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.
Global Bifurcation of a Novel Computer Virus Propagation Model
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.
Global bifurcations in a piecewise-smooth Cournot duopoly game
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.
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.
Pandey, Vikas; Singh, Suneet, E-mail: suneet.singh@iitb.ac.in
2017-04-15
Highlights: • Non-linear stability analysis of nuclear reactor is carried out. • Global and local stability boundaries are drawn in the parameter space. • Globally stable, bi-stable, and unstable regions have been demarcated. • The identification of the regions is verified by numerical simulations. - Abstract: Nonlinear stability study of the neutron coupled thermal hydraulics instability has been carried out by several researchers for boiling water reactors (BWRs). The focus of these studies has been to identify subcritical and supercritical Hopf bifurcations. Supercritical Hopf bifurcation are soft or safe due to the fact that stable limit cycles arise in linearly unstable region; linear and global stability boundaries are same for this bifurcation. It is well known that the subcritical bifurcations can be considered as hard or dangerous due to the fact that unstable limit cycles (nonlinear phenomena) exist in the (linearly) stable region. The linear stability leads to a stable equilibrium in such regions, only for infinitesimally small perturbations. However, finite perturbations lead to instability due to the presence of unstable limit cycles. Therefore, it is evident that the linear stability analysis is not sufficient to understand the exact stability characteristics of BWRs. However, the effect of these bifurcations on the stability boundaries has been rarely discussed. In the present work, the identification of global stability boundary is demonstrated using simplified models. Here, five different models with different thermal hydraulics feedback have been investigated. In comparison to the earlier works, current models also include the impact of adding the rate of change in temperature on void reactivity as well as effect of void reactivity on rate of change of temperature. Using the bifurcation analysis of these models the globally stable region in the parameter space has been identified. The globally stable region has only stable solutions and
Pandey, Vikas; Singh, Suneet
2017-01-01
Highlights: • Non-linear stability analysis of nuclear reactor is carried out. • Global and local stability boundaries are drawn in the parameter space. • Globally stable, bi-stable, and unstable regions have been demarcated. • The identification of the regions is verified by numerical simulations. - Abstract: Nonlinear stability study of the neutron coupled thermal hydraulics instability has been carried out by several researchers for boiling water reactors (BWRs). The focus of these studies has been to identify subcritical and supercritical Hopf bifurcations. Supercritical Hopf bifurcation are soft or safe due to the fact that stable limit cycles arise in linearly unstable region; linear and global stability boundaries are same for this bifurcation. It is well known that the subcritical bifurcations can be considered as hard or dangerous due to the fact that unstable limit cycles (nonlinear phenomena) exist in the (linearly) stable region. The linear stability leads to a stable equilibrium in such regions, only for infinitesimally small perturbations. However, finite perturbations lead to instability due to the presence of unstable limit cycles. Therefore, it is evident that the linear stability analysis is not sufficient to understand the exact stability characteristics of BWRs. However, the effect of these bifurcations on the stability boundaries has been rarely discussed. In the present work, the identification of global stability boundary is demonstrated using simplified models. Here, five different models with different thermal hydraulics feedback have been investigated. In comparison to the earlier works, current models also include the impact of adding the rate of change in temperature on void reactivity as well as effect of void reactivity on rate of change of temperature. Using the bifurcation analysis of these models the globally stable region in the parameter space has been identified. The globally stable region has only stable solutions and
A global qualitative view of bifurcations and dynamics in the Roessler system
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
Local and global bifurcations at infinity in models of glycolytic oscillations
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...
Experimental Investigation of Bifurcations in a Thermoacoustic Engine
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.
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
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
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...
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.
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.
Global Bifurcation from Intervals for the Monge-Ampère Equations and Its Applications
Wenguo Shen
2018-01-01
Full Text Available We shall establish the global bifurcation results from the trivial solutions axis or from infinity for the Monge-Ampère equations: det(D2u=λm(x-uN+m(xf1(x,-u,-u′,λ+f2(x,-u,-u′,λ, in B, u(x=0, on ∂B, where D2u=(∂2u/∂xi∂xj is the Hessian matrix of u, where B is the unit open ball of RN, m∈C(B¯,[0,+∞ is a radially symmetric weighted function and m(r:=m(x≢0 on any subinterval of [0,1], λ is a positive parameter, and the nonlinear term f1,f2∈C(B¯×R+3,R+, but f1 is not necessarily differentiable at the origin and infinity with respect to u, where R+=[0,+∞. Some applications are given to the Monge-Ampère equations and we use global bifurcation techniques to prove our main results.
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
Investigative Journalism: global perspectives
Price, Stuart
2017-01-01
This volume contains the work of nine members or associates of the Media Discourse Group. Investigative Journalism: Global Perspectives presents a theoretical and practical guide to contemporary international investigative journalism to outline principles of modern investigative work in the digital world. A diverse range of contributions from academics, journalists, and activists interrogate wide ranging issues such as state power, freedom of speech and social justice, as well as exploring...
Dai, Guowei; Romero, Alfonso; Torres, Pedro J.
2018-06-01
We study the existence of spacelike graphs for the prescribed mean curvature equation in the Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime. By using a conformal change of variable, this problem is translated into an equivalent problem in the Lorentz-Minkowski spacetime. Then, by using Rabinowitz's global bifurcation method, we obtain the existence and multiplicity of positive solutions for this equation with 0-Dirichlet boundary condition on a ball. Moreover, the global structure of the positive solution set is studied.
Liu, Xiaojun [State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi' an Jiaotong University, Xi' an 710049 (China); School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001 (China); Hong, Ling, E-mail: hongling@mail.xjtu.edu.cn; Jiang, Jun [State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi' an Jiaotong University, Xi' an 710049 (China)
2016-08-15
Global bifurcations include sudden changes in chaotic sets due to crises. There are three types of crises defined by Grebogi et al. [Physica D 7, 181 (1983)]: boundary crisis, interior crisis, and metamorphosis. In this paper, by means of the extended generalized cell mapping (EGCM), boundary and interior crises of a fractional-order Duffing system are studied as one of the system parameters or the fractional derivative order is varied. It is found that a crisis can be generally defined as a collision between a chaotic basic set and a basic set, either periodic or chaotic, to cause a sudden discontinuous change in chaotic sets. Here chaotic sets involve three different kinds: a chaotic attractor, a chaotic saddle on a fractal basin boundary, and a chaotic saddle in the interior of a basin and disjoint from the attractor. A boundary crisis results from the collision of a periodic (or chaotic) attractor with a chaotic (or regular) saddle in the fractal (or smooth) boundary. In such a case, the attractor, together with its basin of attraction, is suddenly destroyed as the control parameter passes through a critical value, leaving behind a chaotic saddle in the place of the original attractor and saddle after the crisis. An interior crisis happens when an unstable chaotic set in the basin of attraction collides with a periodic attractor, which causes the appearance of a new chaotic attractor, while the original attractor and the unstable chaotic set are converted to the part of the chaotic attractor after the crisis. These results further demonstrate that the EGCM is a powerful tool to reveal the mechanism of crises in fractional-order systems.
Suarez-Antola, Roberto, E-mail: roberto.suarez@miem.gub.u, E-mail: rsuarez@ucu.edu.u [Universidad Catolica del Uruguay, Montevideo (Uruguay). Fac. de Ingenieria y Tecnologias. Dept. de Matematica; Ministerio de Industria, Energia y Mineria, Montevideo (Uruguay). Direccion General de Secretaria
2011-07-01
One of the goals of nuclear power systems design and operation is to restrict the possible states of certain critical subsystems to remain inside a certain bounded set of admissible states and state variations. In the framework of an analytic or numerical modeling process of a BWR power plant, this could imply first to find a suitable approximation to the solution manifold of the differential equations describing the stability behavior, and then a classification of the different solution types concerning their relation with the operational safety of the power plant. 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 generalized and used to exemplify the analytical approach developed here. A nonlinear integral-differential equation in the logarithmic power is derived. Introducing a KBM Ansatz, a coupled set of two nonlinear ordinary differential equations is obtained. Analytical formulae are derived for the frequency of oscillation and the parameters that determine the stability of the steady states, including sub- and supercritical PAH bifurcations. A Bautin's bifurcation scenario seems possible on the power-flow plane: near the boundary of stability, a region where stable steady states are surrounded by unstable limit cycles surrounded at their turn by stable limit cycles. The analytical results are compared with recent digital simulations and applications of semi-analytical bifurcation theory done with reduced order models of BWR. (author)
Suarez-Antola, Roberto; Ministerio de Industria, Energia y Mineria, Montevideo
2011-01-01
One of the goals of nuclear power systems design and operation is to restrict the possible states of certain critical subsystems to remain inside a certain bounded set of admissible states and state variations. In the framework of an analytic or numerical modeling process of a BWR power plant, this could imply first to find a suitable approximation to the solution manifold of the differential equations describing the stability behavior, and then a classification of the different solution types concerning their relation with the operational safety of the power plant. 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 generalized and used to exemplify the analytical approach developed here. A nonlinear integral-differential equation in the logarithmic power is derived. Introducing a KBM Ansatz, a coupled set of two nonlinear ordinary differential equations is obtained. Analytical formulae are derived for the frequency of oscillation and the parameters that determine the stability of the steady states, including sub- and supercritical PAH bifurcations. A Bautin's bifurcation scenario seems possible on the power-flow plane: near the boundary of stability, a region where stable steady states are surrounded by unstable limit cycles surrounded at their turn by stable limit cycles. The analytical results are compared with recent digital simulations and applications of semi-analytical bifurcation theory done with reduced order models of BWR. (author)
Gul, R; Bernhard, S
2015-11-01
In computational cardiovascular models, parameters are one of major sources of uncertainty, which make the models unreliable and less predictive. In order to achieve predictive models that allow the investigation of the cardiovascular diseases, sensitivity analysis (SA) can be used to quantify and reduce the uncertainty in outputs (pressure and flow) caused by input (electrical and structural) model parameters. In the current study, three variance based global sensitivity analysis (GSA) methods; Sobol, FAST and a sparse grid stochastic collocation technique based on the Smolyak algorithm were applied on a lumped parameter model of carotid bifurcation. Sensitivity analysis was carried out to identify and rank most sensitive parameters as well as to fix less sensitive parameters at their nominal values (factor fixing). In this context, network location and temporal dependent sensitivities were also discussed to identify optimal measurement locations in carotid bifurcation and optimal temporal regions for each parameter in the pressure and flow waves, respectively. Results show that, for both pressure and flow, flow resistance (R), diameter (d) and length of the vessel (l) are sensitive within right common carotid (RCC), right internal carotid (RIC) and right external carotid (REC) arteries, while compliance of the vessels (C) and blood inertia (L) are sensitive only at RCC. Moreover, Young's modulus (E) and wall thickness (h) exhibit less sensitivities on pressure and flow at all locations of carotid bifurcation. Results of network location and temporal variabilities revealed that most of sensitivity was found in common time regions i.e. early systole, peak systole and end systole. Copyright © 2015 Elsevier Inc. All rights reserved.
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
A Genealogy of Convex Solids Via Local and Global Bifurcations of Gradient Vector Fields
Domokos, Gábor; Holmes, Philip; Lángi, Zsolt
2016-12-01
Three-dimensional convex bodies can be classified in terms of the number and stability types of critical points on which they can balance at rest on a horizontal plane. For typical bodies, these are non-degenerate maxima, minima, and saddle points, the numbers of which provide a primary classification. Secondary and tertiary classifications use graphs to describe orbits connecting these critical points in the gradient vector field associated with each body. In previous work, it was shown that these classifications are complete in that no class is empty. Here, we construct 1- and 2-parameter families of convex bodies connecting members of adjacent primary and secondary classes and show that transitions between them can be realized by codimension 1 saddle-node and saddle-saddle (heteroclinic) bifurcations in the gradient vector fields. Our results indicate that all combinatorially possible transitions can be realized in physical shape evolution processes, e.g., by abrasion of sedimentary particles.
Hamdipour, Mohammad
2018-04-01
We study an array of coupled Josephson junction of superconductor/insulator/superconductor type (SIS junction) as a model for high temperature superconductors with layered structure. In the current-voltage characteristics of this system there is a breakpoint region in which a net electric charge appear on superconducting layers, S-layers, of junctions which motivate us to study the charge dynamics in this region. In this paper first of all we show a current voltage characteristics (CVC) of Intrinsic Josephson Junctions (IJJs) with N=3 Junctions, then we show the breakpoint region in that CVC, then we try to investigate the chaos in this region. We will see that at the end of the breakpoint region, behavior of the system is chaotic and Lyapunov exponent become positive. We also study the route by which the system become chaotic and will see this route is bifurcation. Next goal of this paper is to show the self similarity in the bifurcation diagram of the system and detailed analysis of bifurcation diagram.
Pagiatakis, Catherine; Tardif, Jean-Claude; L'Allier, Philippe L; Mongrain, Rosaire
2015-09-18
The intervention of coronary bifurcation lesions is associated with higher rates of peri- and post-procedural clinical events compared to the treatment of isolated lesions. Overall, the factors that influence the dynamics of these types of configurations are still not well understood. A geometric multiscale model, consisting of a 3D representation of the left main coronary artery bifurcation and a 0D representation of the rest of the cardiovascular system, was developed. Computational fluid dynamics simulations of the 3D domain were executed by implementing the multiscale algorithm, in order to characterize the functionality of different multilesional configurations as a function of stenosis severity. The investigation found that coronary branch steal has a significant impact on the functionality of the disease and can render a two-lesion configuration more severe compared to a three-lesion configuration. As a result of the complexity of this phenomenon, it was also suggested that certain lesion configurations could result in false negatives in diagnosis when employing a pullback pressure recording across the tandem lesions. In conclusion, this study showed that coronary bifurcation lesions are subject to intricate haemodynamic interactions which render the characterization of their functionality complex and could have significant clinical implications with regards to their diagnosis and prognosis. Copyright © 2015 Elsevier Ltd. All rights reserved.
Experimental and numerical investigations of shock wave propagation through a bifurcation
Marty, A.; Daniel, E.; Massoni, J.; Biamino, L.; Houas, L.; Leriche, D.; Jourdan, G.
2018-02-01
The propagation of a planar shock wave through a split channel is both experimentally and numerically studied. Experiments were conducted in a square cross-sectional shock tube having a main channel which splits into two symmetric secondary channels, for three different shock wave Mach numbers ranging from about 1.1 to 1.7. High-speed schlieren visualizations were used along with pressure measurements to analyze the main physical mechanisms that govern shock wave diffraction. It is shown that the flow behind the transmitted shock wave through the bifurcation resulted in a highly two-dimensional unsteady and non-uniform flow accompanied with significant pressure loss. In parallel, numerical simulations based on the solution of the Euler equations with a second-order Godunov scheme confirmed the experimental results with good agreement. Finally, a parametric study was carried out using numerical analysis where the angular displacement of the two channels that define the bifurcation was changed from 90° , 45° , 20° , and 0° . We found that the angular displacement does not significantly affect the overpressure experience in either of the two channels and that the area of the expansion region is the important variable affecting overpressure, the effect being, in the present case, a decrease of almost one half.
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.
Suarez Antola, R.
2009-01-01
In the framework of an analytic or numerical model of a BWR power plant, this could imply first to find an suitable approximation to the solution manifold of the differential equations describing the stability behaviour 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. Then the goal is to obtain the best attainable qualitative and quantitative global picture of plant dynamics. To do this, the construction and the analysis of the so called reduced order models (Rom) seems a necessary step. A reduced order model results after the full system of coupled nonlinear partial differential equations of the plant is reduced to a system of coupled nonlinear ordinary differential equations
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...
Analysis of stability and Hopf bifurcation for a delayed logistic equation
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.
Buchmann, N. A.; Atkinson, C.; Jeremy, M. C.; Soria, J.
2011-04-01
Hemodynamic forces within the human carotid artery are well known to play a key role in the initiation and progression of vascular diseases such as atherosclerosis. The degree and extent of the disease largely depends on the prevailing three-dimensional flow structure and wall shear stress (WSS) distribution. This work presents tomographic PIV (Tomo-PIV) measurements of the flow structure and WSS in a physiologically accurate model of the human carotid artery bifurcation. The vascular geometry is reconstructed from patient-specific data and reproduced in a transparent flow phantom to demonstrate the feasibility of Tomo-PIV in a complex three-dimensional geometry. Tomographic reconstruction is performed with the multiplicative line-of-sight (MLOS) estimation and simultaneous multiplicative algebraic reconstruction (SMART) technique. The implemented methodology is validated by comparing the results with Stereo-PIV measurements in the same facility. Using a steady flow assumption, the measurement error and RMS uncertainty are directly inferred from the measured velocity field. It is shown that the measurement uncertainty increases for increasing light sheet thickness and increasing velocity gradients, which are largest near the vessel walls. For a typical volume depth of 6 mm (or 256 pixel), the analysis indicates that the velocity derived from 3D cross-correlation can be measured within ±2% of the maximum velocity (or ±0.2 pixel) near the center of the vessel and within ±5% (±0.6 pixel) near the vessel wall. The technique is then applied to acquire 3D-3C velocity field data at multiple axial locations within the carotid artery model, which are combined to yield the flow field and WSS in a volume of approximately 26 mm × 27 mm × 60 mm. Shear stress is computed from the velocity gradient tensor and a method for inferring the WSS distribution on the vessel wall is presented. The results indicate the presence of a complex and three-dimensional flow structure, with
Bifurcation analysis on a delayed SIS epidemic model with stage structure
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.
