This mean field model describes the nonlinear dynamics of light circulating in fiber cavities and microresonators. In the case of anomalous group velocity dispersion and low values of the intracavity phase detuning these bright states are organized in a homoclinic snaking bifurcation structure. We describe how this bifurcation structure is destroyed when the detuning is increased across a critical value, and determine how a bifurcation structure known as foliated snaking emerges.
Hopf bifurcation in a delayed reaction-diffusion-advection population model
Chen, Shanshan; Lou, Yuan; Wei, Junjie
2018-04-01
In this paper, we investigate a reaction-diffusion-advection model with time delay effect. The stability/instability of the spatially nonhomogeneous positive steady state and the associated Hopf bifurcation are investigated when the given parameter of the model is near the principle eigenvalue of an elliptic operator. Our results imply that time delay can make the spatially nonhomogeneous positive steady state unstable for a reaction-diffusion-advection model, and the model can exhibit oscillatory pattern through Hopf bifurcation. The effect of advection on Hopf bifurcation values is also considered, and our results suggest that Hopf bifurcation is more likely to occur when the advection rate increases.
A numerical study of crack initiation in a bcc iron system based on dynamic bifurcation theory
International Nuclear Information System (INIS)
Li, Xiantao
2014-01-01
Crack initiation under dynamic loading conditions is studied under the framework of dynamic bifurcation theory. An atomistic model for BCC iron is considered to explicitly take into account the detailed molecular interactions. To understand the strain-rate dependence of the crack initiation process, we first obtain the bifurcation diagram from a computational procedure using continuation methods. The stability transition associated with a crack initiation, as well as the connection to the bifurcation diagram, is studied by comparing direct numerical results to the dynamic bifurcation theory [R. Haberman, SIAM J. Appl. Math. 37, 69–106 (1979)].
Numerical Hopf bifurcation of Runge-Kutta methods for a class of delay differential equations
International Nuclear Information System (INIS)
Wang Qiubao; Li Dongsong; Liu, M.Z.
2009-01-01
In this paper, we consider the discretization of parameter-dependent delay differential equation of the form y ' (t)=f(y(t),y(t-1),τ),τ≥0,y element of R d . It is shown that if the delay differential equation undergoes a Hopf bifurcation at τ=τ * , then the discrete scheme undergoes a Hopf bifurcation at τ(h)=τ * +O(h p ) for sufficiently small step size h, where p≥1 is the order of the Runge-Kutta method applied. The direction of numerical Hopf bifurcation and stability of bifurcating invariant curve are the same as that of delay differential equation.
Bifurcation analysis of a discrete SIS model with bilinear incidence depending on new infection.
Cao, Hui; Zhou, Yicang; Ma, Zhien
2013-01-01
A discrete SIS epidemic model with the bilinear incidence depending on the new infection is formulated and studied. The condition for the global stability of the disease free equilibrium is obtained. The existence of the endemic equilibrium and its stability are investigated. More attention is paid to the existence of the saddle-node bifurcation, the flip bifurcation, and the Hopf bifurcation. Sufficient conditions for those bifurcations have been obtained. Numerical simulations are conducted to demonstrate our theoretical results and the complexity of the model.
Delay Induced Hopf Bifurcation of an Epidemic Model with Graded Infection Rates for Internet Worms
Directory of Open Access Journals (Sweden)
Tao Zhao
2017-01-01
Full Text Available A delayed SEIQRS worm propagation model with different infection rates for the exposed computers and the infectious computers is investigated in this paper. The results are given in terms of the local stability and Hopf bifurcation. Sufficient conditions for the local stability and the existence of Hopf bifurcation are obtained by using eigenvalue method and choosing the delay as the bifurcation parameter. In particular, the direction and the stability of the Hopf bifurcation are investigated by means of the normal form theory and center manifold theorem. Finally, a numerical example is also presented to support the obtained theoretical results.
Bifurcation of the Kuroshio Extension at the Shatsky Rise
Hurlburt, Harley E.; Metzger, E. Joseph
1998-04-01
A 1/16° six-layer Pacific Ocean model north of 20°S is used to investigate the bifurcation of the Kuroshio Extension at the main Shatsky Rise and the pathway of the northern branch from the bifurcation to the subarctic front. Upper ocean-topographic coupling via a mixed barotropic-baroclinic instability is essential to this bifurcation and to the formation and mean pathway of the northern branch as are several aspects of the Shatsky Rise complex of topography and the latitude of the Kuroshio Extension in relation to the topography. The flow instabilities transfer energy to the abyssal layer where it is constrained by geostrophic contours of the bottom topography. The topographically constrained abyssal currents in turn steer upper ocean currents, which do not directly impinge on the bottom topography. This includes steering of mean pathways. Obtaining sufficient coupling requires very fine resolution of mesoscale variability and sufficient eastward penetration of the Kuroshio as an unstable inertial jet. Resolution of 1/8° for each variable was not sufficient in this case. The latitudinal extent of the main Shatsky Rise (31°N-36°N) and the shape of the downward slope on the north side are crucial to the bifurcation at the main Shatsky Rise, with both branches passing north of the peak. The well-defined, relatively steep and straight eastern edge of the Shatsky Rise topographic complex (30°N-42°N) and the southwestward abyssal flow along it play a critical role in forming the rest of the Kuroshio northern branch which flows in the opposite direction. A deep pass between the main Shatsky Rise and the rest of the ridge to the northeast helps to link the northern fork of the bifurcation at the main rise to the rest of the northern branch. Two 1/16° "identical twin" interannual simulations forced by daily winds 1981-1995 show that the variability in this region is mostly nondeterministic on all timescales that could be examined (up to 7 years in these 15-year
International Nuclear Information System (INIS)
Rouben, D.C.
1997-01-01
A semiclassical method for resonant tunneling in a quantum well in the presence of a magnetic field tilted with regard to an electric field is developed. In particular a semiclassical formula is derived for the total current of electrons after the second barrier of the quantum well. The contribution of the stable and unstable orbits is studied. It appears that the parameters which describe the classical chaos in the quantum well have an important effect on the tunneling current. A numerical experiment is led, the contributions to the current of some particular orbits are evaluated and the results are compared with those given by the quantum theory. (A.C.)
James F. Selgrade; James H. Roberds
1998-01-01
This study considers a general class of two-dimensional, discrete population models where each per capita transition function (fitness) depends on a linear combination of the densities of the interacting populations. The fitness functions are either monotone decreasing functions (pioneer fitnesses) or one-humped functions (climax fitnesses). Conditions are derived...
Dynamical Regimes and the Dynamo Bifurcation in Geodynamo Simulations
Petitdemange, L.
2017-12-01
We investigate the nature of the dynamo bifurcation in a configuration applicable to the Earth's liquid outer core : in a rotating spherical shell with thermally driven motions with no-slip boundaries. Unlike previous studies on dynamo bifurcations, the control parameters have been varied significantly in order to deduce general tendencies. Numerical studies on the stability domain of dipolar magnetic fields found a dichotomy between non-reversing dipole-dominated dynamos and the reversing non-dipole-dominated multipolar solutions. We show that, by considering weak initial fields, the above transition is replaced by a region of bistability for which dipolar and multipolar dynamos coexist. Such a result was also observed in models with free-slip boundaries in which the strong shear of geostrophic zonal flows can develop and gives rise to non-dipolar fields. We show that a similar process develops in no-slip models when viscous effects are reduced sufficiently.Close to the onset of convection (Rac), the axial dipole grows exponentially in the kinematic phase and saturation occurs by marginally changing the flow structure close to the dynamo threshold Rmc. The resulting bifurcation is then supercritical.In the range 3RacIf (Ra/Ra_c>10), important zonal flows develop in non-magnetic models with low viscosity. The field topology depends on the initial magnetic field. The dipolar branch has a subcritical behaviour whereas the multipolar branch is supercritical. By approaching more realistic parameters, the extension of this bistable regime increases (lower Rossby numbers). An hysteretic behaviour questions the common interpretation for geomagnetic reversals. Far above Rm_c$, the Lorentz force becomes dominant, as it is expected in planetary cores.