Bifurcation Control of an Electrostatically-Actuated MEMS Actuator with Time-Delay Feedback
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.
Bifurcation of the spin-wave equations
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)
Resonant Homoclinic Flips Bifurcation in Principal Eigendirections
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.
Shahbani-Zahiri, A.; Hassanzadeh, H.; Shahmardan, M. M.; Norouzi, M.
2017-11-01
In this paper, the inertial and non-isothermal flows of the viscoelastic fluid through a planar channel with symmetric sudden expansion are numerically simulated. Effects of pitchfork bifurcation phenomena on the heat transfer rate are examined for the thermally developing and fully developed flow of the viscoelastic fluid inside the expanded part of the planar channel with an expansion ratio of 1:3. The rheological model of exponential Phan Thien-Tanner is used to include both the effects of shear-thinning and elasticity in fluid viscosity. The properties of fluids are temperature-dependent, and the viscous dissipation and heat stored by fluid elasticity are considered in the heat transfer equation. For coupling the governing equations, the PISO algorithm (Pressure Implicit with Splitting of Operator) is applied and the system of equations is linearized using the finite volume method on the collocated grids. The main purpose of this study is to examine the pitchfork bifurcation phenomena and its influences on the temperature distribution, the local and mean Nusselt numbers, and the first and second normal stress differences at different Reynolds, elasticity, and Brinkman numbers. The results show that by increasing the Brinkman number for the heated flow of the viscoelastic fluid inside the expanded part of the channel, the value of the mean Nusselt number is almost linearly decreased. Also, the maximum values of the local Nusselt number for the thermally developing flow and the local Nusselt number of the thermally fully developed flow are decremented by enhancing the Brinkman number.
Anastasiou, A D; Spyrogianni, A S; Koskinas, K C; Giannoglou, G D; Paras, S V
2012-03-01
The scope of this work is to study the pulsatile flow of a blood mimicking fluid in a micro channel that simulates a bifurcated small artery, in which the Fahraeus-Lindqvist effect is insignificant. An aqueous glycerol solution with small amounts of xanthan gum was used for simulating viscoelastic properties of blood and in vivo flow conditions were reproduced. Local flow velocities were measured using micro Particle Image Velocimetry (μ-PIV). From the measured velocity distributions, the wall shear stress (WSS) and its variation during a pulse were estimated. The Reynolds numbers employed are relatively low, i.e. similar to those prevailing during blood flow in small arteries. Experiments both with a Newtonian and a non-Newtonian fluid (having asymptotic viscosity equal to the viscosity of the Newtonian one) proved that the common assumption that blood behaves as a Newtonian fluid is not valid for blood flow in small arteries. It was also shown that the outer wall of the bifurcation, which is exposed to a lower WSS, is more predisposed to atherosclerotic plaque formation. Moreover, this region in small vessels is shorter than the one in large arteries, as the developed secondary flow decays faster. Finally, the WSS values in small arteries were found to be lower than those in large ones. Copyright © 2011 IPEM. Published by Elsevier Ltd. All rights reserved.
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.
Pierce instability and bifurcating equilibria
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
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.
Bifurcation of steady tearing states
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
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.
Jianguo Ren
2014-01-01
Full Text Available A new computer virus propagation model with delay and incomplete antivirus ability is formulated and its global dynamics is analyzed. The existence and stability of the equilibria are investigated by resorting to the threshold value R0. By analysis, it is found that the model may undergo a Hopf bifurcation induced by the delay. Correspondingly, the critical value of the Hopf bifurcation is obtained. Using Lyapunov functional approach, it is proved that, under suitable conditions, the unique virus-free equilibrium is globally asymptotically stable if R01. Numerical examples are presented to illustrate possible behavioral scenarios of the mode.
Unfolding the Riddling Bifurcation
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....
Bifurcation and chaos in neural excitable system
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
Bifurcation theory of ac electric arcing
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)
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
Bifurcation Behavior Analysis in a Predator-Prey Model
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.
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.
Hopf bifurcation for tumor-immune competition systems with delay
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.
Relative Lyapunov Center Bifurcations
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....
A codimension two bifurcation in a railway bogie system
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...
Bifurcations of transition states: Morse bifurcations
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)
Olmstead, W.E.; Davis, S.H.; Rosenblat, S.; Kath, W.L.
1986-01-01
A model equation containing a memory integral is posed. The extent of the memory, the relaxation time lambda, controls the bifurcation behavior as the control parameter R is increased. Small (large) lambda gives steady (periodic) bifurcation. There is a double eigenvalue at lambda = lambda 1 , separating purely steady (lambda 1 ) from combined steady/T-periodic (lambda > lambda 1 ) states with T → infinity as lambda → lambda + 1 . Analysis leads to the co-existence of stable steady/periodic states and as R is increased, the periodic states give way to the steady states. Numerical solutions show that this behavior persists away from lambda = lambda 1
Bifurcation analysis and stability design for aircraft longitudinal motion with high angle of attack
Xin Qi
2015-02-01
Full Text Available Bifurcation analysis and stability design for aircraft longitudinal motion are investigated when the nonlinearity in flight dynamics takes place severely at high angle of attack regime. To predict the special nonlinear flight phenomena, bifurcation theory and continuation method are employed to systematically analyze the nonlinear motions. With the refinement of the flight dynamics for F-8 Crusader longitudinal motion, a framework is derived to identify the stationary bifurcation and dynamic bifurcation for high-dimensional system. Case study shows that the F-8 longitudinal motion undergoes saddle node bifurcation, Hopf bifurcation, Zero-Hopf bifurcation and branch point bifurcation under certain conditions. Moreover, the Hopf bifurcation renders series of multiple frequency pitch oscillation phenomena, which deteriorate the flight control stability severely. To relieve the adverse effects of these phenomena, a stabilization control based on gain scheduling and polynomial fitting for F-8 longitudinal motion is presented to enlarge the flight envelope. Simulation results validate the effectiveness of the proposed scheme.
Bifurcations of 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.
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.
Digital subtraction angiography of carotid bifurcation
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.)
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.
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.
Bifurcations of heterodimensional cycles with two saddle points
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
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.
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
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.
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
Numerical analysis of bifurcations
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
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 → ∞.
Investigation of global Alfven instabilities in TFTR
Wong, K.L.; Paul, S.F.; Fredrickson, E.D.; Nazikian, R.; Park, H.K.; Bell, M.; Bretz, N.L.; Budny, R.; Cheng, C.Z.; Cohen, S.; Hammett, G.W.; Jobes, F.C.; Johnson, L.; Meade, D.M.; Medley, S.S.; Mueller, D.; Nagayama, Y.; Owens, D.K.; Synakowski, E.J.; Roberts, D.R.; Sabbagh, S.
1992-01-01
Toroidal Alfven Eigenmodes (TAE) were excited by the energetic neutral beam ions tangentially injected into TFTR plasmas at low magnetic field such that the injection velocities were comparable to the Alfven speed. The modes were identified by measurements from Mirnov coils and beam emission spectroscopy (BES). TAE modes appear in bursts whose repetition rate increases with beam power. The neutron emission rate exhibits sawtooth-like behavior and the crashes always coincide with TAE bursts. This indicates ejection of fast ions from the plasma until these modes are stabilized. The dynamics of growth and stabilization was investigated at various plasma current and magnetic field. The results indicate that the instability can effectively clamp the number of energetic ions in the plasma. The observed instability threshold is discussed in the light of recent theories. In addition to these TAE modes, intermittent oscillations at three times the fundamental TAE frequency were observed by Mirnov coils, but no corresponding signal was found in BES. It appears that these high frequency oscillations do not have direct effect on the plasma neutron source strength
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.
Hopf bifurcation of the stochastic model on business cycle
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
Hopf Bifurcation of Compound Stochastic van der Pol System
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.
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.
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
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...
Bifurcations and chaos of DNA solitonic dynamics
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
Stability and bifurcation analysis in a kind of business cycle model with delay
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
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.
Riddling bifurcation and interstellar journeys
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
Bursting oscillations, bifurcation and synchronization in neuronal systems
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.
Dynamic bifurcations on financial markets
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 dynamics of the tempered fractional Langevin equation
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.
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...
Stability and bifurcation of a discrete BAM neural network model with delays
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
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
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.
Delay Induced Hopf Bifurcation of an Epidemic Model with Graded Infection Rates for Internet Worms
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.
Three dimensional nilpotent singularity and Sil'nikov bifurcation
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
Quantitative angiography methods for bifurcation lesions
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...
Sliding bifurcations and chaos induced by dry friction in a braking system
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
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)
Stochastic stability and bifurcation in a macroeconomic model
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
Analysis of stability and Hopf bifurcation for a viral infectious model with delay
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, bifurcation and a new chaos in the logistic differential equation with delay
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
Homoclinic bifurcation in Chua's circuit
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.
Bifurcation theory for toroidal MHD instabilities
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
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.
Stamatiou, George; Ghikas, Demetris P.K.
2007-01-01
Properties related to entanglement in quantum systems, are known to be associated with distinct properties of the corresponding classical systems, as for example stability, integrability and chaos. This means that the detailed topology, both local and global, of the classical phase space may reveal, or influence, the entangling power of the quantum system. As it has been shown in the literature, the bifurcation points, in autonomous dynamical systems, play a crucial role for the onset of entanglement. Similarly, the existence of scars among the quantum states seems to be a factor in the dynamics of entanglement. Here we study these issues for a non-autonomous system, the quantum kicked top, as a collective model of a multi-qubit system. Using the bifurcation diagram of the corresponding classical limit (the classical kicked top), we analyzed the pair-wise and the bi-partite entanglement of the qubits and their relation to scars, as a function of the critical parameter of the system. We found that the pair-wise entanglement and pair-wise negativity show a strong maximum precisely at the bifurcation points, while the bi-partite entanglement changes slope at these points. We have also investigated the connection between entanglement and the fixed points on the branch of the bifurcation diagram between the two first bifurcation points and we found that the entanglement measures take their extreme values precisely on these points. We conjecture that our results on this behavior of entanglement is generic for many quantum systems with a nonlinear classical analogue
Philip Tröster
2018-02-01
Full Text Available A cGMP signaling cascade composed of C-type natriuretic peptide, the guanylyl cyclase receptor Npr2 and cGMP-dependent protein kinase I (cGKI controls the bifurcation of sensory axons upon entering the spinal cord during embryonic development. However, the impact of axon bifurcation on sensory processing in adulthood remains poorly understood. To investigate the functional consequences of impaired axon bifurcation during adult stages we generated conditional mouse mutants of Npr2 and cGKI (Npr2fl/fl;Wnt1Cre and cGKIKO/fl;Wnt1Cre that lack sensory axon bifurcation in the absence of additional phenotypes observed in the global knockout mice. Cholera toxin labeling in digits of the hind paw demonstrated an altered shape of sensory neuron termination fields in the spinal cord of conditional Npr2 mouse mutants. Behavioral testing of both sexes indicated that noxious heat sensation and nociception induced by chemical irritants are impaired in the mutants, whereas responses to cold sensation, mechanical stimulation, and motor coordination are not affected. Recordings from C-fiber nociceptors in the hind limb skin showed that Npr2 function was not required to maintain normal heat sensitivity of peripheral nociceptors. Thus, the altered behavioral responses to noxious heat found in Npr2fl/fl;Wnt1Cre mice is not due to an impaired C-fiber function. Overall, these data point to a critical role of axonal bifurcation for the processing of pain induced by heat or chemical stimuli.
Bifurcations and degenerate periodic points in a three dimensional chaotic fluid flow
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.
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.
Bifurcation Analysis of Gene Propagation Model Governed by Reaction-Diffusion Equations
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.
Stability and Hopf bifurcations in a competitive Lotka-Volterra system with two delays
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
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
Magneto-elastic dynamics and bifurcation of rotating annular plate*
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)
Stochastic Bifurcation Analysis of an Elastically Mounted Flapping Airfoil
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.
Hopf bifurcation and chaos in macroeconomic models with policy lag
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
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
Bifurcations in the optimal elastic foundation for a buckling column
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
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.
Transportation and concentration inequalities for bifurcating Markov chains
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...
Bifurcation routes and economic stability
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
Bifurcations of Fibonacci generating functions
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
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
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.
Global investigation of the nonlinear dynamics of carbon nanotubes
Xu, Tiantian
2016-11-17
Understanding the complex nonlinear dynamics of carbon nanotubes (CNTs) is essential to enable utilization of these structures in devices and practical applications. We present in this work an investigation of the global nonlinear dynamics of a slacked CNT when actuated by large electrostatic and electrodynamic excitations. The coexistence of several attractors is observed. The CNT is modeled as an Euler–Bernoulli beam. A reduced-order model based on the Galerkin method is developed and utilized to simulate the static and dynamic responses. Critical computational challenges are posed due to the complicated form of the electrostatic force, which describes the interaction between the upper electrode, consisting of the cylindrically shaped CNT, and the lower electrode. Toward this, we approximate the electrostatic force using the Padé expansion. We explore the dynamics near the primary and superharmonic resonances. The nanostructure exhibits several attractors with different characteristics. To achieve deep insight and describe the complexity and richness of the behavior, we analyze the nonlinear response from an attractor-basins point of view. The competition of attractors is highlighted. Compactness and/or fractality of their basins are discussed. Both the effects of varying the excitation frequency and amplitude are examined up to the dynamic pull-in instability.
Stability and Hopf bifurcation analysis of a new system
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.
Bifurcation analysis and the travelling wave solutions of the Klein
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 ...
Experimental bifurcation analysis of an impact oscillator – Determining stability
Bureau, Emil; Schilder, Frank; Elmegård, Michael
2014-01-01
We propose and investigate three different methods for assessing stability of dynamical equilibrium states during experimental bifurcation analysis, using a control-based continuation method. The idea is to modify or turn off the control at an equilibrium state and study the resulting behavior...
Bifurcation 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.
Bifurcation and chaos in a Tessiet type food chain chemostat with pulsed input and washout
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
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.
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)
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
Backward Bifurcation in a Cholera Model: A Case Study of Outbreak in Zimbabwe and Haiti
Sharma, Sandeep; Kumari, Nitu
In this paper, a nonlinear deterministic model is proposed with a saturated treatment function. The expression of the basic reproduction number for the proposed model was obtained. The global dynamics of the proposed model was studied using the basic reproduction number and theory of dynamical systems. It is observed that proposed model exhibits backward bifurcation as multiple endemic equilibrium points exist when R0 cholera in the community. We also obtain a unique endemic equilibria when R0 > 1. The global stability of unique endemic equilibria is performed using the geometric approach. An extensive numerical study is performed to support our analytical results. Finally, we investigate two major cholera outbreaks, Zimbabwe (2008-09) and Haiti (2010), with the help of the present study.
Heteroclinic Bifurcation Behaviors of a Duffing Oscillator with Delayed Feedback
Shao-Fang Wen
2018-01-01
Full Text Available The heteroclinic bifurcation and chaos of a Duffing oscillator with forcing excitation under both delayed displacement feedback and delayed velocity feedback are studied by Melnikov method. The Melnikov function is analytically established to detect the necessary conditions for generating chaos. Through the analysis of the analytical necessary conditions, we find that the influences of the delayed displacement feedback and delayed velocity feedback are separable. Then the influences of the displacement and velocity feedback parameters on heteroclinic bifurcation and threshold value of chaotic motion are investigated individually. In order to verify the correctness of the analytical conditions, the Duffing oscillator is also investigated by numerical iterative method. The bifurcation curves and the largest Lyapunov exponents are provided and compared. From the analysis of the numerical simulation results, it could be found that two types of period-doubling bifurcations occur in the Duffing oscillator, so that there are two paths leading to the chaos in this oscillator. The typical dynamical responses, including time histories, phase portraits, and Poincare maps, are all carried out to verify the conclusions. The results reveal some new phenomena, which is useful to design or control this kind of system.
Bifurcations and Patterns in Nonlinear Dissipative Systems
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.
Equilibrium-torus bifurcation in nonsmooth systems
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...
Bifurcation Analysis and Chaos Control in a Discrete Epidemic System
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.
Efficient algorithm for bifurcation problems of variational inequalities
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
Voltage stability, bifurcation parameters and continuation methods
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.