Dynamic stability and bifurcation analysis in fractional thermodynamics
Béda, Péter B.
2018-02-01
In mechanics, viscoelasticity was the first field of applications in studying geomaterials. Further possibilities arise in spatial non-locality. Non-local materials were already studied in the 1960s by several authors as a part of continuum mechanics and are still in focus of interest because of the rising importance of materials with internal micro- and nano-structure. When material instability gained more interest, non-local behavior appeared in a different aspect. The problem was concerned to numerical analysis, because then instability zones exhibited singular properties for local constitutive equations. In dynamic stability analysis, mathematical aspects of non-locality were studied by using the theory of dynamic systems. There the basic set of equations describing the behavior of continua was transformed to an abstract dynamic system consisting of differential operators acting on the perturbation field variables. Such functions should satisfy homogeneous boundary conditions and act as indicators of stability of a selected state of the body under consideration. Dynamic systems approach results in conditions for cases, when the differential operators have critical eigenvalues of zero real parts (dynamic stability or instability conditions). When the critical eigenvalues have non-trivial eigenspace, the way of loss of stability is classified as a typical (or generic) bifurcation. Our experiences show that material non-locality and the generic nature of bifurcation at instability are connected, and the basic functions of the non-trivial eigenspace can be used to determine internal length quantities of non-local mechanics. Fractional calculus is already successfully used in thermo-elasticity. In the paper, non-locality is introduced via fractional strain into the constitutive relations of various conventional types. Then, by defining dynamic systems, stability and bifurcation are studied for states of thermo-mechanical solids. Stability conditions and genericity
Technique and results of femoral bifurcation endarterectomy by eversion.
Dufranc, Julie; Palcau, Laura; Heyndrickx, Maxime; Gouicem, Djelloul; Coffin, Olivier; Felisaz, Aurélien; Berger, Ludovic
2015-03-01
This study evaluated, in a contemporary prospective series, the safety and efficacy of femoral endarterectomy using the eversion technique and compared our results with results obtained in the literature for the standard endarterectomy with patch closure. Between 2010 and 2012, 121 patients (76% male; mean age, 68.7 years; diabetes, 28%; renal insufficiency, 20%) underwent 147 consecutive femoral bifurcation endarterectomies using the eversion technique, associating or not inflow or outflow concomitant revascularization. The indications were claudication in 89 procedures (60%) and critical limb ischemia in 58 (40%). Primary, primary assisted, and secondary patency of the femoral bifurcation, clinical improvement, limb salvage, and survival were assessed using Kaplan-Meier life-table analysis. Factors associated with those primary end-points were evaluated with univariate analysis. The technical success of eversion was of 93.2%. The 30-day mortality was 0%, and the complication rate was 8.2%; of which, half were local and benign. Median follow-up was 16 months (range, 1.6-31.2 months). Primary, primary assisted, and secondary patencies were, respectively, 93.2%, 97.2%, and 98.6% at 2 years. Primary, primary assisted, and secondary maintenance of clinical improvement were, respectively, 79.9%, 94.6%, and 98.6% at 2 years. The predictive factors for clinical degradation were clinical stage (Rutherford category 5 or 6, P = .024), platelet aggregation inhibitor treatment other than clopidogrel (P = .005), malnutrition (P = .025), and bad tibial runoff (P = .0016). A reintervention was necessary in 18.3% of limbs at 2 years: 2% involving femoral bifurcation, 6.1% inflow improvement, and 9.5% outflow improvement. The risk factors of reintervention were platelet aggregation inhibitor (other than clopidogrel, P = .049) and cancer (P = .011). Limb preservation at 2 years was 100% in the claudicant population. Limb salvage was 88.6% in the critical limb ischemia population
One-dimensional map lattices: Synchronization, bifurcations, and chaotic structures
DEFF Research Database (Denmark)
Belykh, Vladimir N.; Mosekilde, Erik
1996-01-01
The paper presents a qualitative analysis of coupled map lattices (CMLs) for the case of arbitrary nonlinearity of the local map and with space-shift as well as diffusion coupling. The effect of synchronization where, independently of the initial conditions, all elements of a CML acquire uniform...... dynamics is investigated and stable chaotic time behaviors, steady structures, and traveling waves are described. Finally, the bifurcations occurring under the transition from spatiotemporal chaos to chaotic synchronization and the peculiarities of CMLs with specific symmetries are discussed....
Stochastic Calculus: Application to Dynamic Bifurcations and Threshold Crossings
Jansons, Kalvis M.; Lythe, G. D.
1998-01-01
For the dynamic pitchfork bifurcation in the presence of white noise, the statistics of the last time at zero are calculated as a function of the noise level ∈ and the rate of change of the parameter μ. The threshold crossing problem used, for example, to model the firing of a single cortical neuron is considered, concentrating on quantities that may be experimentally measurable but have so far received little attention. Expressions for the statistics of pre-threshold excursions, occupation density, and last crossing time of zero are compared with results from numerical generation of paths.
Bifurcation and stability analysis of a nonlinear milling process
Weremczuk, Andrzej; Rusinek, Rafal; Warminski, Jerzy
2018-01-01
Numerical investigations of milling operations dynamics are presented in this paper. A two degree of freedom nonlinear model is used to study workpiece-tool vibrations. The analyzed model takes into account both flexibility of the tool and the workpiece. The dynamics of the milling process is described by the discontinuous ordinary differential equation with time delay, which can cause process instability. First, stability lobes diagrams are created on the basis of the parameters determined in impact test of an end mill and workpiece. Next, the bifurcations diagrams are performed for different values of rotational speeds.
Square-lattice random Potts model: criticality and pitchfork bifurcation
International Nuclear Information System (INIS)
Costa, U.M.S.; Tsallis, C.
1983-01-01
Within a real space renormalization group framework based on self-dual clusters, the criticality of the quenched bond-mixed q-state Potts ferromagnet on square lattice is discussed. On qualitative grounds it is exhibited that the crossover from the pure fixed point to the random one occurs, while q increases, through a pitchfork bifurcation; the relationship with Harris criterion is analyzed. On quantitative grounds high precision numerical values are presented for the critical temperatures corresponding to various concentrations of the coupling constants J 1 and J 2 , and various ratios J 1 /J 2 . The pure, random and crossover critical exponents are discussed as well. (Author) [pt
Bifurcation analysis of dengue transmission model in Baguio City, Philippines
Libatique, Criselda P.; Pajimola, Aprimelle Kris J.; Addawe, Joel M.
2017-11-01
In this study, we formulate a deterministic model for the transmission dynamics of dengue fever in Baguio City, Philippines. We analyzed the existence of the equilibria of the dengue model. We computed and obtained conditions for the existence of the equilibrium states. Stability analysis for the system is carried out for disease free equilibrium. We showed that the system becomes stable under certain conditions of the parameters. A particular parameter is taken and with the use of the Theory of Centre Manifold, the proposed model demonstrates a bifurcation phenomenon. We performed numerical simulation to verify the analytical results.
Tu, W.; Cunningham, G.