Bifurcation from infinity and nodal solutions of quasilinear elliptic differential equations
Bian-Xia Yang
2014-01-01
Full Text Available In this article, we establish a unilateral global bifurcation theorem from infinity for a class of $N$-dimensional p-Laplacian problems. As an application, we study the global behavior of the components of nodal solutions of the problem $$\\displaylines{ \\operatorname{div}(\\varphi_p(\
Zizhen Zhang
2017-01-01
Full Text Available Hopf bifurcation for an SEIRS-V model with delays on the transmission of worms in a wireless sensor network is investigated. We focus on existence of the Hopf bifurcation by regarding the diverse delay as a bifurcation parameter. The results show that propagation of worms in the wireless sensor network can be controlled when the delay is suitably small under some certain conditions. Then, we study properties of the Hopf bifurcation by using the normal form theory and center manifold theorem. Finally, we give a numerical example to support the theoretical results.
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
Wang, Zhen; Wang, Xiaohong; Li, Yuxia; Huang, Xia
2017-12-01
In this paper, the problems of stability and Hopf bifurcation in a class of fractional-order complex-valued single neuron model with time delay are addressed. With the help of the stability theory of fractional-order differential equations and Laplace transforms, several new sufficient conditions, which ensure the stability of the system are derived. Taking the time delay as the bifurcation parameter, Hopf bifurcation is investigated and the critical value of the time delay for the occurrence of Hopf bifurcation is determined. Finally, two representative numerical examples are given to show the effectiveness of the theoretical results.
Zhu, Zhi-Wen; Zhang, Qing-Xin; Xu, Jia
2014-01-01
A kind of shape memory alloy (SMA) hysteretic nonlinear model was developed, and the nonlinear dynamics and bifurcation characteristics of the SMA thin film subjected to in-plane stochastic excitation were investigated. Van der Pol difference item was introduced to describe the hysteretic phenomena of the SMA strain–stress curves, and the nonlinear dynamic model of the SMA thin film subjected to in-plane stochastic excitation was developed. The conditions of global stochastic stability of the system were determined in singular boundary theory, and the probability density function of the system response was obtained. Finally, the conditions of stochastic Hopf bifurcation were analyzed. The results of theoretical analysis and numerical simulation indicate that self-excited vibration is induced by the hysteretic nonlinear characteristics of SMA, and stochastic Hopf bifurcation appears when the bifurcation parameter was changed; there are two limit cycles in the stationary probability density of the dynamic response of the system in some cases, which means that there are two vibration amplitudes whose probabilities are both very high, and jumping phenomena between the two vibration amplitudes appear with the change in conditions. The results obtained in this current paper are helpful for the application of the SMA thin film in stochastic vibration fields. - Highlights: • Hysteretic nonlinear model of shape memory alloy was developed. • Van der Pol item was introduced to interpret hysteretic strain–stress curves. • Nonlinear dynamic characteristics of the shape memory alloy film were analyzed. • Jumping phenomena were observed in the change of the parameters
Stability and Hopf Bifurcation for a Delayed SLBRS Computer Virus Model
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.
Stability and Hopf bifurcation analysis of a prey-predator system with two delays
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.
Bifurcation analysis of the logistic map via two periodic impulsive forces
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)
Numerical bifurcation analysis of conformal formulations of the Einstein constraints
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
Analysis of the flow at a T-bifurcation for a ternary unit
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
Investigating Student Use of Technology for Engaged Citizenship in A Global Age
Brad M. Maguth
2012-05-01
Full Text Available This study undertook a five month qualitative investigation into technology use amongst twelve high school social studies students in two different sites in the Midwestern United States. This study examined students’ use of technology and its relationship to three dimensions of citizenship in a global age: understand global events, issues, and perspectives, participate in global networks to communicate and collaborate with global audiences, and advocate on global problems and issues to think and act globally. Collecting data through semi-structured student interviews, online-threaded discussions and document analysis, I triangulated findings, and employed a qualitative approach. The study finds a relationship between student participants’ use of technology and their serving as engaged citizenship in a global age. In using technology, students accessed international news and information, joined global networks to communicate and collaborate with global audiences, and produced digital content for international audiences.
A bench top experimental model of bubble transport in multiple arteriole bifurcations
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.
Nonlinear stability control and λ-bifurcation
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
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.
Investigation of Global Imbalances Based on a Gravity Model
Hyun-Hoon Lee
2011-06-01
Full Text Available Using the US Treasury International Capital (TIC data, this paper attempts to analyze the size and trend of foreign investment in the U.S. in the form of equities, bonds and bank lending during the period of 2001-2007. In addition, this paper assesses the determinants of foreign investment in the U.S., using the financial gravity model which includes an East Asian dummy as an explanatory variable. The results show that most East Asian countries have invested more in the U.S. than the optimal level suggested by the gravity model. Such an over-investment is more evident in long-term bond investment than in equity investment or bank lending. Thus, the results confirm that global imbalance does exist between East Asian countries and the U.S.
Quantum entanglement and fixed-point bifurcations
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.
Stability and Hopf bifurcation on a model for HIV infection of CD4{sup +} T cells with delay
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.
Multistability and gluing bifurcation to butterflies in coupled networks with non-monotonic feedback
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
Bifurcation analysis in delayed feedback Jerk systems and application of chaotic control
Zheng Baodong; Zheng Huifeng
2009-01-01
Jerk systems with delayed feedback are considered. Firstly, by employing the polynomial theorem to analyze the distribution of the roots to the associated characteristic equation, the conditions of ensuring the existence of Hopf bifurcation are given. Secondly, the stability and direction of the Hopf bifurcation are determined by applying the normal form method and center manifold theorem. Finally, the application to chaotic control is investigated, and some numerical simulations are carried out to illustrate the obtained results.
Stability and Hopf bifurcation in a delayed competitive web sites model
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
Bifurcation Control of Chaotic Dynamical Systems
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 and instability problems in vortex wakes
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...
Bifurcation structure of successive torus doubling
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
Hopf bifurcation in an Internet congestion control model
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
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.
Bifurcation and synchronization of synaptically coupled FHN models with time delay
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.
Hopf bifurcation in a environmental defensive expenditures model with time delay
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
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.
Bifurcation in the Lengyel–Epstein system for the coupled reactors with diffusion
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.
Delay-induced stochastic bifurcations in a bistable system under white noise
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
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.
Hopf bifurcation and chaos from torus breakdown in voltage-mode controlled DC drive systems
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 complex dynamics of a discrete-time predator-prey system involving group defense
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.
Delay-induced stochastic bifurcations in a bistable system under white noise
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.
Bifurcation and chaos of an axially accelerating viscoelastic beam
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
Fold points and singularity induced bifurcation in inviscid transonic flow
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.
Global population variability in Qiagen Investigator HDplex STRs.
Phillips, C; Fernandez-Formoso, L; Gelabert-Besada, M; García-Magariños, M; Amigo, J; Carracedo, A; Lareu, M V
2014-01-01
Supplementary short tandem repeats (STRs) can be added to forensic analyses if the 15-24 core STRs in routine use fail to give sufficient discrimination power in complex identification or relationship testing scenarios. In this study, 10 of 12 supplementary STRs in the Qiagen Investigator HDplex kit (SE33, D2S1360, D3S1744, D4S2366, D5S2500, D6S474, D7S1517, D8S1132, D10S2325, D21S2055) were genotyped in 941 individuals from the 51 populations of the CEPH Human Genome Diversity Panel (HGDP-CEPH). The other two components of the 12-STR HDplex kit are established STRs D12S391 and D18S51 that we previously genotyped for the HGDP-CEPH panel. We describe the rare alleles identified and outline allele frequency distributions in the seven population groups of the HGDP-CEPH panel. The HDplex STRs novel to forensic application were found to be both highly informative and comparable in their power across all populations studied: at least six of the nine loci showing above average forensic discrimination power in each population group. In some rare instances certain low frequency alleles in D2S1360 were found to overlap in mobility with the neighbouring allele size ranges of D12S391, as well as those of D7S1517 with neighbouring D3S1744 and D10S2325 with neighbouring SE33. Lastly, since expanded five-dye multiplex kits of 20 STRs (Promega Powerplex 21) and 22 STRs (Promega Powerplex Fusion) have recently been introduced, we assess through simulations the increased power to analyse pairwise relationships in deficient pedigrees that can be expected from an optimum kit pair: combining HDplex with either of the above sets to provide 30 or 32 unique STRs and just two overlapping loci. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.
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
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.
Bieniek, M. S.; Santos, D. F. N.; Almeida, P. G. C.; Benilov, M. S.
2018-04-01
General scenarios of transitions between different spot patterns on electrodes of DC gas discharges and their relation to bifurcations of steady-state solutions are analyzed. In the case of cathodes of arc discharges, it is shown that any transition between different modes of current transfer is related to a bifurcation of steady-state solutions. In particular, transitions between diffuse and spot modes on axially symmetric cathodes, frequently observed in the experiment, represent an indication of the presence of pitchfork or fold bifurcations of steady-state solutions. Experimental observations of transitions on cathodes of DC glow microdischarges are analyzed and those potentially related to bifurcations of steady-state solutions are identified. The relevant bifurcations are investigated numerically and the computed patterns are found to conform to those observed in the course of the corresponding transitions in the experiment.
Meng, Xin-You; Wu, Yu-Qian
In this paper, a delayed differential algebraic phytoplankton-zooplankton-fish model with taxation and nonlinear fish harvesting is proposed. In the absence of time delay, the existence of singularity induced bifurcation is discussed by regarding economic interest as bifurcation parameter. A state feedback controller is designed to eliminate singularity induced bifurcation. Based on Liu’s criterion, Hopf bifurcation occurs at the interior equilibrium when taxation is taken as bifurcation parameter and is more than its corresponding critical value. In the presence of time delay, by analyzing the associated characteristic transcendental equation, the interior equilibrium loses local stability when time delay crosses its critical value. What’s more, the direction of Hopf bifurcation and stability of the bifurcating periodic solutions are investigated based on normal form theory and center manifold theorem, and nonlinear state feedback controller is designed to eliminate Hopf bifurcation. Furthermore, Pontryagin’s maximum principle has been used to obtain optimal tax policy to maximize the benefit as well as the conservation of the ecosystem. Finally, some numerical simulations are given to demonstrate our theoretical analysis.
Ternary choices in repeated games and border collision bifurcations
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.
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.
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.
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...
Eisner, J.; Väth, Martin
2016-01-01
Roč. 135, April (2016), s. 158-193 ISSN 0362-546X Institutional support: RVO:67985840 Keywords : reaction-diffusion system * turing instability * global bifurcation Subject RIV: BA - General Mathematics Impact factor: 1.192, year: 2016 http://www.sciencedirect.com/science/article/pii/S0362546X16000146
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.
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.
Hsieh, Ya-Yun
2010-01-01
This study aims to investigate how consumers in a newly developed country, Taiwan, perceive local brands and global brands in the computer industry. To access an in-depth understanding and evaluate factors that influence consumers’ assessment of local and global brands, the country-of-origin effect and the association of brand origin are investigated; the effect of consumer ethnocentrism is addressed; and the cultural aspects on collectivism and face concept are examined. The study adopts...
Bifurcation analysis of a three dimensional system
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.
Bifurcations of Tumor-Immune Competition Systems with Delay
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 Stability in a Delayed Predator-Prey Model with Mixed Functional Responses
Yafia, R.; Aziz-Alaoui, M. A.; Merdan, H.; Tewa, J. J.
2015-06-01
The model analyzed in this paper is based on the model set forth by Aziz Alaoui et al. [Aziz Alaoui & Daher Okiye, 2003; Nindjin et al., 2006] with time delay, which describes the competition between the predator and prey. This model incorporates a modified version of the Leslie-Gower functional response as well as that of Beddington-DeAngelis. In this paper, we consider the model with one delay consisting of a unique nontrivial equilibrium E* and three others which are trivial. Their dynamics are studied in terms of local and global stabilities and of the description of Hopf bifurcation at E*. At the third trivial equilibrium, the existence of the Hopf bifurcation is proven as the delay (taken as a parameter of bifurcation) that crosses some critical values.
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.
Attractors near grazing–sliding bifurcations
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
Neimark-Sacker bifurcations and evidence of chaos in a discrete dynamical model of walkers
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.
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
Lee, Cheng-Hung [Division of Cardiology, Department of Internal Medicine, Chang Gung Memorial Hospital, Linkou, Chang Gung University College of Medicine, Tao-Yuan, Taiwan (China); Department of Mechanical Engineering, Chang Gung University, Tao-Yuan, Taiwan (China); Jhong, Guan-Heng [Graduate Institute of Medical Mechatronics, Chang Gung University, Tao-Yuan, Taiwan (China); Hsu, Ming-Yi; Wang, Chao-Jan [Department of Medical Imaging and Intervention, Chang Gung Memorial Hospital, Linkou, Tao-Yuan, Taiwan (China); Liu, Shih-Jung, E-mail: shihjung@mail.cgu.edu.tw [Department of Mechanical Engineering, Chang Gung University, Tao-Yuan, Taiwan (China); Hung, Kuo-Chun [Division of Cardiology, Department of Internal Medicine, Chang Gung Memorial Hospital, Linkou, Chang Gung University College of Medicine, Tao-Yuan, Taiwan (China)
2014-05-28
The deployment of metallic stents during percutaneous coronary intervention has become common in the treatment of coronary bifurcation lesions. However, restenosis occurs mostly at the bifurcation area even in present era of drug-eluting stents. To achieve adequate deployment, physicians may unintentionally apply force to the strut of the stents through balloon, guiding catheters, or other devices. This force may deform the struts and impose excessive mechanical stresses on the arterial vessels, resulting in detrimental outcomes. This study investigated the relationship between the distribution of stress in a stent and bifurcation angle using finite element analysis. The unintentionally applied force following stent implantation was measured using a force sensor that was made in the laboratory. Geometrical information on the coronary arteries of 11 subjects was extracted from contrast-enhanced computed tomography scan data. The numerical results reveal that the application of force by physicians generated significantly higher mechanical stresses in the arterial bifurcation than in the proximal and distal parts of the stent (post hoc P < 0.01). The maximal stress on the vessels was significantly higher at bifurcation angle <70° than at angle ≧70° (P < 0.05). The maximal stress on the vessels was negatively correlated with bifurcation angle (P < 0.01). Stresses at the bifurcation ostium may cause arterial wall injury and restenosis, especially at small bifurcation angles. These finding highlight the effect of force-induced mechanical stress at coronary artery bifurcation stenting, and potential mechanisms of in-stent restenosis, along with their relationship with bifurcation angle.
Lee, Cheng-Hung; Jhong, Guan-Heng; Hsu, Ming-Yi; Wang, Chao-Jan; Liu, Shih-Jung; Hung, Kuo-Chun
2014-01-01
The deployment of metallic stents during percutaneous coronary intervention has become common in the treatment of coronary bifurcation lesions. However, restenosis occurs mostly at the bifurcation area even in present era of drug-eluting stents. To achieve adequate deployment, physicians may unintentionally apply force to the strut of the stents through balloon, guiding catheters, or other devices. This force may deform the struts and impose excessive mechanical stresses on the arterial vessels, resulting in detrimental outcomes. This study investigated the relationship between the distribution of stress in a stent and bifurcation angle using finite element analysis. The unintentionally applied force following stent implantation was measured using a force sensor that was made in the laboratory. Geometrical information on the coronary arteries of 11 subjects was extracted from contrast-enhanced computed tomography scan data. The numerical results reveal that the application of force by physicians generated significantly higher mechanical stresses in the arterial bifurcation than in the proximal and distal parts of the stent (post hoc P < 0.01). The maximal stress on the vessels was significantly higher at bifurcation angle <70° than at angle ≧70° (P < 0.05). The maximal stress on the vessels was negatively correlated with bifurcation angle (P < 0.01). Stresses at the bifurcation ostium may cause arterial wall injury and restenosis, especially at small bifurcation angles. These finding highlight the effect of force-induced mechanical stress at coronary artery bifurcation stenting, and potential mechanisms of in-stent restenosis, along with their relationship with bifurcation angle.
Barnett, William H; Cymbalyuk, Gennady S
2014-01-01
The dynamics of individual neurons are crucial for producing functional activity in neuronal networks. An open question is how temporal characteristics can be controlled in bursting activity and in transient neuronal responses to synaptic input. Bifurcation theory provides a framework to discover generic mechanisms addressing this question. We present a family of mechanisms organized around a global codimension-2 bifurcation. The cornerstone bifurcation is located at the intersection of the border between bursting and spiking and the border between bursting and silence. These borders correspond to the blue sky catastrophe bifurcation and the saddle-node bifurcation on an invariant circle (SNIC) curves, respectively. The cornerstone bifurcation satisfies the conditions for both the blue sky catastrophe and SNIC. The burst duration and interburst interval increase as the inverse of the square root of the difference between the corresponding bifurcation parameter and its bifurcation value. For a given set of burst duration and interburst interval, one can find the parameter values supporting these temporal characteristics. The cornerstone bifurcation also determines the responses of silent and spiking neurons. In a silent neuron with parameters close to the SNIC, a pulse of current triggers a single burst. In a spiking neuron with parameters close to the blue sky catastrophe, a pulse of current temporarily silences the neuron. These responses are stereotypical: the durations of the transient intervals-the duration of the burst and the duration of latency to spiking-are governed by the inverse-square-root laws. The mechanisms described here could be used to coordinate neuromuscular control in central pattern generators. As proof of principle, we construct small networks that control metachronal-wave motor pattern exhibited in locomotion. This pattern is determined by the phase relations of bursting neurons in a simple central pattern generator modeled by a chain of
Bifurcation of Jovian magnetotail current sheet
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
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.