2017-12-01
The relativistic electron flux in Earth's radiation belt are observed to drop by orders of magnitude on timescale of a few hours. Where do the electrons go during the dropout? This is one of the most important outstanding questions in radiation belt studies. Here we will study the 22 June 2015 dropout event which occurred during one of the largest geomagnetic storms in the last decade. A sudden and nearly complete loss of all the outer zone relativistic and ultra-relativistic electrons were observed after a strong interplanetary shock. The Last Closed Drift Shell (LCDS) calculated using the TS04 model reached as low as L*=3.7 during the shock and stay below L*=4 for 1 hour. The unusually low LCDS values suggest that magnetopause shadowing and the associated outward radial diffusion can contribute significantly to the observed dropout. In addition, Drift Orbit Bifurcation (DOB) has been suggested as an important loss mechanism for radiation belt electrons, especially when the solar wind dynamic pressure is high, but its relative importance has not been quantified. Here, we will model the June 2015 dropout event using a radial diffusion model that includes physical and event-specific inputs. First, we will trace electron drift shells based on TS04 model to identify the LCDS and bifurcation regions as a function of the 2nd adiabatic invariant (K) and time. To model magnetopause shadowing, electron lifetimes in our model will be set to electron drift periods at L*>LCDS. Electron lifetimes inside the bifurcation region have been estimated by Ukhorskiy et al. [JGR 2011, doi:10.1029/2011JA016623] as a function of L* and K, which will also be implemented in the model. This will be the first effort to include the DOB loss in a comprehensive radiation belt model. Furthermore, to realistically simulate outward radial diffusion, the new radial diffusion coefficients that are calculated based on the realistic TS04 model and include physical K dependence [Cunningham, JGR 2016
Energy Technology Data Exchange (ETDEWEB)
Li, K., E-mail: likai@imech.ac.cn [Key Laboratory of Microgravity, Chinese Academy of Sciences, Beijing 100190, China and National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190 (China); University of Chinese Academy of Sciences, Beijing 100190 (China); Xun, B.; Hu, W. R. [Key Laboratory of Microgravity, Chinese Academy of Sciences, Beijing 100190, China and National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190 (China)
2016-05-15
As a part of the preliminary studies for the future space experiment (Zona-K) in the Russian module of the International Space Station, some bifurcation routes to chaos of thermocapillary convection in two-dimensional liquid layers filled with 10 cSt silicone oil have been numerically studied in this paper. As the laterally applied temperature difference is raised, variations in the spatial structure and temporal evolution of the thermocapillary convection and a complex sequence of transitions are observed. The results show that the finite extent of the liquid layer significantly influences the tempo-spatial evolution of the thermocapillary convection. Moreover, the bifurcation route of the thermocapillary convection changes very sensitively by the aspect ratio of the liquid layer. With the increasing Reynolds number (applied temperature difference), the steady thermocapillary convection experiences two consecutive transitions from periodic oscillatory state to quasi-periodic oscillatory state with frequency-locking before emergence of chaotic convection in a liquid layer of aspect ratio 14.25, and the thermocapillary convection undergoes period-doubling cascades leading to chaotic convection in a liquid layer of aspect ratio 13.0.
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.
International Nuclear Information System (INIS)
Li, K.; Xun, B.; Hu, W. R.
2016-01-01
As a part of the preliminary studies for the future space experiment (Zona-K) in the Russian module of the International Space Station, some bifurcation routes to chaos of thermocapillary convection in two-dimensional liquid layers filled with 10 cSt silicone oil have been numerically studied in this paper. As the laterally applied temperature difference is raised, variations in the spatial structure and temporal evolution of the thermocapillary convection and a complex sequence of transitions are observed. The results show that the finite extent of the liquid layer significantly influences the tempo-spatial evolution of the thermocapillary convection. Moreover, the bifurcation route of the thermocapillary convection changes very sensitively by the aspect ratio of the liquid layer. With the increasing Reynolds number (applied temperature difference), the steady thermocapillary convection experiences two consecutive transitions from periodic oscillatory state to quasi-periodic oscillatory state with frequency-locking before emergence of chaotic convection in a liquid layer of aspect ratio 14.25, and the thermocapillary convection undergoes period-doubling cascades leading to chaotic convection in a liquid layer of aspect ratio 13.0.
Bifurcations in two-image photometric stereo for orthogonal illuminations
Kozera, R.; Prokopenya, A.; Noakes, L.; Śluzek, A.
2017-07-01
This paper discusses the ambiguous shape recovery in two-image photometric stereo for a Lambertian surface. The current uniqueness analysis refers to linearly independent light-source directions p = (0, 0, -1) and q arbitrary. For this case necessary and sufficient condition determining ambiguous reconstruction is governed by a second-order linear partial differential equation with constant coefficients. In contrast, a general position of both non-colinear illumination directions p and q leads to a highly non-linear PDE which raises a number of technical difficulties. As recently shown, the latter can also be handled for another family of orthogonal illuminations parallel to the OXZ-plane. For the special case of p = (0, 0, -1) a potential ambiguity stems also from the possible bifurcations of sub-local solutions glued together along a curve defined by an algebraic equation in terms of the data. This paper discusses the occurrence of similar bifurcations for such configurations of orthogonal light-source directions. The discussion to follow is supplemented with examples based on continuous reflectance map model and generated synthetic images.
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.
Local viscosity distribution in bifurcating microfluidic blood flows
Kaliviotis, E.; Sherwood, J. M.; Balabani, S.
2018-03-01
The red blood cell (RBC) aggregation phenomenon is majorly responsible for the non-Newtonian nature of blood, influencing the blood flow characteristics in the microvasculature. Of considerable interest is the behaviour of the fluid at the bifurcating regions. In vitro experiments, using microchannels, have shown that RBC aggregation, at certain flow conditions, affects the bluntness and skewness of the velocity profile, the local RBC concentration, and the cell-depleted layer at the channel walls. In addition, the developed RBC aggregates appear unevenly distributed in the outlets of these channels depending on their spatial distribution in the feeding branch, and on the flow conditions in the outlet branches. In the present work, constitutive equations of blood viscosity, from earlier work of the authors, are applied to flows in a T-type bifurcating microchannel to examine the local viscosity characteristics. Viscosity maps are derived for various flow distributions in the outlet branches of the channel, and the location of maximum viscosity magnitude is obtained. The viscosity does not appear significantly elevated in the branches of lower flow rate as would be expected on the basis of the low shear therein, and the maximum magnitude appears in the vicinity of the junction, and towards the side of the outlet branch with the higher flow rate. The study demonstrates that in the branches of lower flow rate, the local viscosity is also low, helping us to explain why the effects of physiological red blood cell aggregation have no adverse effects in terms of in vivo vascular resistance.
Prediction of fibre architecture and adaptation in diseased carotid bifurcations.
LENUS (Irish Health Repository)
Creane, Arthur
2011-12-01
Many studies have used patient-specific finite element models to estimate the stress environment in atherosclerotic plaques, attempting to correlate the magnitude of stress to plaque vulnerability. In complex geometries, few studies have incorporated the anisotropic material response of arterial tissue. This paper presents a fibre remodelling algorithm to predict the fibre architecture, and thus anisotropic material response in four patient-specific models of the carotid bifurcation. The change in fibre architecture during disease progression and its affect on the stress environment in the plaque were predicted. The mean fibre directions were assumed to lie at an angle between the two positive principal strain directions. The angle and the degree of dispersion were assumed to depend on the ratio of principal strain values. Results were compared with experimental observations and other numerical studies. In non-branching regions of each model, the typical double helix arterial fibre pattern was predicted while at the bifurcation and in regions of plaque burden, more complex fibre architectures were found. The predicted change in fibre architecture in the arterial tissue during plaque progression was found to alter the stress environment in the plaque. This suggests that the specimen-specific anisotropic response of the tissue should be taken into account to accurately predict stresses in the plaque. Since determination of the fibre architecture in vivo is a difficult task, the system presented here provides a useful method of estimating the fibre architecture in complex arterial geometries.