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
Bifurcations of a class of singular biological economic models
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 structure of a model of bursting pancreatic cells
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...
Codimension-2 bifurcations of the Kaldor model of business cycle
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.
Comments on the Bifurcation Structure of 1D Maps
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
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).
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
Bifurcation structure of an optical ring cavity
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...
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
Percutaneous coronary intervention for coronary bifurcation disease
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...
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.
One-dimensional map lattices: Synchronization, bifurcations, and chaotic structures
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....
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.
Bifurcation parameters of a reflected shock wave in cylindrical channels of different roughnesses
Penyazkov, O.; Skilandz, A.
2018-03-01
To investigate the effect of bifurcation on the induction time in cylindrical shock tubes used for chemical kinetic experiments, one should know the parameters of the bifurcation structure of a reflected shock wave. The dynamics and parameters of the shock wave bifurcation, which are caused by reflected shock wave-boundary layer interactions, are studied experimentally in argon, in air, and in a hydrogen-nitrogen mixture for Mach numbers M = 1.3-3.5 in a 76-mm-diameter shock tube without any ramp. Measurements were taken at a constant gas density behind the reflected shock wave. Over a wide range of experimental conditions, we studied the axial projection of the oblique shock wave and the pressure distribution in the vicinity of the triple Mach configuration at 50, 150, and 250 mm from the endwall, using side-wall schlieren and pressure measurements. Experiments on a polished shock tube and a shock tube with a surface roughness of 20 {μ }m Ra were carried out. The surface roughness was used for initiating small-scale turbulence in the boundary layer behind the incident shock wave. The effect of small-scale turbulence on the homogenization of the transition zone from the laminar to turbulent boundary layer along the shock tube perimeter was assessed, assuming its influence on a subsequent stabilization of the bifurcation structure size versus incident shock wave Mach number, as well as local flow parameters behind the reflected shock wave. The influence of surface roughness on the bifurcation development and pressure fluctuations near the wall, as well as on the Mach number, at which the bifurcation first develops, was analyzed. It was found that even small additional surface roughness can lead to an overshoot in pressure growth by a factor of two, but it can stabilize the bifurcation structure along the shock tube perimeter.
Xue Yunjing; Gao Peiyi; Lin Yan
2008-01-01
Objective: To investigate variation in the carotid bifurcation geometry of adults of different age by MR angiography images combining image post-processing technique. Methods: Images of the carotid bifurcations of 27 young adults (≤40 years old) and 30 older subjects ( > 40 years old) were acquired via contrast-enhanced MR angiography. Three dimensional (3D) geometries of the bifurcations were reconstructed and geometric parameters were measured by post-processing technique. Results: The geometric parameters of the young versus older groups were as follows: bifurcation angle (70.268 degree± 16.050 degree versus 58.857 degree±13.294 degree), ICA angle (36.893 degree±11.837 degree versus 30.275 degree±9.533 degree), ICA planarity (6.453 degree ± 5.009 degree versus 6.263 degree ±4.250 degree), CCA tortuosity (0.023±0.011 versus 0.014± 0.005), ICA tortuosity (0.070±0.042 versus 0.046±0.022), ICA/CCA diameter ratio (0.693± 0.132 versus 0.728±0.106), ECA/CCA diameter ratio (0.750±0.123 versus 0.809±0.122), ECA/ ICA diameter ratio (1.103±0.201 versus 1.127±0.195), bifurcation area ratio (1.057±0.281 versus 1.291±0.252). There was significant statistical difference between young group and older group in-bifurcation angle, ICA angle, CCA tortuosity, ICA tortuosity, ECA/CCA and bifurcation area ratio (F= 17.16, 11.74, 23.02, 13.38, 6.54, 22.80, respectively, P<0.05). Conclusions: MR angiography images combined with image post-processing technique can reconstruct 3D carotid bifurcation geometry and measure the geometric parameters of carotid bifurcation in vivo individually. It provides a new and convenient method to investigate the relationship of vascular geometry and flow condition with atherosclerotic pathological changes. (authors)
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.
2012-06-25
... Bilateral Safeguard Actions, Market Disruption, Trade Diversion, and Review of Relief Actions AGENCY: United... disruption, trade diversion, and review of relief actions (part 206 of its Rules). The final rule principally...--INVESTIGATIONS RELATING TO GLOBAL AND BILATERAL SAFEGUARG ACTIONS, MARKET DISRUPTION, TRADE DIVERSION, AND REVIEW...
Forced phase-locked response of a nonlinear system with time delay after Hopf bifurcation
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
Von Bertalanffy's dynamics under a polynomial correction: Allee effect and big bang bifurcation
Leonel Rocha, J.; Taha, A. K.; Fournier-Prunaret, D.
2016-02-01
In this work we consider new one-dimensional populational discrete dynamical systems in which the growth of the population is described by a family of von Bertalanffy's functions, as a dynamical approach to von Bertalanffy's growth equation. The purpose of introducing Allee effect in those models is satisfied under a correction factor of polynomial type. We study classes of von Bertalanffy's functions with different types of Allee effect: strong and weak Allee's functions. Dependent on the variation of four parameters, von Bertalanffy's functions also includes another class of important functions: functions with no Allee effect. The complex bifurcation structures of these von Bertalanffy's functions is investigated in detail. We verified that this family of functions has particular bifurcation structures: the big bang bifurcation of the so-called “box-within-a-box” type. The big bang bifurcation is associated to the asymptotic weight or carrying capacity. This work is a contribution to the study of the big bang bifurcation analysis for continuous maps and their relationship with explosion birth and extinction phenomena.
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.
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
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
Yu-Xuan Fu
2018-02-01
Full Text Available The FitzHugh–Nagumo model is improved to consider the effect of the electromagnetic induction on single neuron. On the basis of investigating the Hopf bifurcation behavior of the improved model, stochastic resonance in the stochastic version is captured near the bifurcation point. It is revealed that a weak harmonic oscillation in the electromagnetic disturbance can be amplified through stochastic resonance, and it is the cooperative effect of random transition between the resting state and the large amplitude oscillating state that results in the resonant phenomenon. Using the noise dependence of the mean of interburst intervals, we essentially suggest a biologically feasible clue for detecting weak signal by means of neuron model with subcritical Hopf bifurcation. These observations should be helpful in understanding the influence of the magnetic field to neural electrical activity.
Hopf Bifurcation Analysis for a Stochastic Discrete-Time Hyperchaotic System
Jie Ran
2015-01-01
Full Text Available The dynamics of a discrete-time hyperchaotic system and the amplitude control of Hopf bifurcation for a stochastic discrete-time hyperchaotic system are investigated in this paper. Numerical simulations are presented to exhibit the complex dynamical behaviors in the discrete-time hyperchaotic system. Furthermore, the stochastic discrete-time hyperchaotic system with random parameters is transformed into its equivalent deterministic system with the orthogonal polynomial theory of discrete random function. In addition, the dynamical features of the discrete-time hyperchaotic system with random disturbances are obtained through its equivalent deterministic system. By using the Hopf bifurcation conditions of the deterministic discrete-time system, the specific conditions for the existence of Hopf bifurcation in the equivalent deterministic system are derived. And the amplitude control with random intensity is discussed in detail. Finally, the feasibility of the control method is demonstrated by numerical simulations.
Metamorphosis of plasma turbulence-shear-flow dynamics through a transcritical bifurcation
Ball, R.; Dewar, R.L.; Sugama, H.
2002-01-01
The structural properties of an economical model for a confined plasma turbulence governor are investigated through bifurcation and stability analyses. A close relationship is demonstrated between the underlying bifurcation framework of the model and typical behavior associated with low- to high-confinement transitions such as shear-flow stabilization of turbulence and oscillatory collective action. In particular, the analysis evinces two types of discontinuous transition that are qualitatively distinct. One involves classical hysteresis, governed by viscous dissipation. The other is intrinsically oscillatory and nonhysteretic, and thus provides a model for the so-called dithering transitions that are frequently observed. This metamorphosis, or transformation, of the system dynamics is an important late side-effect of symmetry breaking, which manifests as an unusual nonsymmetric transcritical bifurcation induced by a significant shear-flow drive
Computing closest saddle node bifurcations in a radial system via conic programming
Jabr, R.A. [Electrical, Computer and Communication Engineering Department, Notre Dame University, P.O. Box 72, Zouk Mikhael, Zouk Mosbeh (Lebanon); Pal, B.C. [Department of Electrical and Electronic Engineering, Imperial College London, SW7 2BT (United Kingdom)
2009-07-15
This paper considers the problem of computing the loading limits in a radial system which are (i) locally closest to current operating load powers and (ii) at which saddle node bifurcation occurs. The procedure is based on a known technique which requires iterating between two computational steps until convergence. In essence, step 1 produces a vector normal to the real and/or reactive load solution space boundary, whereas step 2 computes the bifurcation point along that vector. The paper shows that each of the above computational steps can be formulated as a second-order cone program for which polynomial time interior-point methods and efficient implementations exist. The proposed conic programming approach is used to compute the closest bifurcation points and the corresponding worst case load power margins of eleven different distribution systems. The approach is validated graphically and the existence of multiple load power margins is investigated. (author)
Laser Pulse Production for NASA's Global Ecosystem Dynamics Investigation (GEDI) Lidar
Stysley, Paul R.; Coyle, D. Barry; Clarke, Greg B.; Frese, Erich; Blalock, Gordon; Morey, Peter; Kay, Richard B.; Poulios, Demetrios; Hersh, Michael
2016-01-01
The Lasers and Electro-Optics Branch at Goddard Space Flight Center has been tasked with building the Lasers for the Global Ecosystems Dynamics Investigation (GEDI) Lidar Mission, to be installed on the Japanese Experiment Module (JEM) on the International Space Station (ISS)1. GEDI will use three NASA-developed lasers, each coupled with a Beam Dithering Unit (BDU) to produce three sets of staggered footprints on the Earth's surface to accurately measure global biomass. We will report on the design, assembly progress, test results, and delivery process of this laser system.
Symmetry breaking bifurcations of a current sheet
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
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
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.
Bifurcation analysis of Rössler system with multiple delayed feedback
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.
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.
Torus bifurcations in multilevel converter systems
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....
Perturbed period-doubling bifurcation. I. Theory
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....
Sex differences in intracranial arterial bifurcations
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
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
Tulio Rosembuj
2006-12-01
Full Text Available There is no singular globalization, nor is the result of an individual agent. We could start by saying that global action has different angles and subjects who perform it are different, as well as its objectives. The global is an invisible invasion of materials and immediate effects.
Tulio Rosembuj
2006-01-01
There is no singular globalization, nor is the result of an individual agent. We could start by saying that global action has different angles and subjects who perform it are different, as well as its objectives. The global is an invisible invasion of materials and immediate effects.
Applicability of ultralow-frequency global resonances for investigating lightning activity on Venus
Nikolaenko, A.P.; Rabinovich, L.M.
1987-01-01
The application to experiments on Venus of methods of investigating global lightning activity that are used on earth in the ultralow-frequency range is discussed. Calculations of the electromagnetic fields in the range from a few Hertz to tens of Hertz are carried out in the framework of the model of the lower ionosphere of Venus, which generalizes the information about the planet's atmosphere which is presently available. The calculations showed that observations of global resonances on Venus must, as on the earth, allow one to obtain data about the global distribution of lightning in space and time, and to make the values of the parameters of the lower ionosphere model more precise
Kaslik, E.; Balint, St.
2009-01-01
In this paper, a bifurcation analysis is undertaken for a discrete-time Hopfield neural network of two neurons with two different delays and self-connections. Conditions ensuring the asymptotic stability of the null solution are found, with respect to two characteristic parameters of the system. It is shown that for certain values of these parameters, Fold or Neimark-Sacker bifurcations occur, but Flip and codimension 2 (Fold-Neimark-Sacker, double Neimark-Sacker, resonance 1:1 and Flip-Neimark-Sacker) bifurcations may also be present. The direction and the stability of the Neimark-Sacker bifurcations are investigated by applying the center manifold theorem and the normal form theory
Yamane, Kanji; Shima, Takeshi; Okada, Yoshikazu; Nishida, Masahiro; Okita, Shinji; Hanaguri, Katsuro [Chugoku Rousai Hospital, Kure, Hiroshima (Japan)
1993-11-01
Blood flow in the cervical carotid bifurcation was investigated by cine magnetic resonance imaging. In patients with stenosis, a low-intensity stream was demonstrated from the beginning of the carotid bulb, which was more distinct in the systolic phase. In patients with stenotic carotid bifurcations,the low-intensity flow was also present but was more prominent than in the non-stenotic bifurcation. This low-intensity stream may be due to the change from steady to turbulent flow due to the geometric characteristics of the carotid bifurcation or atheromatous plaque, similar to the flow separation phenomenon in fluid dynamics because of the coincidence of location and flow pattern. After carotid endarterectomy, turbulent flow was seen at the proximal and distal ends of the endarterectomy. Close follow-up and administration of antiplatelet agents are necessary to prevent restenosis due to mural thrombosis induced by such turbulent flow. (author).
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.
Investigation of equilibrium, global modes and microinstabilities in the stellarator W7-AS
Weller, A.; Anton, M.; Brakel, R.
1999-01-01
Equilibrium and stability properties in the WENDELSTEIN 7-AS stellarator are investigated experimentally and compared with theoretical predictions for particular cases. The topology of equilibrium magnetic surfaces and of global MHD modes is inferred from X-ray tomography. The predicted effects of externally driven currents and internal currents on the equilibrium surfaces could be confirmed experimentally. In particular the reduced Shafranov shift due to reduced Pfirsch-Schlueter currents in W7-AS could be verified. Up to the maximum accessible β ((β) ∼ 2%) plasmas can be confined without significant deterioration by pressure driven MHD-activity. However, global modes in the stable MHD spectrum such as global and toroidal Alfven eigenmodes (GAE, TAE) can be destabilised by energetic ions from neutral beam heating. These instabilities appear as very coherent low frequency modes (≤ 40 kHz) in the lower β regime without significant impact on the global confinement. At medium β very strong particle driven MHD modes with frequencies up to the range of 500 kHz can be observed. These modes can show nonlinear behaviour including periodic bursting and frequency chirping in combination with significant plasma energy losses. With increasing β Alfven modes are widely stable, because under these conditions the damping relative to the particle drive is increased. Besides the global mode activity small scale turbulent structures have been investigated in the plasma core and at the edge. The measured data of electron temperature, density and magnetic fluctuations do not yet allow to assess turbulence driven transport fluxes. However, correlations with the global confinement have been found, and the measured amplitudes are in the range expected to be relevant for anomalous transport. The observed dependence of the confinement on the edge rotational transform and magnetic shear can be explained in terms of enhanced transport at rational surfaces, however, the underlying
Investigation of equilibrium, global modes and microinstabilities in the stellarator W7-AS
Weller, A.; Anton, M.; Brakel, R.
2001-01-01
Equilibrium and stability properties in the WENDELSTEIN 7-AS stellarator are investigated experimentally and compared with theoretical predictions for particular cases. The topology of equilibrium magnetic surfaces and of global MHD modes is inferred from X-ray tomography. The predicted effects of externally driven currents and internal currents on the equilibrium surfaces could be confirmed experimentally. In particular the reduced Shafranov shift due to reduced Pfirsch-Schlueter currents in W7-AS could be verified. Up to the maximum accessible β ( ∼2%) plasmas can be confined without significant deterioration by pressure driven MHD-activity. However, global modes in the stable MHD spectrum such as global and toroidal Alfven eigenmodes (GAE, TAE) can be destabilised by energetic ions from neutral beam heating. These instabilities appear as very coherent low frequency modes (≤40 kHz) in the lower β regime without significant impact on the global confinement. At medium β very strong particle driven MHD modes with frequencies up to the range of 500 kHz can be observed. These modes can show nonlinear behaviour including periodic bursting and frequency chirping in combination with significant plasma energy losses. With increasing β Alfven modes are widely stable, because under these conditions the damping relative to the particle drive is increased. Besides the global mode activity small scale turbulent structures have been investigated in the plasma core and at the edge. The measured data of electron temperature, density and magnetic fluctuations do not yet allow to assess turbulence driven transport fluxes. However, correlations with the global confinement have been found, and the measured amplitudes are in the range expected to be relevant for anomalous transport. The observed dependence of the confinement on the edge rotational transform and magnetic shear can be explained in terms of enhanced transport at rational surfaces, however, the underlying
Bishop, Michael P.; Olsenholler, Jeffrey A.; Shroder, John F.; Barry, Roger G.; Rasup, Bruce H.; Bush, Andrew B. G.; Copland, Luke; Dwyer, John L.; Fountain, Andrew G.; Haeberli, Wilfried; Kääb, Andreas; Paul, Frank; Hall, Dorothy K.; Kargel, Jeffrey S.; Molnia, Bruce F.; Trabant, Dennis C.; Wessels, Rick L.