Partitioning of red blood cell aggregates in bifurcating microscale flows
Kaliviotis, E.; Sherwood, J. M.; Balabani, S.
2017-03-01
Microvascular flows are often considered to be free of red blood cell aggregates, however, recent studies have demonstrated that aggregates are present throughout the microvasculature, affecting cell distribution and blood perfusion. This work reports on the spatial distribution of red blood cell aggregates in a T-shaped bifurcation on the scale of a large microvessel. Non-aggregating and aggregating human red blood cell suspensions were studied for a range of flow splits in the daughter branches of the bifurcation. Aggregate sizes were determined using image processing. The mean aggregate size was marginally increased in the daughter branches for a range of flow rates, mainly due to the lower shear conditions and the close cell and aggregate proximity therein. A counterintuitive decrease in the mean aggregate size was apparent in the lower flow rate branches. This was attributed to the existence of regions depleted by aggregates of certain sizes in the parent branch, and to the change in the exact flow split location in the T-junction with flow ratio. The findings of the present investigation may have significant implications for microvascular flows and may help explain why the effects of physiological RBC aggregation are not deleterious in terms of in vivo vascular resistance.
Bifurcation to Enhanced Performance H-mode on NSTX
Battaglia, D. J.; Chang, C. S.; Gerhardt, S. P.; Kaye, S. M.; Maingi, R.; Smith, D. R.
2015-11-01
The bifurcation from H-mode (H98 Performance (EP)H-mode (H98 = 1.2 - 2.0) on NSTX is found to occur when the ion thermal (χi) and momentum transport become decoupled from particle transport, such that the ion temperature (Ti) and rotation pedestals increase independent of the density pedestal. The onset of the EPH-mode transition is found to correlate with decreased pedestal collisionality (ν*ped) and an increased broadening of the density fluctuation (dn/n) spectrum in the pedestal as measured with beam emission spectroscopy. The spectrum broadening at decreased ν*ped is consistent with GEM simulations that indicate the toroidal mode number of the most unstable instability increases as ν*ped decreases. The lowest ν*ped, and thus largest spectrum broadening, is achieved with low pedestal density via lithium wall conditioning and when Zeff in the pedestal is significantly reduced via large edge rotation shear from external 3D fields or a large ELM. Kinetic neoclassical transport calculations (XGC0) confirm that Zeff is reduced when edge rotation braking leads to a more negative Er that shifts the impurity density profiles inward relative to the main ion density. These calculations also describe the role kinetic neoclassical and anomalous transport effects play in the decoupling of energy, momentum and particle transport at the bifurcation to EPH-mode. This work was sponsored by the U.S. Department of Energy.
LENUS (Irish Health Repository)
Creane, Arthur
2012-07-01
Many soft biological tissues contain collagen fibres, which act as major load bearing constituents. The orientation and the dispersion of these fibres influence the macroscopic mechanical properties of the tissue and are therefore of importance in several areas of research including constitutive model development, tissue engineering and mechanobiology. Qualitative comparisons between these fibre architectures can be made using vector plots of mean orientations and contour plots of fibre dispersion but quantitative comparison cannot be achieved using these methods. We propose a \\'remodelling metric\\' between two angular fibre distributions, which represents the mean rotational effort required to transform one into the other. It is an adaptation of the earth mover\\'s distance, a similarity measure between two histograms\\/signatures used in image analysis, which represents the minimal cost of transforming one distribution into the other by moving distribution mass around. In this paper, its utility is demonstrated by considering the change in fibre architecture during a period of plaque growth in finite element models of the carotid bifurcation. The fibre architecture is predicted using a strain-based remodelling algorithm. We investigate the remodelling metric\\'s potential as a clinical indicator of plaque vulnerability by comparing results between symptomatic and asymptomatic carotid bifurcations. Fibre remodelling was found to occur at regions of plaque burden. As plaque thickness increased, so did the remodelling metric. A measure of the total predicted fibre remodelling during plaque growth, TRM, was found to be higher in the symptomatic group than in the asymptomatic group. Furthermore, a measure of the total fibre remodelling per plaque size, TRM\\/TPB, was found to be significantly higher in the symptomatic vessels. The remodelling metric may prove to be a useful tool in other soft tissues and engineered scaffolds where fibre adaptation is also present.
DEFF Research Database (Denmark)
Maeng, M.; Holm, N. R.; Erglis, A.
2013-01-01
Objectives This study sought to report the 5-year follow-up results of the Nordic Bifurcation Study. Background Randomized clinical trials with short-term follow-up have indicated that coronary bifurcation lesions may be optimally treated using the optional side branch stenting strategy. Methods...... complex strategy of planned stenting of both the main vessel and the side branch. (C) 2013 by the American College of Cardiology Foundation...
Bifurcation Analysis of Gene Propagation Model Governed by Reaction-Diffusion Equations
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Guichen Lu
2016-01-01
Full Text Available We present a theoretical analysis of the attractor bifurcation for gene propagation model governed by reaction-diffusion equations. We investigate the dynamical transition problems of the model under the homogeneous boundary conditions. By using the dynamical transition theory, we give a complete characterization of the bifurcated objects in terms of the biological parameters of the problem.
International Nuclear Information System (INIS)
Kwok, Philip Chong-hei; Ng, Wai Fu; Lam, Christine Suk-yee; Tsui, Polly Po; Faruqi, Asma
2003-01-01
Purpose: The relationship of the portalvein bifurcation to the liver capsule in Asians, which is an important landmark for transjugular intrahepatic portosystemic shunt, has not previously been described. Methods: The anatomy of the portal vein bifurcation was studied in 70 adult Chinese cadavers; it was characterized as intrahepatic or extrahepatic. The length of the exposed portion of the right and left portal veins was measured when the bifurcation was extrahepatic. Results: The portal vein bifurcation was intrahepatic in 37 cadavers (53%) and extrahepatic in 33 cadavers (47%). The mean length of the right and left extrahepatic portal veins was 0.96 cm and 0.85 cm respectively.Both were less than or equal to 2 cm in 94% of the cadavers with extrahepatic bifurcation. There was no correlation between the presence of cirrhosis and the location of the portal vein bifurcation(p 1.0). There was no statistically significant difference in liver mass in cadavers with either extrahepatic or intrahepatic bifurcation (p =0.40). Conclusions: These findings suggest that fortransjugular intrahepatic portosystemic shunt placement, a portal vein puncture 2 cm from the bifurcation will be safe in most cases
Hopf bifurcation of a free boundary problem modeling tumor growth with two time delays
International Nuclear Information System (INIS)
Xu Shihe
2009-01-01
In this paper, a free boundary problem modeling tumor growth with two discrete delays is studied. The delays respectively represents the time taken for cells to undergo mitosis and the time taken for the cell to modify the rate of cell loss due to apoptosis. We show the influence of time delays on the Hopf bifurcation when one of delays as a bifurcation parameter.
Bifurcation approach to the predator-prey population models (Version of the computer book)
International Nuclear Information System (INIS)
Bazykin, A.D.; Zudin, S.L.
1993-09-01
Hierarchically organized family of predator-prey systems is studied. The classification is founded on two interacting principles: the biological and mathematical ones. The different combinations of biological factors included correspond to different bifurcations (up to codimension 3). As theoretical so computing methods are used for analysis, especially concerning non-local bifurcations. (author). 6 refs, figs
Bifurcation direction and exchange of stability for variational inequalities on nonconvex sets
Czech Academy of Sciences Publication Activity Database
Eisner, Jan; Kučera, Milan; Recke, L.
2007-01-01
Roč. 67, č. 5 (2007), s. 1082-1101 ISSN 0362-546X R&D Projects: GA AV ČR IAA100190506 Institutional research plan: CEZ:AV0Z10190503 Keywords : multiparameter variational inequality * direction of bifurcation * stability of bifurcating solutions Subject RIV: BA - General Mathematics Impact factor: 1.097, year: 2007
Convectons in periodic and bounded domains
International Nuclear Information System (INIS)
Mercader, Isabel; Batiste, Oriol; Alonso, Arantxa; Knobloch, Edgar
2010-01-01
Numerical continuation is used to compute spatially localized convection in a binary fluid with no-slip laterally insulating boundary conditions and the results are compared with the corresponding ones for periodic boundary conditions (PBC). The change in the boundary conditions produces a dramatic change in the snaking bifurcation diagram that describes the organization of localized states with PBC: the snaking branches turn continuously into a large amplitude state that resembles periodic convection with defects at the sidewalls. Odd parity convectons are more affected by the boundary conditions since the sidewalls suppress the horizontal pumping action that accompanies these states in spatially periodic domains.
Convectons in periodic and bounded domains
Energy Technology Data Exchange (ETDEWEB)
Mercader, Isabel; Batiste, Oriol; Alonso, Arantxa [Departament de Fisica Aplicada, Universitat Politecnica de Catalunya, Barcelona (Spain); Knobloch, Edgar [Department of Physics, University of California, Berkeley, CA 94720 (United States)
2010-04-15
Numerical continuation is used to compute spatially localized convection in a binary fluid with no-slip laterally insulating boundary conditions and the results are compared with the corresponding ones for periodic boundary conditions (PBC). The change in the boundary conditions produces a dramatic change in the snaking bifurcation diagram that describes the organization of localized states with PBC: the snaking branches turn continuously into a large amplitude state that resembles periodic convection with defects at the sidewalls. Odd parity convectons are more affected by the boundary conditions since the sidewalls suppress the horizontal pumping action that accompanies these states in spatially periodic domains.
Attractors of the periodically forced Rayleigh system
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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.
Experimental observation of bifurcation nature of radial electric field in CHS heliotron/torsatron
International Nuclear Information System (INIS)
Fujisawa, Akihide; Iguchi, Harukazu; Yoshimura, Yasuo; Minami, Takashi; Tanaka, Kenji; Okamura, Shoichi; Matsuoka, Keisuke; Fujiwara, Masami
1999-01-01
Several interesting phenomena, such as the formation of a particular potential profile with a protuberance around the core and oscillatory stationary states termed electric pulsation, have been discovered using a heavy ion beam probe in the electron cyclotron heated plasmas of the CHS. This paper presents experimental observations which indicate that bifurcation of the radial electric field is responsible for such phenomena; existence of an ECH power threshold to obtain the profile with a protuberance, and its striking sensitivity to density. In particular, Flip-flop behavior of the potential near the power threshold clearly demonstrates bifurcation characteristics. Bifurcation of radial electric field in neoclassical theory is presented, and its qualitative expectation is discussed in the bifurcation phenomena. The neoclassical transition time scale between two bifurcative sates is compared with the experimental observations during the electric pulsation. It is confirmed that the neoclassical transition time is not contradictory with the experimental one. (author)
Bifurcation diagram features of a dc-dc converter under current-mode control
International Nuclear Information System (INIS)
Ruzbehani, Mohsen; Zhou Luowei; Wang Mingyu
2006-01-01
A common tool for analysis of the systems dynamics when the system has chaotic behaviour is the bifurcation diagram. In this paper, the bifurcation diagram of an ideal model of a dc-dc converter under current-mode control is analysed. Algebraic relations that give the critical points locations and describe the pattern of the bifurcation diagram are derived. It is shown that these simple algebraic and geometrical relations are responsible for the complex pattern of the bifurcation diagrams in such circuits. More explanation about the previously observed properties and introduction of some new ones are exposited. In addition, a new three-dimensional bifurcation diagram that can give better imagination of the parameters role is introduced
International Nuclear Information System (INIS)
Xue Yunjing; Gao Peiyi; Lin Yan
2007-01-01
Objective: To investigate flow patterns at carotid bifurcation in vivo by combining computational fluid dynamics (CFD)and MR angiography imaging. Methods: Seven subjects underwent contrast-enhanced MR angiography of carotid artery in Siemens 3.0 T MR. Flow patterns of the carotid artery bifurcation were calculated and visualized by combining MR vascular imaging post-processing and CFD. Results: The flow patterns of the carotid bifurcations in 7 subjects were varied with different phases of a cardiac cycle. The turbulent flow and back flow occurred at bifurcation and proximal of internal carotid artery (ICA) and external carotid artery (ECA), their occurrence and conformation were varied with different phase of a cardiac cycle. The turbulent flow and back flow faded out quickly when the blood flow to the distal of ICA and ECA. Conclusion: CFD combined with MR angiography can be utilized to visualize the cyclical change of flow patterns of carotid bifurcation with different phases of a cardiac cycle. (authors)
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...
Liu, Xia; Zhang, Tonghua; Meng, Xinzhu; Zhang, Tongqian
2018-04-01
In this paper, we propose a predator-prey model with herd behavior and prey-taxis. Then, we analyze the stability and bifurcation of the positive equilibrium of the model subject to the homogeneous Neumann boundary condition. By using an abstract bifurcation theory and taking prey-tactic sensitivity coefficient as the bifurcation parameter, we obtain a branch of stable nonconstant solutions bifurcating from the positive equilibrium. Our results show that prey-taxis can yield the occurrence of spatial patterns.
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)
Active control of continuous air jet with bifurcated synthetic jets
Directory of Open Access Journals (Sweden)
Dančová Petra
2017-01-01
Full Text Available The synthetic jets (SJs have many significant applications and the number of applications is increasing all the time. In this research the main focus is on the primary flow control which can be used effectively for the heat transfer increasing. This paper deals with the experimental research of the effect of two SJs worked in the bifurcated mode used for control of an axisymmetric air jet. First, the control synthetic jets were measured alone. After an adjustment, the primary axisymmetric jet was added in to the system. For comparison, the primary flow without synthetic jets control was also measured. All experiments were performed using PIV method whereby the synchronization between synthetic jets and PIV system was necessary to do.
10th International Workshop on Bifurcation and Degradation in Geomaterials
Zhao, Jidong
2015-01-01
This book contains contributions to the 10th International Workshop on Bifurcation and Degradation in Geomaterials held in Hong Kong, May 28-30, 2014. This event marks the silver Jubilee anniversary of an international conference series dedicated to the research on localization, instability, degradation and failure of geomaterials since 1988 when its first workshop was organized in Germany. This volume of book collects the latest progresses and state-of-the-art research from top researchers around the world, and covers topics including multiscale modeling, experimental characterization and theoretical analysis of various instability and degradation phenomena in geomaterials as well as their relevance to contemporary issues in engineering practice. This book can be used as a useful reference for research students, academics and practicing engineers who are interested in the instability and degradation problems in geomechanics and geotechnical engineering.
Stents in Renal Artery Bifurcation Stenosis: A Case Report
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Polytimi Leonardou
2011-01-01
Full Text Available A 39-year-old patient presented with poorly controlled hypertension, and she was referred to renal angiogram and potential renal angioplasty. Renal angiogram showed a bifurcation lesion of the right renal artery. A guide wire was used to cross the upper branch, while the lower branch was protected by another same-type guide wire through the same introducer. Two thin monorail balloons were used to dilate the two branches; however, despite balloon dilatation, the stenosis of the vessels persisted. The “kissing balloon” technique was then attempted by simultaneously inflating both branches using the same balloons, but more than a 70% residual stenosis persisted in each branch. Two stents were finally placed in a “kissing” way through the main renal artery. The imaging and clinical results were good, without any procedure-related complications. Three years clinical followup was also good, without any reason for further interventional approach.