2004-01-01
Concerns over greenhouse‐gas forcing and global temperatures have initiated research into understanding climate forcing and associated Earth‐system responses. A significant component is the Earth's cryosphere, as glacier‐related, feedback mechanisms govern atmospheric, hydrospheric and lithospheric response. Predicting the human and natural dimensions of climate‐induced environmental change requires global, regional and local information about ice‐mass distribution, volumes, and fluctuations. The Global Land‐Ice Measurements from Space (GLIMS) project is specifically designed to produce and augment baseline information to facilitate glacier‐change studies. This requires addressing numerous issues, including the generation of topographic information, anisotropic‐reflectance correction of satellite imagery, data fusion and spatial analysis, and GIS‐based modeling. Field and satellite investigations indicate that many small glaciers and glaciers in temperate regions are downwasting and retreating, although detailed mapping and assessment are still required to ascertain regional and global patterns of ice‐mass variations. Such remote sensing/GIS studies, coupled with field investigations, are vital for producing baseline information on glacier changes, and improving our understanding of the complex linkages between atmospheric, lithospheric, and glaciological processes.
Explicit Solutions and Bifurcations for a Class of Generalized Boussinesq Wave Equation
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)
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....
Stability and Bifurcation in Magnetic Flux Feedback Maglev Control System
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.
Modal bifurcation in a high-Tc superconducting levitation system
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.
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.
A Note on the Bogdanov-Takens Bifurcation in the Romer Model with Learning by Doing
Bella, Giovanni
This paper is aimed at describing the whole set of necessary and sufficient conditions for the emergence of multiple equilibria and global indeterminacy in the standard endogenous growth framework with learning by doing. The novelty of this paper relies on the application of the original Bogdanov-Takens bifurcation theorem, which allows us to characterize the full dynamics of the model, and determine the emergence of an unavoidable poverty trap.
Smart, C.A.
1980-01-01
One of the atmospheric parameters that may be affected by variations in the electrosphere potential is thunderstorm activity. The author made preliminary investigations into the simultaneous monitoring of global thunderstorm incidence and electrosphere potential. The author looked at the structure of the sun and the earth solar activity and solar emissions as well as the sun-weather relationships. Measurement were made by the author during 1978 at Sanae, Antarctica. The objective was to investigate the fluctuations of global thunderstorm activity and electrosphere potential and to establish some link between these and with solar activity. Potential gradient of the lower atmosphere was measured by means of a field mill and fluctuations taken to be representative of those of the electrosphere potential. Thunderstorm incidence was monitored by measurement of extra low frequency (ELF) electromagnetic noise radiated by lightning. A dipole or loop antenna was used for the recording of extra low frequency electromagnetic noise. A computer program was developed to facilitate the data analysis
Stability and Bifurcation Analysis of a Three-Species Food Chain Model with Fear
Panday, Pijush; Pal, Nikhil; Samanta, Sudip; Chattopadhyay, Joydev
In the present paper, we investigate the impact of fear in a tri-trophic food chain model. We propose a three-species food chain model, where the growth rate of middle predator is reduced due to the cost of fear of top predator, and the growth rate of prey is suppressed due to the cost of fear of middle predator. Mathematical properties such as equilibrium analysis, stability analysis, bifurcation analysis and persistence have been investigated. We also describe the global stability analysis of the equilibrium points. Our numerical simulations reveal that cost of fear in basal prey may exhibit bistability by producing unstable limit cycles, however, fear in middle predator can replace unstable limit cycles by a stable limit cycle or a stable interior equilibrium. We observe that fear can stabilize the system from chaos to stable focus through the period-halving phenomenon. We conclude that chaotic dynamics can be controlled by the fear factors. We apply basic tools of nonlinear dynamics such as Poincaré section and maximum Lyapunov exponent to identify the chaotic behavior of the system.
Andru?cã Maria Carmen
2013-01-01
The field of globalization has highlighted an interdependence implied by a more harmonious understanding determined by the daily interaction between nations through the inducement of peace and the management of streamlining and the effectiveness of the global economy. For the functioning of the globalization, the developing countries that can be helped by the developed ones must be involved. The international community can contribute to the institution of the development environment of the gl...
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.
Bifurcation structure of a model of bursting pancreatic cells
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...
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
Stability and bifurcation analysis in a delayed SIR model
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 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.
Kučera, Milan; Navrátil, J.
2018-01-01
Roč. 166, January (2018), s. 154-180 ISSN 0362-546X Institutional support: RVO:67985840 Keywords : global bifurcation * maximal eigenvalue * positively homogeneous operators Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.192, year: 2016 http://www. science direct.com/ science /article/pii/S0362546X17302559?via%3Dihub
Kučera, Milan; Navrátil, J.
2018-01-01
Roč. 166, January (2018), s. 154-180 ISSN 0362-546X Institutional support: RVO:67985840 Keywords : global bifurcation * maximal eigenvalue * positively homogeneous operators Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.192, year: 2016 http://www.sciencedirect.com/science/article/pii/S0362546X17302559?via%3Dihub
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.
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.
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.
Double Hopf bifurcation in delay differential equations
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.
Complex dynamics and bifurcation analysis of host–parasitoid models with impulsive control strategy
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.
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.
Analysis of Spatiotemporal Dynamic and Bifurcation in a Wetland Ecosystem
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.
Investigations of radial electric field and global circulation layer in limiter tokamaks
Zagorski, R.; Gerhauser, H.; Lehnen, M.; Loarer, T.
2002-01-01
An updated version of the 2D multifluid code TECXY is used to study the radial electric field structure and the appearance of a global circulation layer (GCL) inside the separatrix of the limiter tokamaks TEXTOR-94 and Tore-Supra-CIEL. The dependence of the driving forces on device geometry, limiter position, magnetic field orientation, impurity content and other parameters is investigated. The centrifugal force in the vicinity of the limiter head always determines the direction of the poloidal velocity in the GCL. There is good agreement with experimentally measured profiles of the poloidal velocity at the TEXTOR low field side. (orig.)
Li, Yan; Rui, Xue; Li, Shuyu; Pu, Fang
2014-11-01
Graph theoretical analysis has recently become a popular research tool in neuroscience, however, there have been very few studies on brain responses to music perception, especially when culturally different styles of music are involved. Electroencephalograms were recorded from ten subjects listening to Chinese traditional music, light music and western classical music. For event-related potentials, phase coherence was calculated in the alpha band and then constructed into correlation matrices. Clustering coefficients and characteristic path lengths were evaluated for global properties, while clustering coefficients and efficiency were assessed for local network properties. Perception of light music and western classical music manifested small-world network properties, especially with a relatively low proportion of weights of correlation matrices. For local analysis, efficiency was more discernible than clustering coefficient. Nevertheless, there was no significant discrimination between Chinese traditional and western classical music perception. Perception of different styles of music introduces different network properties, both globally and locally. Research into both global and local network properties has been carried out in other areas; however, this is a preliminary investigation aimed at suggesting a possible new approach to brain network properties in music perception. Copyright © 2014 Elsevier Ltd. All rights reserved.
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.
Kanchan Kulkarni
2015-01-01
Full Text Available Sudden cardiac death instigated by ventricular fibrillation (VF is the largest cause of natural death in the USA. Alternans, a beat-to-beat alternation in the action potential duration, has been implicated as being proarrhythmic. The onset of alternans is mediated via a bifurcation, which may occur through either a smooth or a border-collision mechanism. The objective of this study was to characterize the mechanism of bifurcation to alternans based on experiments in isolated whole rabbit hearts. High resolution optical mapping was performed and the electrical activity was recorded from the left ventricle (LV epicardial surface of the heart. Each heart was paced using an “alternate pacing protocol,” where the basic cycle length (BCL was alternatively perturbed by ±δ. Local onset of alternans in the heart, BCLstart, was measured in the absence of perturbations (δ=0 and was defined as the BCL at which 10% of LV exhibited alternans. The influences of perturbation size were investigated at two BCLs: one prior to BCLstart (BCLprior=BCLstart+20 ms and one preceding BCLprior (BCLfar=BCLstart+40 ms. Our results demonstrate significant spatial correlation of the region exhibiting alternans with smooth bifurcation characteristics, indicating that transition to alternans in isolated rabbit hearts occurs predominantly through smooth bifurcation.
Allee’s dynamics and bifurcation structures in von Bertalanffy’s population size functions
Leonel Rocha, J.; Taha, Abdel-Kaddous; Fournier-Prunaret, D.
2018-03-01
The interest and the relevance of the study of the population dynamics and the extinction phenomenon are our main motivation to investigate the induction of Allee Effect in von Bertalanffy’s population size functions. The adjustment or correction factor of rational type introduced allows us to analyze simultaneously strong and weak Allee’s functions and functions with no Allee effect, whose classification is dependent on the stability of the fixed point x = 0. This classification is founded on the concepts of strong and weak Allee’s effects to the population growth rates associated. The transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, is verified with the evolution of the rarefaction critical density or Allee’s limit. The existence of cusp points on a fold bifurcation curve is related to this phenomenon of transition on Allee’s dynamics. Moreover, the “foliated” structure of the parameter plane considered is also explained, with respect to the evolution of the Allee limit. The bifurcation analysis is based on the configurations of fold and flip bifurcation curves. The chaotic semistability and the nonadmissibility bifurcation curves are proposed to this family of 1D maps, which allow us to define and characterize the corresponding Allee effect region.
Bifurcation and complex dynamics of a discrete-time predator-prey system
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.
Bifurcation study of phase oscillator systems with attractive and repulsive interaction
Burylko, Oleksandr; Kazanovich, Yakov; Borisyuk, Roman
2014-08-01
We study a model of globally coupled phase oscillators that contains two groups of oscillators with positive (synchronizing) and negative (desynchronizing) incoming connections for the first and second groups, respectively. This model was previously studied by Hong and Strogatz (the Hong-Strogatz model) in the case of a large number of oscillators. We consider a generalized Hong-Strogatz model with a constant phase shift in coupling. Our approach is based on the study of invariant manifolds and bifurcation analysis of the system. In the case of zero phase shift, various invariant manifolds are analytically described and a new dynamical mode is found. In the case of a nonzero phase shift we obtained a set of bifurcation diagrams for various systems with three or four oscillators. It is shown that in these cases system dynamics can be complex enough and include multistability and chaotic oscillations.
Stability and Bifurcation of a Fishery Model with Crowley-Martin Functional Response
Maiti, Atasi Patra; Dubey, B.
To understand the dynamics of a fishery system, a nonlinear mathematical model is proposed and analyzed. In an aquatic environment, we considered two populations: one is prey and another is predator. Here both the fish populations grow logistically and interaction between them is of Crowley-Martin type functional response. It is assumed that both the populations are harvested and the harvesting effort is assumed to be dynamical variable and tax is considered as a control variable. The existence of equilibrium points and their local stability are examined. The existence of Hopf-bifurcation, stability and direction of Hopf-bifurcation are also analyzed with the help of Center Manifold theorem and normal form theory. The global stability behavior of the positive equilibrium point is also discussed. In order to find the value of optimal tax, the optimal harvesting policy is used. To verify our analytical findings, an extensive numerical simulation is carried out for this model system.
Analysis of Vehicle Steering and Driving Bifurcation Characteristics
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
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
Jebbink, Erik Groot; Engelhard, Stefan; Lajoinie, Guillaume; de Vries, Jean-Paul P.M.; Versluis, Michel; Reijnen, Michel M.P.J.
2017-01-01
Purpose: To investigate the effect of distal stenotic lesions on flow patterns near a covered endovascular reconstruction of the aortic bifurcation (CERAB) configuration used in the treatment of aortoiliac occlusive disease. Method: Laser particle image velocimetry measurements were performed using
Bifurcation diagram of a cubic three-parameter autonomous system
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
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.
Plum, Maja
Globalization is often referred to as external to education - a state of affair facing the modern curriculum with numerous challenges. In this paper it is examined as internal to curriculum; analysed as a problematization in a Foucaultian sense. That is, as a complex of attentions, worries, ways...... of reasoning, producing curricular variables. The analysis is made through an example of early childhood curriculum in Danish Pre-school, and the way the curricular variable of the pre-school child comes into being through globalization as a problematization, carried forth by the comparative practices of PISA...
F. Gerard Adams
2008-01-01
The rapid globalization of the world economy is causing fundamental changes in patterns of trade and finance. Some economists have argued that globalization has arrived and that the world is â€œflatâ€ . While the geographic scope of markets has increased, the author argues that new patterns of trade and finance are a result of the discrepancies between â€œoldâ€ countries and â€œnewâ€ . As the differences are gradually wiped out, particularly if knowledge and technology spread worldwide, the t...
A Visual Approach to Investigating Shared and Global Memory Behavior of CUDA Kernels
Rosen, Paul
2013-06-01
We present an approach to investigate the memory behavior of a parallel kernel executing on thousands of threads simultaneously within the CUDA architecture. Our top-down approach allows for quickly identifying any significant differences between the execution of the many blocks and warps. As interesting warps are identified, we allow further investigation of memory behavior by visualizing the shared memory bank conflicts and global memory coalescence, first with an overview of a single warp with many operations and, subsequently, with a detailed view of a single warp and a single operation. We demonstrate the strength of our approach in the context of a parallel matrix transpose kernel and a parallel 1D Haar Wavelet transform kernel. © 2013 The Author(s) Computer Graphics Forum © 2013 The Eurographics Association and Blackwell Publishing Ltd.
A Visual Approach to Investigating Shared and Global Memory Behavior of CUDA Kernels
Rosen, Paul
2013-01-01
We present an approach to investigate the memory behavior of a parallel kernel executing on thousands of threads simultaneously within the CUDA architecture. Our top-down approach allows for quickly identifying any significant differences between the execution of the many blocks and warps. As interesting warps are identified, we allow further investigation of memory behavior by visualizing the shared memory bank conflicts and global memory coalescence, first with an overview of a single warp with many operations and, subsequently, with a detailed view of a single warp and a single operation. We demonstrate the strength of our approach in the context of a parallel matrix transpose kernel and a parallel 1D Haar Wavelet transform kernel. © 2013 The Author(s) Computer Graphics Forum © 2013 The Eurographics Association and Blackwell Publishing Ltd.
Climate bifurcation during the last deglaciation?
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
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).
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
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
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
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.
Luminal flow amplifies stent-based drug deposition in arterial bifurcations.
Vijaya B Kolachalama
2009-12-01
Full Text Available Treatment of arterial bifurcation lesions using drug-eluting stents (DES is now common clinical practice and yet the mechanisms governing drug distribution in these complex morphologies are incompletely understood. It is still not evident how to efficiently determine the efficacy of local drug delivery and quantify zones of excessive drug that are harbingers of vascular toxicity and thrombosis, and areas of depletion that are associated with tissue overgrowth and luminal re-narrowing.We constructed two-phase computational models of stent-deployed arterial bifurcations simulating blood flow and drug transport to investigate the factors modulating drug distribution when the main-branch (MB was treated using a DES. Simulations predicted extensive flow-mediated drug delivery in bifurcated vascular beds where the drug distribution patterns are heterogeneous and sensitive to relative stent position and luminal flow. A single DES in the MB coupled with large retrograde luminal flow on the lateral wall of the side-branch (SB can provide drug deposition on the SB lumen-wall interface, except when the MB stent is downstream of the SB flow divider. In an even more dramatic fashion, the presence of the SB affects drug distribution in the stented MB. Here fluid mechanic effects play an even greater role than in the SB especially when the DES is across and downstream to the flow divider and in a manner dependent upon the Reynolds number.The flow effects on drug deposition and subsequent uptake from endovascular DES are amplified in bifurcation lesions. When only one branch is stented, a complex interplay occurs - drug deposition in the stented MB is altered by the flow divider imposed by the SB and in the SB by the presence of a DES in the MB. The use of DES in arterial bifurcations requires a complex calculus that balances vascular and stent geometry as well as luminal flow.
Clausius entropy for arbitrary bifurcate null surfaces
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)
Stability and Hopf bifurcation in a delayed model for HIV infection of CD4{sup +}T cells
Cai Liming [Department of Mathematics, Xinyang Normal University, Xinyang, 464000 Henan (China); Beijing Institute of Information Control, Beijing 100037 (China)], E-mail: lmcai06@yahoo.com.cn; Li Xuezhi [Department of Mathematics, Xinyang Normal University, Xinyang, 464000 Henan (China)
2009-10-15
In this paper, we consider a delayed mathematical model for the interactions of HIV infection and CD4{sup +}T cells. We first investigate the existence and stability of the Equilibria. We then study the effect of the time delay on the stability of the infected equilibrium. Criteria are given to ensure that the infected equilibrium is asymptotically stable for all delay. Moreover, by applying Nyquist criterion, the length of delay is estimated for which stability continues to hold. Finally by using a delay {tau} as a bifurcation parameter, the existence of Hopf bifurcation is also investigated. Numerical simulations are presented to illustrate the analytical results.