Stents in Renal Artery Bifurcation Stenosis: A Case Report
Leonardou, Polytimi; Pappas, Paris
2011-01-01
A 39-year-old patient presented with poorly controlled hypertension, and she was referred to renal angiogram and potential renal angioplasty. Renal angiogram showed a bifurcation lesion of the right renal artery. A guide wire was used to cross the upper branch, while the lower branch was protected by another same-type guide wire through the same introducer. Two thin monorail balloons were used to dilate the two branches; however, despite balloon dilatation, the stenosis of the vessels persisted. The “kissing balloon” technique was then attempted by simultaneously inflating both branches using the same balloons, but more than a 70% residual stenosis persisted in each branch. Two stents were finally placed in a “kissing” way through the main renal artery. The imaging and clinical results were good, without any procedure-related complications. Three years clinical followup was also good, without any reason for further interventional approach. PMID:21789043
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...
Analysis of Spatiotemporal Dynamic and Bifurcation in a Wetland Ecosystem
Directory of Open Access Journals (Sweden)
Yi Wang
2015-01-01
Full Text Available A wetland ecosystem is studied theoretically and numerically to reveal the rules of dynamics which can be quite accurate to better describe the observed spatial regularity of tussock vegetation. Mathematical theoretical works mainly investigate the stability of constant steady states, the existence of nonconstant steady states, and bifurcation, which can deduce a standard parameter control relation and in return can provide a theoretical basis for the numerical simulation. Numerical analysis indicates that the theoretical works are correct and the wetland ecosystem can show rich dynamical behaviors not only regular spatial patterns. Our results further deepen and expand the study of dynamics in the wetland ecosystem. In addition, it is successful to display tussock formation in the wetland ecosystem may have important consequences for aquatic community structure, especially for species interactions and biodiversity. All these results are expected to be useful in the study of the dynamic complexity of wetland ecosystems.
Stability of River Bifurcations from Bedload to Suspended Load Dominated Conditions
de Haas, T.; Kleinhans, M. G.
2010-12-01
Bifurcations (also called diffluences) are as common as confluences in braided and anabranched rivers, and more common than confluences on alluvial fans and deltas where the network is essentially distributary. River bifurcations control the partitioning of both water and sediment through these systems with consequences for immediate river and coastal management and long-term evolution. Their stability is poorly understood and seems to differ between braided rivers, meandering river plains and deltas. In particular, it is the question to what extent the division of flow is asymmetrical in stable condition, where highly asymmetrical refers to channel closure and avulsion. Recent work showed that bifurcations in gravel bed braided rivers become more symmetrical with increasing sediment mobility, whereas bifurcations in a lowland sand delta become more asymmetrical with increasing sediment mobility. This difference is not understood and our objective is to resolve this issue. We use a one-dimensional network model with Y-shaped bifurcations to explore the parameter space from low to high sediment mobility. The model solves gradually varied flow, bedload transport and morphological change in a straightforward manner. Sediment is divided at the bifurcation including the transverse slope effect and the spiral flow effect caused by bends at the bifurcation. Width is evolved whilst conserving mass of eroded or built banks with the bed balance. The bifurcations are perturbed from perfect symmetry either by a subtle gradient advantage for one branch or a gentle bend at the bifurcation. Sediment transport was calculated with and without a critical threshold for sediment motion. Sediment mobility, determined in the upstream channel, was varied in three different ways to isolate the causal factor: by increasing discharge, increasing channel gradient and decreasing particle size. In reality the sediment mobility is mostly determined by particle size: gravel bed rivers are near
Ko, Jun Kyeung; Han, In Ho; Cho, Won Ho; Choi, Byung Kwan; Cha, Seung Heon; Choi, Chang Hwa; Lee, Sang Weon; Lee, Tae Hong
2015-05-01
Double stenting in a Y-configuration is a promising therapeutic option for wide-necked cerebral aneurysms not amenable to reconstruction with a single stent. We retrospectively evaluated the efficacy and safety of the crossing Y-stent technique for coiling of wide-necked bifurcation aneurysms. By collecting clinical and radiological data we evaluated from January 2007 through December 2013, 20 wide-necked bifurcation aneurysms. Twelve unruptured and eight ruptured aneurysms in 20 patients were treated with crossing Y-stent-assisted coiling. Aneurysm size and neck size ranged from 3.2 to 28.2mm (mean 7.5mm) and from 1.9 to 9.1mm (mean 4.5mm). A Y-configuration was established successfully in all 20 patients. All aneurysms were treated with a pair of Neuroform stents. The immediate angiographic results were total occlusion in 17 aneurysms, residual neck in two, and residual sac in one. Peri-operative morbidity was only 5%. Fifteen of 18 surviving patients underwent follow-up conventional angiography (mean, 10.9 months). The result showed stable occlusion in all 15 aneurysms and asymptomatic in-stent occlusion in one branch artery. At the end of the observation period (mean, 33.5 months), all 12 patients without subarachnoid hemorrhage had excellent clinical outcomes (mRS 0), except one (mRS 2). Of eight patients with subarachnoid hemorrhage, four remained symptom free (mRS 0), while the other four had were dependent or dead (mRS score, 3-6). In this report on 20 patients, crossing Y-stent technique for coiling of wide-necked bifurcation aneurysms showed a good technical safety and favorable clinical and angiographic outcome. Copyright © 2015. Published by Elsevier B.V.
Bifurcation Control of an Electrostatically-Actuated MEMS Actuator with Time-Delay Feedback
Directory of Open Access Journals (Sweden)
Lei Li
2016-10-01
Full Text Available The parametric excitation system consisting of a flexible beam and shuttle mass widely exists in microelectromechanical systems (MEMS, which can exhibit rich nonlinear dynamic behaviors. This article aims to theoretically investigate the nonlinear jumping phenomena and bifurcation conditions of a class of electrostatically-driven MEMS actuators with a time-delay feedback controller. Considering the comb structure consisting of a flexible beam and shuttle mass, the partial differential governing equation is obtained with both the linear and cubic nonlinear parametric excitation. Then, the method of multiple scales is introduced to obtain a slow flow that is analyzed for stability and bifurcation. Results show that time-delay feedback can improve resonance frequency and stability of the system. What is more, through a detailed mathematical analysis, the discriminant of Hopf bifurcation is theoretically derived, and appropriate time-delay feedback force can make the branch from the Hopf bifurcation point stable under any driving voltage value. Meanwhile, through global bifurcation analysis and saddle node bifurcation analysis, theoretical expressions about the system parameter space and maximum amplitude of monostable vibration are deduced. It is found that the disappearance of the global bifurcation point means the emergence of monostable vibration. Finally, detailed numerical results confirm the analytical prediction.
A bench top experimental model of bubble transport in multiple arteriole bifurcations
International Nuclear Information System (INIS)
Eshpuniyani, Brijesh; Fowlkes, J. Brian; Bull, Joseph L.