Hughes, Stephen; Pearce, Darren
2015-01-01
A teaching laboratory experiment is described that uses Archimedes’ principle to precisely investigate the effect of global warming on the oceans. A large component of sea level rise is due to the increase in the volume of water due to the decrease in water density with increasing temperature. Water close to 0 °C is placed in a beaker and a glass marble hung from an electronic balance immersed in the water. As the water warms, the weight of the marble increases as the water is less buoyant due to the decrease in density. In the experiment performed in this paper a balance with a precision of 0.1 mg was used with a marble 40.0 cm 3 and mass of 99.3 g, yielding water density measurements with an average error of −0.008 ± 0.011%. (paper)
Global Precipitation Measurement (GPM) Spacecraft Lithium Ion Battery Micro-Cycling Investigation
Dakermanji, George; Lee, Leonine; Spitzer, Thomas
2016-01-01
The Global Precipitation Measurement (GPM) spacecraft was jointly developed by NASA and JAXA. It is a Low Earth Orbit (LEO) spacecraft launched on February 27, 2014. The power system is a Direct Energy Transfer (DET) system designed to support 1950 watts orbit average power. The batteries use SONY 18650HC cells and consist of three 8s by 84p batteries operated in parallel as a single battery. During instrument integration with the spacecraft, large current transients were observed in the battery. Investigation into the matter traced the cause to the Dual-Frequency Precipitation Radar (DPR) phased array radar which generates cyclical high rate current transients on the spacecraft power bus. The power system electronics interaction with these transients resulted in the current transients in the battery. An accelerated test program was developed to bound the effect, and to assess the impact to the mission.
Frese, Erich A.; Chiragh, Furqan L.; Switzer, Robert; Vasilyev, Aleksey A.; Thomes, Joe; Coyle, D. Barry; Stysley, Paul R.
2018-01-01
Flight quality solid-state lasers require a unique and extensive set of testing and qualification processes, both at the system and component levels to insure the laser's promised performance. As important as the overall laser transmitter design is, the quality and performance of individual subassemblies, optics, and electro-optics dictate the final laser unit's quality. The Global Ecosystem Dynamics Investigation (GEDI) laser transmitters employ all the usual components typical for a diode-pumped, solid-state laser, yet must each go through their own individual process of specification, modeling, performance demonstration, inspection, and destructive testing. These qualification processes and results for the laser crystals, laser diode arrays, electro-optics, and optics, will be reviewed as well as the relevant critical issues encountered, prior to their installation in the GEDI flight laser units.
Fractional noise destroys or induces a stochastic bifurcation
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
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
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
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....
Global Risk Diversification: An Empirical Investigation From The U. S. Perspective
H. Christine Hsu
2011-01-01
The case for global risk diversification has been built on correlations between the U.S. and international stock markets. Now that we witness how tightly the world stock markets are correlated, especially after the global financial crisis of 2008-2009, does it still make sense to diversify globally? Can the investments in global equity portfolios be protected in todays volatile markets? These questions have preoccupied a growing number of portfolio managers in recent years, as well as many of...
Chaos and Hopf bifurcation of a hybrid ratio-dependent three species food chain
Wang Fengyan; Pang Guoping
2008-01-01
In this paper, we propose and study a model of a hybrid ratio-dependent three species food chain, which is constituted by a hybrid type subsystem of prey and middle-predator and a middle-top predators' subsystem with Holling type-II functional response. We investigate the persistence and Hopf bifurcation of the system. Computer simulations are carried out to explain the mathematical conclusions. The chaotic attractor is obtained for suitable choice of parametric values
Investigation of global particulate nitrate from the AeroCom phase III experiment
H. Bian
2017-11-01
Full Text Available An assessment of global particulate nitrate and ammonium aerosol based on simulations from nine models participating in the Aerosol Comparisons between Observations and Models (AeroCom phase III study is presented. A budget analysis was conducted to understand the typical magnitude, distribution, and diversity of the aerosols and their precursors among the models. To gain confidence regarding model performance, the model results were evaluated with various observations globally, including ground station measurements over North America, Europe, and east Asia for tracer concentrations and dry and wet depositions, as well as with aircraft measurements in the Northern Hemisphere mid-to-high latitudes for tracer vertical distributions. Given the unique chemical and physical features of the nitrate occurrence, we further investigated the similarity and differentiation among the models by examining (1 the pH-dependent NH3 wet deposition; (2 the nitrate formation via heterogeneous chemistry on the surface of dust and sea salt particles or thermodynamic equilibrium calculation including dust and sea salt ions; and (3 the nitrate coarse-mode fraction (i.e., coarse/total. It is found that HNO3, which is simulated explicitly based on full O3-HOx-NOx-aerosol chemistry by all models, differs by up to a factor of 9 among the models in its global tropospheric burden. This partially contributes to a large difference in NO3−, whose atmospheric burden differs by up to a factor of 13. The atmospheric burdens of NH3 and NH4+ differ by 17 and 4, respectively. Analyses at the process level show that the large diversity in atmospheric burdens of NO3−, NH3, and NH4+ is also related to deposition processes. Wet deposition seems to be the dominant process in determining the diversity in NH3 and NH4+ lifetimes. It is critical to correctly account for contributions of heterogeneous chemical production of nitrate on dust and sea salt, because this process
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.
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.
Deformable 4DCT lung registration with vessel bifurcations
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.)
Multiple bifurcations and periodic 'bubbling' in a delay population model
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
Periodic solutions and bifurcations of delay-differential equations
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
Ball, R.; Dewar, R.L.; Sugama, H.
2003-01-01
The structural properties of an economical model for a confined plasma turbulence governor are investigated through bifurcation and stability analyses. Two types of discontinuous low to high confinement transition are found. One involves classical hysteresis, governed by viscous dissipation. The other is intrinsically oscillatory and non-hysteretic, and thus provides a model for observed 'dithering' transitions. This metamorphosis of the system dynamics is an important late side-effect of symmetry-breaking, which manifests as an unusual non-symmetric transcritical bifurcation induced by a significant shear flow drive
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.
Bunch lengthening with bifurcation in electron storage rings
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)
Iterative Controller Tuning for Process with Fold Bifurcations
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
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
D. Putero
2016-11-01
Full Text Available Stratospheric intrusion (SI events are a topic of ongoing research, especially because of their ability to change the oxidation capacity of the troposphere and their contribution to tropospheric ozone levels. In this work, a novel tool called STEFLUX (Stratosphere-to-Troposphere Exchange Flux is presented, discussed, and used to provide a first long-term investigation of SI over two global hot-spot regions for climate change and air pollution: the southern Himalayas and the central Mediterranean Basin. The main purpose of STEFLUX is to obtain a fast-computing and reliable identification of the SI events occurring at a specific location and during a specified time window. It relies on a compiled stratosphere-to-troposphere exchange (STE climatology, which makes use of the ERA-Interim reanalysis dataset from the ECMWF, as well as a refined version of a well-established Lagrangian methodology. STEFLUX results are compared to the SI observations (SIO at two high-mountain WMO/GAW global stations in these climate hot spots, i.e., the Nepal Climate Observatory-Pyramid (NCO-P, 5079 m a.s.l. and Mt. Cimone (2165 m a.s.l., which are often affected by SI events. Compared to the observational datasets at the two specific measurement sites, STEFLUX is able to detect SI events on a regional scale. Furthermore, it has the advantage of retaining additional information concerning the pathway of stratospheric-affected air masses, such as the location of tropopause crossing and other meteorological parameters along the trajectories. However, STEFLUX neglects mixing and dilution that air masses undergo along their transport within the troposphere. Therefore, the regional-scale STEFLUX events cannot be expected to perfectly reproduce the point measurements at NCO-P and Mt. Cimone, which are also affected by small-scale (orographic circulations. Still, the seasonal variability in SI events according to SIO and STEFLUX agrees fairly well. By exploiting the
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
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.
Bifurcation magnetic resonance in films magnetized along hard magnetization axis
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
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.
Border-Collision Bifurcations and Chaotic Oscillations in a Piecewise-Smooth Dynamical System
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...
Study of intermittent bifurcations and chaos in boost PFC converters by nonlinear discrete models
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
A financial market model with two discontinuities: Bifurcation structures in the chaotic domain
Panchuk, Anastasiia; Sushko, Iryna; Westerhoff, Frank
2018-05-01
We continue the investigation of a one-dimensional piecewise linear map with two discontinuity points. Such a map may arise from a simple asset-pricing model with heterogeneous speculators, which can help us to explain the intricate bull and bear behavior of financial markets. Our focus is on bifurcation structures observed in the chaotic domain of the map's parameter space, which is associated with robust multiband chaotic attractors. Such structures, related to the map with two discontinuities, have been not studied before. We show that besides the standard bandcount adding and bandcount incrementing bifurcation structures, associated with two partitions, there exist peculiar bandcount adding and bandcount incrementing structures involving all three partitions. Moreover, the map's three partitions may generate intriguing bistability phenomena.
Experimental bifurcation analysis—Continuation for noise-contaminated zero problems
Schilder, Frank; Bureau, Emil; Santos, Ilmar Ferreira
2015-01-01
Noise contaminated zero problems involve functions that cannot be evaluated directly, but only indirectly via observations. In addition, such observations are affected by a non-deterministic observation error (noise). We investigate the application of numerical bifurcation analysis for studying...... the solution set of such noise contaminated zero problems, which is highly relevant in the context of equation-free analysis (coarse grained analysis) and bifurcation analysis in experiments, and develop specialized algorithms to address challenges that arise due to the presence of noise. As a working example......, we demonstrate and test our algorithms on a mechanical nonlinear oscillator experiment using control based continuation, which we used as a main application and test case for development of the Coco compatible Matlab toolbox Continex that implements our algorithms....
Bifurcations and Periodic Solutions for an Algae-Fish Semicontinuous System
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.
Bifurcation Regulations Governed by Delay Self-Control Feedback in a Stochastic Birhythmic System
Ma, Zhidan; Ning, Lijuan
2017-12-01
We aim to investigate bifurcation behaviors in a stochastic birhythmic van der Pol (BVDP) system subjected to delay self-control feedback. First, the harmonic approximation is adopted to drive the delay self-control feedback to state variables without delay. Then, Fokker-Planck-Kolmogorov (FPK) equation and stationary probability density function (SPDF) for amplitude are obtained by applying stochastic averaging method. Finally, dynamical scenarios of the change of delay self-control feedback as well as noise that markedly influence bifurcation performance are observed. It is found that: the big feedback strength and delay will suppress the large amplitude limit cycle (LC) while the relatively big noise strength facilitates the large amplitude LC, which imply the proposed regulation strategies are feasible. Interestingly enough, the inner LC is never destroyed due to noise. Furthermore, the validity of analytical results was verified by Monte Carlo simulation of the dynamics.
Neimark-Sacker Bifurcation and Chaos Control in a Fractional-Order Plant-Herbivore Model
Qamar Din
2017-01-01
Full Text Available This work is related to dynamics of a discrete-time 3-dimensional plant-herbivore model. We investigate existence and uniqueness of positive equilibrium and parametric conditions for local asymptotic stability of positive equilibrium point of this model. Moreover, it is also proved that the system undergoes Neimark-Sacker bifurcation for positive equilibrium with the help of an explicit criterion for Neimark-Sacker bifurcation. The chaos control in the model is discussed through implementation of two feedback control strategies, that is, pole-placement technique and hybrid control methodology. Finally, numerical simulations are provided to illustrate theoretical results. These results of numerical simulations demonstrate chaotic long-term behavior over a broad range of parameters. The computation of the maximum Lyapunov exponents confirms the presence of chaotic behavior in the model.
Bifurcations in the response of a flexible rotor in squeeze-film dampers with retainer springs
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
雷, 紫雯
2014-01-01
This study investigates on China’s national public relations strategy under the globalization by analyzing the national media. In recent years, in order to improve the global public opinion environment, and to improve its national public relations capabilities that match its economic power status, China has actively strengthened its national public relations strategies, including making the national “media go out”, and building world-class media. By researching on the localization of Chinese ...
Axisymmetric bifurcations of thick spherical shells under inflation and compression
deBotton, G.; Bustamante, R.; Dorfmann, A.
2013-01-01
Incremental equilibrium equations and corresponding boundary conditions for an isotropic, hyperelastic and incompressible material are summarized and then specialized to a form suitable for the analysis of a spherical shell subject to an internal or an external pressure. A thick-walled spherical shell during inflation is analyzed using four different material models. Specifically, one and two terms in the Ogden energy formulation, the Gent model and an I1 formulation recently proposed by Lopez-Pamies. We investigate the existence of local pressure maxima and minima and the dependence of the corresponding stretches on the material model and on shell thickness. These results are then used to investigate axisymmetric bifurcations of the inflated shell. The analysis is extended to determine the behavior of a thick-walled spherical shell subject to an external pressure. We find that the results of the two terms Ogden formulation, the Gent and the Lopez-Pamies models are very similar, for the one term Ogden material we identify additional critical stretches, which have not been reported in the literature before.© 2012 Published by Elsevier Ltd.
Elgendi, Mohamed; Norton, Ian; Brearley, Matt; Fletcher, Richard R; Abbott, Derek; Lovell, Nigel H; Schuurmans, Dale
2015-10-14
Recent clinical studies show that the contour of the photoplethysmogram (PPG) wave contains valuable information for characterizing cardiovascular activity. However, analyzing the PPG wave contour is difficult; therefore, researchers have applied first or higher order derivatives to emphasize and conveniently quantify subtle changes in the filtered PPG contour. Our hypothesis is that analyzing the whole PPG recording rather than each PPG wave contour or on a beat-by-beat basis can detect heat-stressed subjects and that, consequently, we will be able to investigate the impact of global warming on human health. Here, we explore the most suitable derivative order for heat stress assessment based on the energy and entropy of the whole PPG recording. The results of our study indicate that the use Int. J. Environ. Res. Public Health 2015, 7 12777 of the entropy of the seventh derivative of the filtered PPG signal shows promising results in detecting heat stress using 20-second recordings, with an overall accuracy of 71.6%. Moreover, the combination of the entropy of the seventh derivative of the filtered PPG signal with the root mean square of successive differences, or RMSSD (a traditional heart rate variability index of heat stress), improved the detection of heat stress to 88.9% accuracy.
Mohamed Elgendi
2015-10-01
Full Text Available Recent clinical studies show that the contour of the photoplethysmogram (PPG wave contains valuable information for characterizing cardiovascular activity. However, analyzing the PPG wave contour is difficult; therefore, researchers have applied first or higher order derivatives to emphasize and conveniently quantify subtle changes in the filtered PPG contour. Our hypothesis is that analyzing the whole PPG recording rather than each PPG wave contour or on a beat-by-beat basis can detect heat-stressed subjects and that, consequently, we will be able to investigate the impact of global warming on human health. Here, we explore the most suitable derivative order for heat stress assessment based on the energy and entropy of the whole PPG recording. The results of our study indicate that the use of the entropy of the seventh derivative of the filtered PPG signal shows promising results in detecting heat stress using 20-second recordings, with an overall accuracy of 71.6%. Moreover, the combination of the entropy of the seventh derivative of the filtered PPG signal with the root mean square of successive differences, or RMSSD (a traditional heart rate variability index of heat stress, improved the detection of heat stress to 88.9% accuracy.