2005-01-01
Motivated by a novel gas embolotherapy technique, a bench top vascular bifurcation model is used to investigate the splitting of long bubbles in a series of liquid-filled bifurcations. The developmental gas embolotherapy technique aims to treat cancer by infarcting tumors with gas emboli that are formed by selective acoustic vaporization of ∼6 μm, intravascular, perfluorcarbon droplets. The resulting gas bubbles are large enough to extend through several vessel bifurcations. The current bench top experiments examine the effects of gravity and flow on bubble transport through multiple bifurcations. The effect of gravity is varied by changing the roll angle of the bifurcating network about its parent tube. Splitting at each bifurcation is nearly even when the roll angle is zero. It is demonstrated that bubbles can either stick at one of the second bifurcations or in the second generation daughter tubes, even though the flow rate in the parent tube is constant. The findings of this work indicate that both gravity and flow are important in determining the bubble transport, and suggest that a treatment strategy that includes multiple doses may be effective in delivering emboli to vessels not occluded by the initial dose
Ishikawa, Takuji; Fujiwara, Hiroki; Matsuki, Noriaki; Yoshimoto, Takefumi; Imai, Yohsuke; Ueno, Hironori; Yamaguchi, Takami
2011-02-01
Bifurcations and confluences are very common geometries in biomedical microdevices. Blood flow at microchannel bifurcations has different characteristics from that at confluences because of the multiphase properties of blood. Using a confocal micro-PIV system, we investigated the behaviour of red blood cells (RBCs) and cancer cells in microchannels with geometrically symmetric bifurcations and confluences. The behaviour of RBCs and cancer cells was strongly asymmetric at bifurcations and confluences whilst the trajectories of tracer particles in pure water were almost symmetric. The cell-free layer disappeared on the inner wall of the bifurcation but increased in size on the inner wall of the confluence. Cancer cells frequently adhered to the inner wall of the bifurcation but rarely to other locations. Because the wall surface coating and the wall shear stress were almost symmetric for the bifurcation and the confluence, the result indicates that not only chemical mediation and wall shear stress but also microscale haemodynamics play important roles in the adhesion of cancer cells to the microchannel walls. These results provide the fundamental basis for a better understanding of blood flow and cell adhesion in biomedical microdevices.
Complex dynamics and bifurcation analysis of host–parasitoid models with impulsive control strategy
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Yang, Jin; Tang, Sanyi; Tan, Yuanshun
2016-01-01
Highlights: • We develop novel host-parasitoid models with impulsive control strategy. • The effects of key parameters on the successful control have been addressed. • The complex dynamics and related biological significance are investigated. • The results between two types of host-parasitoid models have been discussed. - Abstract: In this paper, we propose and analyse two type host–parasitoid models with integrated pest management (IPM) interventions as impulsive control strategies. For fixed pulsed model, the threshold condition for the global stability of the host-eradication periodic solution is provided, and the effects of key parameters including the impulsive period, proportionate killing rate, instantaneous search rate, releasing constant, survival rate and the proportionate release rate on the threshold condition are discussed. Then latin hypercube sampling /partial rank correlation coefficients are used to carry out sensitivity analyses to determine the significance of each parameters. Further, bifurcation analyses are presented and the results show that coexistence of attractors existed for a wide range of parameters, and the switch-like transitions among these attractors indicate that varying dosages and frequencies of insecticide applications and numbers of parasitoid released are crucial for IPM strategy. For unfixed pulsed model, the results show that this model exists very complex dynamics and the host population can be controlled below ET, and it implies that the modelling methods are helpful for improving optimal strategies to design appropriate IPM.
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)
International Nuclear Information System (INIS)
Inayat-Hussain, Jawaid I.
2009-01-01
This work reports on a numerical investigation on the bifurcations of a flexible rotor response in active magnetic bearings taking into account the nonlinearity due to the geometric coupling of the magnetic actuators as well as that arising from the actuator forces that are nonlinear function of the coil current and the air gap. For the values of design and operating parameters of the rotor-bearing system investigated in this work, numerical results showed that the response of the rotor was always synchronous when the values of the geometric coupling parameter α were small. For relatively larger values of α, however, the response of the rotor displayed a rich variety of nonlinear dynamical phenomena including sub-synchronous vibrations of periods-2, -3, -6, -9, and -17, quasi-periodicity and chaos. Numerical results further revealed the co-existence of multiple attractors within certain ranges of the speed parameter Ω. In practical rotating machinery supported by active magnetic bearings, the possibility of synchronous rotor response to become non-synchronous or even chaotic cannot be ignored as preloads, fluid forces or other external excitation forces may cause the rotor's initial conditions to move from one basin of attraction to another. Non-synchronous and chaotic vibrations should be avoided as they induce fluctuating stresses that may lead to premature failure of the machinery's main components.
Analysis of the flow at a T-bifurcation for a ternary unit
International Nuclear Information System (INIS)
Campero, P; Beck, J; Jung, A
2014-01-01
The motivation of this research is to understand the flow behavior through a 90° T- type bifurcation, which connects a Francis turbine and the storage pump of a ternary unit, under different operating conditions (namely turbine, pump and hydraulic short-circuit operation). As a first step a CFD optimization process to define the hydraulic geometry of the bifurcation was performed. The CFD results show the complexity of the flow through the bifurcation, especially under hydraulic short-circuit operation. Therefore, it was decided to perform experimental investigations in addition to the CFD analysis, in order to get a better understanding of the flow. The aim of these studies was to investigate the flow development upstream and downstream the bifurcation, the estimation of the bifurcation loss coefficients and also to provide comprehensive data of the flow behavior for the whole operating range of the machine. In order to evaluate the development of the velocity field Stereo Particle Image Velocimetry (S-PIV) measurements at different sections upstream and downstream of the bifurcation on the main penstock and Laser Doppler Anemometrie (LDA) measurements at bifurcation inlet were performed. This paper presents the CFD results obtained for the final design for different operating conditions, the model test procedures and the model test results with special attention to: 1) The bifurcation head loss coefficients, and their extrapolation to prototype conditions, 2) S-PIV and LDA measurements. Additionally, criteria to define the minimal uniformity conditions for the velocity profiles entering the turbine are evaluated. Finally, based on the gathered flow information a better understanding to define the preferred location of a bifurcation is gained and can be applied to future projects
Analysis of the magnetohydrodynamic equations and study of the nonlinear solution bifurcations
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Morros Tosas, J.
1989-01-01
The nonlinear problems related to the plasma magnetohydrodynamic instabilities are studied. A bifurcation theory is applied and a general magnetohydrodynamic equation is proposed. Scalar functions, a steady magnetic field and a new equation for the velocity field are taken into account. A method allowing the obtention of suitable reduced equations for the instabilities study is described. Toroidal and cylindrical configuration plasmas are studied. In the cylindrical configuration case, analytical calculations are performed and two steady bifurcated solutions are found. In the toroidal configuration case, a suitable reduced equation system is obtained; a qualitative approach of a steady solution bifurcation on a toroidal Kink type geometry is carried out [fr
Stability and Hopf bifurcation analysis of a prey-predator system with two delays
International Nuclear Information System (INIS)
Li Kai; Wei Junjie
2009-01-01
In this paper, we have considered a prey-predator model with Beddington-DeAngelis functional response and selective harvesting of predator species. Two delays appear in this model to describe the time that juveniles take to mature. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, its linear stability is investigated and Hopf bifurcations are demonstrated. The stability and direction of the Hopf bifurcation are determined by applying the normal form method and the center manifold theory. Numerical simulation results are given to support the theoretical predictions.
Clip reconstruction of a large right MCA bifurcation aneurysm. Case report
Directory of Open Access Journals (Sweden)
Giovani A.
2014-06-01
Full Text Available We report a case of complex large middle cerebral artery (MCA bifurcation aneurysm that ruptured during dissection from the very adherent MCA branches but was successfully clipped and the MCA bifurcation reconstructed using 4 Yasargill clips. Through a right pterional craniotomy the sylvian fissure was largely opened as to allow enough workspace for clipping the aneurysm and placing a temporary clip on M1. The pacient recovered very well after surgery and was discharged after 1 week with no neurological deficit. Complex MCA bifurcation aneurysms can be safely reconstructed using regular clips, without the need of using fenestrated clips or complex by-pass procedures.
Lassen, Jens Flensted; Burzotta, Francesco; Banning, Adrian P; Lefèvre, Thierry; Darremont, Olivier; Hildick-Smith, David; Chieffo, Alaide; Pan, Manuel; Holm, Niels Ramsing; Louvard, Yves; Stankovic, Goran
2018-01-20
The European Bifurcation Club (EBC) was initiated in 2004 to support a continuous overview of the field of coronary artery bifurcation interventions and aims to facilitate a scientific discussion and an exchange of ideas on the management of bifurcation disease. The EBC hosts an annual, two-day compact meeting, dedicated to bifurcations, which brings together physicians, pathologists, engineers, biologists, physicists, mathematicians, epidemiologists and statisticians for detailed discussions. Every meeting is finalised with a consensus statement that reflects the unique opportunity of combining the opinion of interventional cardiologists with the opinion of a large variety of other scientists on bifurcation management. A series of consensus sessions dedicated to specific topics, to strengthen the consensus debates and focus the discussions, was introduced at this year's meeting. The sessions comprise an intensive overview of the present literature, a pro and con debate and a voting system, to guide the consensus-building process. The present document represents the summary of the up-to-date EBC consensus and recommendations from the 12th annual EBC meeting in 2016 in Rotterdam.
Rank One Strange Attractors in Periodically Kicked Predator-Prey System with Time-Delay
Yang, Wenjie; Lin, Yiping; Dai, Yunxian; Zhao, Huitao
2016-06-01
This paper is devoted to the study of the problem of rank one strange attractor in a periodically kicked predator-prey system with time-delay. Our discussion is based on the theory of rank one maps formulated by Wang and Young. Firstly, we develop the rank one chaotic theory to delayed systems. It is shown that strange attractors occur when the delayed system undergoes a Hopf bifurcation and encounters an external periodic force. Then we use the theory to the periodically kicked predator-prey system with delay, deriving the conditions for Hopf bifurcation and rank one chaos along with the results of numerical simulations.
Systematic parameter study of dynamo bifurcations in geodynamo simulations
Petitdemange, Ludovic
2018-04-01
We investigate the nature of the dynamo bifurcation in a configuration applicable to the Earth's liquid outer core, i.e. in a rotating spherical shell with thermally driven motions with no-slip boundaries. Unlike in previous studies on dynamo bifurcations, the control parameters have been varied significantly in order to deduce general tendencies. Numerical studies on the stability domain of dipolar magnetic fields found a dichotomy between non-reversing dipole-dominated dynamos and the reversing non-dipole-dominated multipolar solutions. We show that, by considering weak initial fields, the above transition disappears and is replaced by a region of bistability for which dipolar and multipolar dynamos coexist. Such a result was also observed in models with free-slip boundaries in which the geostrophic zonal flow can develop and participate to the dynamo mechanism for non-dipolar fields. We show that a similar process develops in no-slip models when viscous effects are reduced sufficiently. The following three regimes are distinguished: (i) Close to the onset of convection (Rac) with only the most critical convective mode (wave number) being present, dynamos set in supercritically in the Ekman number regime explored here and are dipole-dominated. Larger critical magnetic Reynolds numbers indicate that they are particularly inefficient. (ii) in the range 3 10) , the relative importance of zonal flows increases with Ra in non-magnetic models. The field topology depends on the magnitude of the initial magnetic field. The dipolar branch has a subcritical behavior whereas the multipolar branch has a supercritical behavior. By approaching more realistic parameters, the extension of this bistable regime increases. A hysteretic behavior questions the common interpretation for geomagnetic reversals. Far above the dynamo threshold (by increasing the magnetic Prandtl number), Lorentz forces contribute to the first order force balance, as predicted for planetary dynamos. When
International Nuclear Information System (INIS)
Laney, D.F.
1996-01-01
On larger and/or more complex sites, remediation of soil and groundwater is sometimes bifurcated. This presents some unique advantages with respect to expedited cleanup of one medium, however, it requires skillful planning and significant forethought to ensure that initial remediation efforts do not preclude some long-term options, and/or unduly influence the subsequent selection of a technology for the other operable units and/or media. this paper examines how the decision to bifurcate should be approached, the various methods of bifurcation, the advantages and disadvantages of bifurcation, and the best methods to build flexibility into the design of initial remediation systems so as to allow for consideration of a fuller range of options for remediation of other operable units and/or media at a later time. Pollutants of concern include: metals; petroleum hydrocarbons; and chlorinated solvents
Phenomenological and ratio bifurcations of a class of discrete time stochastic processes
Diks, C.G.H.; Wagener, F.O.O.
2011-01-01
Zeeman proposed a classification of stochastic dynamical systems based on the Morse classification of their invariant probability densities; the associated bifurcations are the ‘phenomenological bifurcations’ of L. Arnold. The classification is however not invariant under diffeomorphisms of the
Small-bubble transport and splitting dynamics in a symmetric bifurcation
Qamar, Adnan; Warnez, Matthew; Valassis, Doug T.; Guetzko, Megan E.; Bull, Joseph L.
2017-01-01
Simulations of small bubbles traveling through symmetric bifurcations are conducted to garner information pertinent to gas embolotherapy, a potential cancer treatment. Gas embolotherapy procedures use intra-arterial bubbles to occlude tumor blood supply. As bubbles pass through bifurcations in the blood stream nonhomogeneous splitting and undesirable bioeffects may occur. To aid development of gas embolotherapy techniques, a volume of fluid method is used to model the splitting process of gas bubbles passing through artery and arteriole bifurcations. The model reproduces the variety of splitting behaviors observed experimentally, including the bubble reversal phenomenon. Splitting homogeneity and maximum shear stress along the vessel walls is predicted over a variety of physical parameters. Small bubbles, having initial length less than twice the vessel diameter, were found unlikely to split in the presence of gravitational asymmetry. Maximum shear stresses were found to decrease exponentially with increasing Reynolds number. Vortex-induced shearing near the bifurcation is identified as a possible mechanism for endothelial cell damage.
Small-bubble transport and splitting dynamics in a symmetric bifurcation
Qamar, Adnan
2017-06-28
Simulations of small bubbles traveling through symmetric bifurcations are conducted to garner information pertinent to gas embolotherapy, a potential cancer treatment. Gas embolotherapy procedures use intra-arterial bubbles to occlude tumor blood supply. As bubbles pass through bifurcations in the blood stream nonhomogeneous splitting and undesirable bioeffects may occur. To aid development of gas embolotherapy techniques, a volume of fluid method is used to model the splitting process of gas bubbles passing through artery and arteriole bifurcations. The model reproduces the variety of splitting behaviors observed experimentally, including the bubble reversal phenomenon. Splitting homogeneity and maximum shear stress along the vessel walls is predicted over a variety of physical parameters. Small bubbles, having initial length less than twice the vessel diameter, were found unlikely to split in the presence of gravitational asymmetry. Maximum shear stresses were found to decrease exponentially with increasing Reynolds number. Vortex-induced shearing near the bifurcation is identified as a possible mechanism for endothelial cell damage.
Step-by-step manual for planning and performing bifurcation PCI: a resource-tailored approach.
Milasinovic, Dejan; Wijns, William; Ntsekhe, Mpiko; Hellig, Farrel; Mohamed, Awad; Stankovic, Goran
2018-02-02
As bifurcation PCI can often be resource-demanding due to the use of multiple guidewires, balloons and stents, different technical options are sometimes being explored, in different local settings, to meet the need of optimally treating a patient with a bifurcation lesion, while being confronted with limited material resources. Therefore, it seems important to keep a proper balance between what is recognised as the contemporary state of the art, and what is known to be potentially harmful and to be discouraged. Ultimately, the resource-tailored approach to bifurcation PCI may be characterised by the notion of minimum technical requirements for each step of a successful procedure. Hence, this paper describes the logical sequence of steps when performing bifurcation PCI with provisional SB stenting, starting with basic anatomy assessment and ending with the optimisation of MB stenting and the evaluation of the potential need to stent the SB, suggesting, for each step, the minimum technical requirement for a successful intervention.
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.