Elgendi, Mohamed; Norton, Ian; Brearley, Matt; Fletcher, Richard R.; Abbott, Derek; Lovell, Nigel H.; Schuurmans, Dale
2015-01-01
Recent clinical studies show that the contour of the photoplethysmogram (PPG) wave contains valuable information for characterizing cardiovascular activity. However, analyzing the PPG wave contour is difficult; therefore, researchers have applied first or higher order derivatives to emphasize and conveniently quantify subtle changes in the filtered PPG contour. Our hypothesis is that analyzing the whole PPG recording rather than each PPG wave contour or on a beat-by-beat basis can detect heat-stressed subjects and that, consequently, we will be able to investigate the impact of global warming on human health. Here, we explore the most suitable derivative order for heat stress assessment based on the energy and entropy of the whole PPG recording. The results of our study indicate that the use of the entropy of the seventh derivative of the filtered PPG signal shows promising results in detecting heat stress using 20-second recordings, with an overall accuracy of 71.6%. Moreover, the combination of the entropy of the seventh derivative of the filtered PPG signal with the root mean square of successive differences, or RMSSD (a traditional heart rate variability index of heat stress), improved the detection of heat stress to 88.9% accuracy. PMID:26473907
Storey, Alice A; Athens, J Stephen; Bryant, David; Carson, Mike; Emery, Kitty; deFrance, Susan; Higham, Charles; Huynen, Leon; Intoh, Michiko; Jones, Sharyn; Kirch, Patrick V; Ladefoged, Thegn; McCoy, Patrick; Morales-Muñiz, Arturo; Quiroz, Daniel; Reitz, Elizabeth; Robins, Judith; Walter, Richard; Matisoo-Smith, Elizabeth
2012-01-01
Data from morphology, linguistics, history, and archaeology have all been used to trace the dispersal of chickens from Asian domestication centers to their current global distribution. Each provides a unique perspective which can aid in the reconstruction of prehistory. This study expands on previous investigations by adding a temporal component from ancient DNA and, in some cases, direct dating of bones of individual chickens from a variety of sites in Europe, the Pacific, and the Americas. The results from the ancient DNA analyses of forty-eight archaeologically derived chicken bones provide support for archaeological hypotheses about the prehistoric human transport of chickens. Haplogroup E mtDNA signatures have been amplified from directly dated samples originating in Europe at 1000 B.P. and in the Pacific at 3000 B.P. indicating multiple prehistoric dispersals from a single Asian centre. These two dispersal pathways converged in the Americas where chickens were introduced both by Polynesians and later by Europeans. The results of this study also highlight the inappropriate application of the small stretch of D-loop, traditionally amplified for use in phylogenetic studies, to understanding discrete episodes of chicken translocation in the past. The results of this study lead to the proposal of four hypotheses which will require further scrutiny and rigorous future testing.
A global analysis approach for investigating structural resilience in urban drainage systems.
Mugume, Seith N; Gomez, Diego E; Fu, Guangtao; Farmani, Raziyeh; Butler, David
2015-09-15
Building resilience in urban drainage systems requires consideration of a wide range of threats that contribute to urban flooding. Existing hydraulic reliability based approaches have focused on quantifying functional failure caused by extreme rainfall or increase in dry weather flows that lead to hydraulic overloading of the system. Such approaches however, do not fully explore the full system failure scenario space due to exclusion of crucial threats such as equipment malfunction, pipe collapse and blockage that can also lead to urban flooding. In this research, a new analytical approach based on global resilience analysis is investigated and applied to systematically evaluate the performance of an urban drainage system when subjected to a wide range of structural failure scenarios resulting from random cumulative link failure. Link failure envelopes, which represent the resulting loss of system functionality (impacts) are determined by computing the upper and lower limits of the simulation results for total flood volume (failure magnitude) and average flood duration (failure duration) at each link failure level. A new resilience index that combines the failure magnitude and duration into a single metric is applied to quantify system residual functionality at each considered link failure level. With this approach, resilience has been tested and characterised for an existing urban drainage system in Kampala city, Uganda. In addition, the effectiveness of potential adaptation strategies in enhancing its resilience to cumulative link failure has been tested. Copyright © 2015 The Authors. Published by Elsevier Ltd.. All rights reserved.
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
Bifurcations and chaos of a vibration isolation system with magneto-rheological damper
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
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.
Bifurcation of Lane Change and Control on Highway for Tractor-Semitrailer under Rainy Weather
Tao Peng
2017-01-01
Full Text Available A new method is proposed for analyzing the nonlinear dynamics and stability in lane changes on highways for tractor-semitrailer under rainy weather. Unlike most of the literature associated with a simulated linear dynamic model for tractor-semitrailers steady steering on dry road, a verified 5DOF mechanical model with nonlinear tire based on vehicle test was used in the lane change simulation on low adhesion coefficient road. According to Jacobian matrix eigenvalues of the vehicle model, bifurcations of steady steering and sinusoidal steering on highways under rainy weather were investigated using a numerical method. Furthermore, based on feedback linearization theory, taking the tractor yaw rate and joint angle as control objects, a feedback linearization controller combined with AFS and DYC was established. The numerical simulation results reveal that Hopf bifurcations are identified in steady and sinusoidal steering conditions, which translate into an oscillatory behavior leading to instability. And simulations of urgent step and single-lane change in high velocity show that the designed controller has good effects on eliminating bifurcations and improving lateral stability of tractor-semitrailer, during lane changing on highway under rainy weather. It is a valuable reference for safety design of tractor-semitrailers to improve the traffic safety with driver-vehicle-road closed-loop system.
Flow studies in canine artery bifurcations using a numerical simulation method.
Xu, X Y; Collins, M W; Jones, C J
1992-11-01
Three-dimensional flows through canine femoral bifurcation models were predicted under physiological flow conditions by solving numerically the time-dependent three-dimensional Navier-stokes equations. In the calculations, two models were assumed for the blood, those of (a) a Newtonian fluid, and (b) a non-Newtonian fluid obeying the power law. The blood vessel wall was assumed to be rigid this being the only approximation to the prediction model. The numerical procedure utilized a finite volume approach on a finite element mesh to discretize the equations, and the code used (ASTEC) incorporated the SIMPLE velocity-pressure algorithm in performing the calculations. The predicted velocity profiles were in good qualitative agreement with the in vivo measurements recently obtained by Jones et al. The non-Newtonian effects on the bifurcation flow field were also investigated, and no great differences in velocity profiles were observed. This indicated that the non-Newtonian characteristics of the blood might not be an important factor in determining the general flow patterns for these bifurcations, but could have local significance. Current work involves modeling wall distensibility in an empirically valid manner. Predictions accommodating these will permit a true quantitative comparison with experiment.
Luo, Kang; Yi, Hong-Liang, E-mail: yihongliang@hit.edu.cn; Tan, He-Ping, E-mail: tanheping@hit.edu.cn [School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001 (China)
2014-05-15
Transitions and bifurcations of transient natural convection in a horizontal annulus with radiatively participating medium are numerically investigated using the coupled lattice Boltzmann and direct collocation meshless (LB-DCM) method. As a hybrid approach based on a common multi-scale Boltzmann-type model, the LB-DCM scheme is easy to implement and has an excellent flexibility in dealing with the irregular geometries. Separate particle distribution functions in the LBM are used to calculate the density field, the velocity field and the thermal field. In the radiatively participating medium, the contribution of thermal radiation to natural convection must be taken into account, and it is considered as a radiative term in the energy equation that is solved by the meshless method with moving least-squares (MLS) approximation. The occurrence of various instabilities and bifurcative phenomena is analyzed for different Rayleigh number Ra and Prandtl number Pr with and without radiation. Then, bifurcation diagrams and dual solutions are presented for relevant radiative parameters, such as convection-radiation parameter Rc and optical thickness τ. Numerical results show that the presence of volumetric radiation changes the static temperature gradient of the fluid, and generally results in an increase in the flow critical value. Besides, the existence and development of dual solutions of transient convection in the presence of radiation are greatly affected by radiative parameters. Finally, the advantage of LB-DCM combination is discussed, and the potential benefits of applying the LB-DCM method to multi-field coupling problems are demonstrated.
Bifurcation of plasma cylinder equilibrium into a stationary helical flow with magnetic islands
Gubarev, V.F.; Dmitrenko, A.G.; Fesenko, A.I.
1985-01-01
Introduction of the low-hydrodynamic viscosity into the system of nonlinear MHD-equations enabled to use the bifurcation theory for the investigation into nonlinear phenomena connected with a tearing mode. The existance of a stable stationary helical flow with magnetic islands in the vicinity of a neutral curve is established. Fransfer from an axisymmetric equilibrium of a plasma cylinder to a helical one takes place only under soft conditions at both sides of the neutral curve. This result confirms the fact that the tearing mode, actually, is not an instability and may be con sidered only as a reason of formation of equilibrium with splitted magnetic surfaces. Really, changing the q 0 parameter (q 0 is the value proportional to a value of stability margin) at the plasma filament boundary a plasma equilibrium is attained corresponding to a stable branch of the bifurcation curve. In this case, a stable branch of the bifurcation curve corresponds to a helical stationary flow with magnetic islands in the instabwility region determined from the linear theory
Magnetic targeting to enhance microbubble delivery in an occluded microarterial bifurcation.
de Saint Victor, M; Carugo, D; Barnsley, L C; Owen, J; Coussios, C-C; Stride, E
2017-09-05
Ultrasound and microbubbles have been shown to accelerate the breakdown of blood clots both in vitro and in vivo. Clinical translation of this technology is still limited, however, in part by inefficient microbubble delivery to the thrombus. This study examines the obstacles to delivery posed by fluid dynamic conditions in occluded vasculature and investigates whether magnetic targeting can improve microbubble delivery. A 2D computational fluid dynamic model of a fully occluded Y-shaped microarterial bifurcation was developed to determine: (i) the fluid dynamic field in the vessel with inlet velocities from 1-100 mm s -1 (corresponding to Reynolds numbers 0.25-25); (ii) the transport dynamics of fibrinolytic drugs; and (iii) the flow behavior of microbubbles with diameters in the clinically-relevant range (0.6-5 µm). In vitro experiments were carried out in a custom-built microfluidic device. The flow field was characterized using tracer particles, and fibrinolytic drug transport was assessed using fluorescence microscopy. Lipid-shelled magnetic microbubbles were fluorescently labelled to determine their spatial distribution within the microvascular model. In both the simulations and experiments, the formation of laminar vortices and an abrupt reduction of fluid velocity were observed in the occluded branch of the bifurcation, severely limiting drug transport towards the occlusion. In the absence of a magnetic field, no microbubbles reached the occlusion, remaining trapped in the first vortex, within 350 µm from the bifurcation center. The number of microbubbles trapped within the vortex decreased as the inlet velocity increased, but was independent of microbubble size. Application of a magnetic field (magnetic flux density of 76 mT, magnetic flux density gradient of 10.90 T m -1 at the centre of the bifurcation) enabled delivery of microbubbles to the occlusion and the number of microbubbles delivered increased with bubble size and with decreasing inlet
Onset of Fast Magnetic Reconnection via Subcritical Bifurcation
ZHIBIN eGUO
2015-04-01
Full Text Available We report a phase transition model for the onset of fast magnetic reconnection. By investigating the joint dynamics of streaming instability(i.e., current driven ion acoustic in this paper and current gradient driven whistler wave {color{blue} {prior to the onset of fast reconnection}}, we show that the nonlinear evolution of current sheet(CS can be described by a Landau-Ginzburg equation. The phase transition from slow reconnection to fast reconnection occurs at a critical thickness, $Delta_csimeq frac{2}{sqrt{pi}}left|frac{v_{the}}{v_c}right|d_e$, where $v_{the}$ is electron thermal velocity and $v_c$ is the velocity threshold of the streaming instability. For current driven ion acoustic, $Delta_c$ is $leq10d_e$. If the thickness of the CS is narrower than $Delta_c$, the CS subcritically bifurcates into a rough state, which facilitates breakage of the CS, and consequently initiates fast reconnection.
Dansgaard–Oeschger events: bifurcation points in the climate system
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.
Barsuk, Alexandr A.; Paladi, Florentin
2018-04-01
The dynamic behavior of thermodynamic system, described by one order parameter and one control parameter, in a small neighborhood of ordinary and bifurcation equilibrium values of the system parameters is studied. Using the general methods of investigating the branching (bifurcations) of solutions for nonlinear equations, we performed an exhaustive analysis of the order parameter dependences on the control parameter in a small vicinity of the equilibrium values of parameters, including the stability analysis of the equilibrium states, and the asymptotic behavior of the order parameter dependences on the control parameter (bifurcation diagrams). The peculiarities of the transition to an unstable state of the system are discussed, and the estimates of the transition time to the unstable state in the neighborhood of ordinary and bifurcation equilibrium values of parameters are given. The influence of an external field on the dynamic behavior of thermodynamic system is analyzed, and the peculiarities of the system dynamic behavior are discussed near the ordinary and bifurcation equilibrium values of parameters in the presence of external field. The dynamic process of magnetization of a ferromagnet is discussed by using the general methods of bifurcation and stability analysis presented in the paper.
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.
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.
Shells, orbit bifurcations, and symmetry restorations in Fermi systems
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.
Inverse bifurcation analysis: application to simple gene systems
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.
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
Tamain, P.; Joffrin, E.; Bufferand, H.; Jarvinen, A.; Brezinsek, S.; Ciraolo, G.; Delabie, E.; Frassinetti, L.; Giroud, C.; Groth, M.; Lipschultz, B.; Lomas, P.; Marsen, S.; Menmuir, S.; Oberkofler, M.; Stamp, M.; Wiesen, S.; JET-EFDA Contributors,
2015-01-01
Abstract The impact of the divertor geometry on global plasma confinement in type I ELMy H-mode has been investigated in the JET tokamak equipped with ITER-Like Wall. Discharges have been performed in which the position of the strike-points was changed while keeping the bulk plasma equilibrium
Ping-Chun Hsiung
2015-07-01
Full Text Available Over the last decade, qualitative researchers have begun to challenge the domination and universalistic claims of the Global North. Nevertheless, it is still unclear what pursuing qualitative research (QR from the Global South might entail. I advance this effort by situating it in the larger context of the decentering endeavor in social science and decolonizing methodologies in aboriginal scholarship. Informed by their locally-grounded approach in the quest for constructing alternative social science accounts and articulating decolonized knowledge, I argue that writing locally-grounded histories is an essential first step to explore methodologies and epistemologies of QR from the Global South. Noting that no national history of QR has been derived from the Global South, I present an example of writing the history of QR by examining MAO Zedong's legacy of "investigative research" (IR. Specifically, I analyze the practices of IR during China's "Great Leap Forward" (1958-62. In conclusion, I discuss the implications of IR to the development of social science research in contemporary China. I lay out key issues in pursuing QR from the Global South and present how such a pursuit is relevant to social science inquiry in the Global North. URN: http://nbn-resolving.de/urn:nbn:de:0114-fqs150325
Investigation on the Patterns of Global Vegetation Change Using a Satellite-Sensed Vegetation Index
Ainong Li
2010-06-01
Full Text Available The pattern of vegetation change in response to global change still remains a controversial issue. A Normalized Difference Vegetation Index (NDVI dataset compiled by the Global Inventory Modeling and Mapping Studies (GIMMS was used for analysis. For the period 1982–2006, GIMMS-NDVI analysis indicated that monthly NDVI changes show homogenous trends in middle and high latitude areas in the northern hemisphere and within, or near, the Tropic of Cancer and Capricorn; with obvious spatio-temporal heterogeneity on a global scale over the past two decades. The former areas featured increasing vegetation activity during growth seasons, and the latter areas experienced an even greater amplitude in places where precipitation is adequate. The discussion suggests that one should be cautious of using the NDVI time-series to analyze local vegetation dynamics because of its coarse resolution and uncertainties.
EXPERIMENTAL STUDY ON SEDIMENT DISTRIBUTION AT CHANNEL BIFURCATION
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
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
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)
Bifurcations of propellant burning rate at oscillatory pressure
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.)
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...
Bifurcation-free design method of pulse energy converter controllers
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.
A bifurcation giving birth to order in an impulsively driven complex system
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.
Grundeken, Maik J; Lu, Huangling; Vos, Nicola; IJsselmuiden, Alexander; van Geuns, Robert-Jan; Wessely, Rainer; Dengler, Thomas; La Manna, Alessio; Silvain, Johanne; Montalescot, Gilles; Spaargaren, René; Tijssen, Jan G P; de Winter, Robbert J; Wykrzykowska, Joanna J; Amoroso, Giovanni; Koch, Karel T
2017-08-01
To investigate outcomes in patients with ST-segment elevation myocardial infarction (STEMI) after treatment with the Stentys self-apposing stent (Stentys SAS; Stentys S.A.) for bifurcation culprit lesions. The nitinol, self-expanding Stentys was initially developed as a dedicated bifurcation stent. The stent facilitates a provisional strategy by accommodating its diameter to both the proximal and distal reference diameters and offering an opportunity to "disconnect" the interconnectors, opening the stent toward the side branch. The APPOSITION (a post-market registry to assess the Stentys self-expanding coronary stent in acute myocardial infarction) III study was a prospective, multicenter, international, observational study including STEMI patients undergoing primary percutaneous coronary intervention (PCI) with the Stentys SAS. Clinical endpoints were evaluated and stratified by bifurcation vs non-bifurcation culprit lesions. From 965 patients included, a total of 123 (13%) were documented as having a bifurcation lesion. Target-vessel revascularization (TVR) rates were higher in the bifurcation subgroup (16.4% vs 10.0%; P=.04). Although not statistically significant, other endpoints were numerically higher in the bifurcation subgroup: major adverse cardiac events (MACE; 12.7% vs 8.8%), myocardial infarction (MI; 3.4% vs 1.8%), and definite/probable stent thrombosis (ST; 5.8% vs 3.1%). However, when postdilation was performed, clinical endpoints were similar between bifurcation and non-bifurcation lesions: MACE (8.7% vs 8.4%), MI (1.2% vs 0.7%), and definite/probable ST (3.7% vs 2.4%). The use of the Stentys SAS was safe and feasible for the treatment of bifurcation lesions in the setting of primary PCI for STEMI treatment with acceptable 1-year cardiovascular event rates, which improved when postdilation was performed.
An Approach to Robust Control of the Hopf Bifurcation
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.
Communication: Mode bifurcation of droplet motion under stationary laser irradiation
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.
Bifurcated transition of radial transport in the HIEI tandem mirror
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
Bifurcation analysis of nephron pressure and flow regulation
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...
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.
Did Fiscal Stimulus Lift Developing Asia Out of the Global Crisis? An Empirical Investigation
Seok-Kyun Hur
2018-03-01
Full Text Available The substantial slowdown of economic growth since the global financial crisis of 2008-2009 is rekindling debate on whether developing Asia should use fiscal expansion to boost aggregate demand. A key factor in the debate is the effectiveness of countercyclical fiscal policy in the region. The global crisis, as well as the fiscal stimulus packages implemented by developing Asian countries at that time, give some clues to this important issue. The region weathered the global crisis well and experienced a robust V-shaped recovery. According to conventional wisdom, the fiscal stimulus packages put in place by Asian governments played a key role in the region’s recovery. The central objective of this paper is to empirically test this wisdom by using cross-country panel data. Our main finding is that the stimulus has had a limited but positive impact on developing Asia’s output during the global crisis. This lends some support to the notion that countercyclical fiscal policy can help the region cope with severe external shocks. The broader, more fundamental implication for regional policymakers is that the region’s long-standing commitment to fiscal discipline can yield significant benefits beyond macroeconomic stability. An important consequence of this commitment - relatively healthy fiscal balance sheets - enabled the region’s governments to quickly and decisively embark upon fiscal stimulus programs.
Prajna P. Kumar
2016-12-01
Conclusion: This unique study performed across ten emerging and developed countries strongly supported the need for systematic global training, education, and implementation of RBM regulatory guidance, with an aim for better safety of subjects and improved quality of clinical trial data. Furthermore, studies with larger sample sizes are recommended to provide an evidence-based approach.
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.
Hopf bifurcation analysis of Chen circuit with direct time delay feedback
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
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.
Merlo, G.; Brunner, S.; Huang, Z.; Coda, S.; Görler, T.; Villard, L.; Bañón Navarro, A.; Dominski, J.; Fontana, M.; Jenko, F.; Porte, L.; Told, D.
2018-03-01
Axisymmetric (n = 0) density fluctuations measured in the TCV tokamak are observed to possess a frequency f 0 which is either varying (radially dispersive oscillations) or a constant over a large fraction of the plasma minor radius (radially global oscillations) as reported in a companion paper (Z Huang et al, this issue). Given that f 0 scales with the sound speed and given the poloidal structure of density fluctuations, these oscillations were interpreted as Geodesic Acoustic Modes, even though f 0 is in fact smaller than the local linear GAM frequency {f}{GAM}. In this work we employ the Eulerian gyrokinetic code GENE to simulate TCV relevant conditions and investigate the nature and properties of these oscillations, in particular their relation to the safety factor profile. Local and global simulations are carried out and a good qualitative agreement is observed between experiments and simulations. By varying also the plasma temperature and density profiles, we conclude that a variation of the edge safety factor alone is not sufficient to induce a transition from global to radially inhomogeneous oscillations, as was initially suggested by experimental results. This transition appears instead to be the combined result of variations in the different plasma profiles, collisionality and finite machine size effects. Simulations also show that radially global GAM-like oscillations can be observed in all fluxes and fluctuation fields, suggesting that they are the result of a complex nonlinear process involving also finite toroidal mode numbers and not just linear global GAM eigenmodes.
Engholm-Keller, Kasper; Størling, Joachim; Pociot, Flemming
in β-cells by which this cytokine can modulate cell-matrix interactions during inflammation, a regulation shown in other cell types. Further data analysis is currently ongoing, and the collective results of the experiments will hopefully facilitate additional insights into the effect of IL-1β......Novel Aspect: Global phosphoproteomic analysis of cytokine signaling in primary β-cells Introduction The insulin-producing β-cells of the pancreatic islets of Langerhans are targeted by aberrant immune system responses in diabetes mellitus involving cytokines, especially interleukin-1β (IL-1 β......), which initiate apoptosis of the β-cells. As only limited amounts of primary β-cells can be isolated from model organisms like mouse and rat, global phosphoproteomic analysis of these signaling events by mass spectrometry has generally been unfeasible. We have therefore developed a strategy...
Using satellites and global models to investigate aerosol-cloud interactions
Gryspeerdt, E.; Quaas, J.; Goren, T.; Sourdeval, O.; Mülmenstädt, J.
2017-12-01
Aerosols are known to impact liquid cloud properties, through both microphysical and radiative processes. Increasing the number concentration of aerosol particles can increase the cloud droplet number concentration (CDNC). Through impacts on precipitation processes, this increase in CDNC may also be able to impact the cloud fraction (CF) and the cloud liquid water path (LWP). Several studies have looked into the effect of aerosols on the CDNC, but as the albedo of a cloudy scene depends much more strongly on LWP and CF, an aerosol influence on these properties could generate a significant radiative forcing. While the impact of aerosols on cloud properties can be seen in case studies involving shiptracks and volcanoes, producing a global estimate of these effects remains challenging due to the confounding effect of local meteorology. For example, relative humidity significantly impacts the aerosol optical depth (AOD), a common satellite proxy for CCN, as well as being a strong control on cloud properties. This can generate relationships between AOD and cloud properties, even when there is no impact of aerosol-cloud interactions. In this work, we look at how aerosol-cloud interactions can be distinguished from the effect of local meteorology in satellite studies. With a combination global climate models and multiple sources of satellite data, we show that the choice of appropriate mediating variables and case studies can be used to develop constraints on the aerosol impact on CF and LWP. This will lead to improved representations of clouds in global climate models and help to reduce the uncertainty in the global impact of anthropogenic aerosols on cloud properties.
NONE
1996-03-01
To know the trend of measures taken for global warming, conducted were overseas surveys, participation in academic society meetings, and literature surveys. The phaseout time of all ozone depleting substances responsible for the ozonospherial destruction was determined for both developed and developing countries in the 7th Meeting of countries which concluded the Montreal Protocol. As information on measures for protecting the ozonosphere, introduced was activities under United Nations Environment Programme (UNEP). New fluorine containing ethers were introduced as cleaning solvent which causes no ozonospherial destruction and is low in global warming index. Toxicity data were obtained on HFC-236ea and HFC-236fa which are promising substitutes in HCFC foaming and refrigerant fields. The paper introduced an outline of the 1st Meeting of countries which concluded the Framework Convention on Climate Change held in 1995. According to the report on the National Institute of Public Health and Environmental Protection of the Netherlands, the amount of emission of fluorine containing greenhouse effect gas (in CO2 conversion) reached 8-14% of all the amount of greenhouse effect gas emitted in 1990 unless the control is reinforced. An outline of the TEWI-3 project was introduced which is useful for comparing effects of substitution technologies on global warming. 14 refs., 11 figs., 29 tabs.
Necessary and sufficient conditions for Hopf bifurcation in tri-neuron equation with a delay
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
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.
Post-Treatment Hemodynamics of a Basilar Aneurysm and Bifurcation
Ortega, J; Hartman, J; Rodriguez, J; Maitland, D
2008-01-16
Aneurysm re-growth and rupture can sometimes unexpectedly occur following treatment procedures that were initially considered to be successful at the time of treatment and post-operative angiography. In some cases, this can be attributed to surgical clip slippage or endovascular coil compaction. However, there are other cases in which the treatment devices function properly. In these instances, the subsequent complications are due to other factors, perhaps one of which is the post-treatment hemodynamic stress. To investigate whether or not a treatment procedure can subject the parent artery to harmful hemodynamic stresses, computational fluid dynamics simulations are performed on a patient-specific basilar aneurysm and bifurcation before and after a virtual endovascular treatment. The simulations demonstrate that the treatment procedure produces a substantial increase in the wall shear stress. Analysis of the post-treatment flow field indicates that the increase in wall shear stress is due to the impingement of the basilar artery flow upon the aneurysm filling material and to the close proximity of a vortex tube to the artery wall. Calculation of the time-averaged wall shear stress shows that there is a region of the artery exposed to a level of wall shear stress that can cause severe damage to endothelial cells. The results of this study demonstrate that it is possible for a treatment procedure, which successfully excludes the aneurysm from the vascular system and leaves no aneurysm neck remnant, to elevate the hemodynamic stresses to levels that are injurious to the immediately adjacent vessel wall.
STABILITY, BIFURCATIONS AND CHAOS IN UNEMPLOYMENT NON-LINEAR DYNAMICS
Pagliari Carmen
2013-07-01
Full Text Available The traditional analysis of unemployment in relation to real output dynamics is based on some empirical evidences deducted from Okun’s studies. In particular the so called Okun’s Law is expressed in a linear mathematical formulation, which cannot explain the fluctuation of the variables involved. Linearity is an heavy limit for macroeconomic analysis and especially for every economic growth study which would consider the unemployment rate among the endogenous variables. This paper deals with an introductive study about the role of non-linearity in the investigation of unemployment dynamics. The main idea is the existence of a non-linear relation between the unemployment rate and the gap of GDP growth rate from its trend. The macroeconomic motivation of this idea moves from the consideration of two concatenate effects caused by a variation of the unemployment rate on the real output growth rate. These two effects are concatenate because there is a first effect that generates a secondary one on the same variable. When the unemployment rate changes, the first effect is the variation in the level of production in consequence of the variation in the level of such an important factor as labour force; the secondary effect is a consecutive variation in the level of production caused by the variation in the aggregate demand in consequence of the change of the individual disposal income originated by the previous variation of production itself. In this paper the analysis of unemployment dynamics is carried out by the use of the logistic map and the conditions for the existence of bifurcations (cycles are determined. The study also allows to find the range of variability of some characteristic parameters that might be avoided for not having an absolute unpredictability of unemployment dynamics (deterministic chaos: unpredictability is equivalent to uncontrollability because of the total absence of information about the future value of the variable to
Longitudinal traveling waves bifurcating from Vlasov plasma equilibria
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
Bifurcation of limit cycles for cubic reversible systems
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
Chaos and bifurcations in periodic windows observed in plasmas
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
Coronary bifurcation lesions treated with simple or complex stenting
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,
Pitchfork bifurcation and vibrational resonance in a fractional-order ...
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 $\\epsilon_c=0.328782\\ldots$.
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 ...
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
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
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
Epidemic model with vaccinated age that exhibits backward bifurcation
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 ...
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
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
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
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
Regularization of the Boundary-Saddle-Node Bifurcation
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 ...
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.
Adaptive global synchrony of inferior olive neurons
Lee, Keum W; Singh, Sahjendra N
2009-01-01
This paper treats the question of global adaptive synchronization of inferior olive neurons (IONs) based on the immersion and invariance approach. The ION exhibits a variety of orbits as the parameter (termed the bifurcation parameter), which appears in its nonlinear functions, is varied. It is seen that once the bifurcation parameter exceeds a critical value, the stability of the equilibrium point of the ION is lost, and periodic orbits are born. The size and shape of the orbits depend on the value of the bifurcation parameter. It is assumed that bifurcation parameters of the IONs are not known. The orbits of IONs beginning from arbitrary initial conditions are not synchronized. For the synchronization of the IONs, a non-certainty equivalent adaptation law is derived. The control system has a modular structure consisting of an identifier and a control module. Using the Lyapunov approach, it is shown that in the closed-loop system, global synchronization of the neurons with a prescribed relative phase is accomplished, and the estimated bifurcation parameters converge to the true parameters. Unlike the certainty-equivalent adaptive control systems, an interesting feature of the designed control system is that whenever the estimated parameters coincide with the true values, the parameter estimates remain frozen thereafter, and the closed-loop system recovers the performance of the deterministic closed-loop system. Simulation results are presented which show that in the closed-loop system, the synchrony of neurons with prescribed phases is accomplished despite the uncertainties in the bifurcation parameters.
Patel, Shivam; Usmani, Abdullah Y.; Muralidhar, K.
2017-06-01
Physiological flows in rigid diseased arterial flow phantoms emulating an abdominal aortic aneurysm (AAA) under rest conditions with aorto-iliac bifurcation and iliac stenosis are examined in vitro through 2D PIV measurements. Flow characteristics are first established in the model resembling a symmetric AAA with a straight outlet tube. The influence of aorto-iliac bifurcation and iliac stenosis on AAA flow dynamics is then explored through a comparison of the nature of flow patterns, vorticity evolution, vortex core trajectory and hemodynamic factors against the reference configuration. Specifically, wall shear stress and oscillatory shear index in the bulge portion of the models are of interest. The results of this investigation indicate overall phenomenological similarity in AAA flow patterns across the models. The pattern is characterized by a central jet and wall-bounded vortices whose strength increases during the deceleration phase as it moves forward. The central jet impacts the wall of AAA at its distal end. In the presence of an aorto-iliac bifurcation as well as iliac stenosis, the flow patterns show diminished strength, expanse and speed of propagation of the primary vortices. The positions of the instantaneous vortex cores, determined using the Q-function, correlate with flow separation in the bulge, flow resistance due to a bifurcation, and the break in symmetry introduced by a stenosis in one of the legs of the model. Time-averaged WSS in a healthy aorta is around 0.70 N m-2 and is lowered to the range ±0.2 N m-2 in the presence of the downstream bifurcation with a stenosed common iliac artery. The consequence of changes in the flow pattern within the aneurysm on disease progression is discussed.
Xue, Y.J.; Gao, P.Y.; Duan, Q.; Lin, Y.; Dai, C.B.
2008-01-01
Background: Regions prone to atherosclerosis, such as bends and bifurcations, tend to exhibit a certain degree of non-planarity or curvature, and these geometric features are known to strongly influence local flow patterns. Recently, computational fluid dynamics (CFD) has been used as a means of enhancing understanding of the mechanisms involved in atherosclerotic plaque formation and development. Purpose: To analyze flow patterns and hemodynamic distribution in stenotic carotid bifurcation in vivo by combining CFD with magnetic resonance angiography (MRA). Material and Methods: Twenty-one patients with carotid atherosclerosis proved by digital subtraction angiography (DSA) and/or Doppler ultrasound underwent contrast-enhanced MR angiography of the carotid bifurcation by a 3.0T MR scanner. Hemodynamic variables and flow patterns of the carotid bifurcation were calculated and visualized by combining vascular imaging postprocessing with CFD. Results: In mild stenotic cases, there was much more streamlined flow in the bulbs, with reduced or disappeared areas of weakly turbulent flow. Also, the corresponding areas of low wall shear stress (WSS) were reduced or even disappeared. As the extent of stenosis increased, stronger blood jets formed at the portion of narrowing, and more prominent eddy flows and slow back flows were noted in the lee of the stenosis. Regions of elevated WSS were predicted at the portion of stenosis and in the path of the downstream jet. Areas of low WSS were predicted on the leeward side of the stenosis, corresponding with the location of slowly turbulent flows. Conclusion: CFD combined with MRA can simulate flow patterns and calculate hemodynamic variables in stenotic carotid bifurcations as well as normal ones. It provides a new method to investigate the relationship of vascular geometry and flow condition with atherosclerotic pathological changes
Patel, Shivam; Usmani, Abdullah Y; Muralidhar, K
2017-01-01
Physiological flows in rigid diseased arterial flow phantoms emulating an abdominal aortic aneurysm (AAA) under rest conditions with aorto-iliac bifurcation and iliac stenosis are examined in vitro through 2D PIV measurements. Flow characteristics are first established in the model resembling a symmetric AAA with a straight outlet tube. The influence of aorto-iliac bifurcation and iliac stenosis on AAA flow dynamics is then explored through a comparison of the nature of flow patterns, vorticity evolution, vortex core trajectory and hemodynamic factors against the reference configuration. Specifically, wall shear stress and oscillatory shear index in the bulge portion of the models are of interest. The results of this investigation indicate overall phenomenological similarity in AAA flow patterns across the models. The pattern is characterized by a central jet and wall-bounded vortices whose strength increases during the deceleration phase as it moves forward. The central jet impacts the wall of AAA at its distal end. In the presence of an aorto-iliac bifurcation as well as iliac stenosis, the flow patterns show diminished strength, expanse and speed of propagation of the primary vortices. The positions of the instantaneous vortex cores, determined using the Q -function, correlate with flow separation in the bulge, flow resistance due to a bifurcation, and the break in symmetry introduced by a stenosis in one of the legs of the model. Time-averaged WSS in a healthy aorta is around 0.70 N m −2 and is lowered to the range ±0.2 N m −2 in the presence of the downstream bifurcation with a stenosed common iliac artery. The consequence of changes in the flow pattern within the aneurysm on disease progression is discussed. (paper)
Patel, Shivam; Usmani, Abdullah Y; Muralidhar, K, E-mail: kmurli@iitk.ac.in [Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016 (India)
2017-06-15
Physiological flows in rigid diseased arterial flow phantoms emulating an abdominal aortic aneurysm (AAA) under rest conditions with aorto-iliac bifurcation and iliac stenosis are examined in vitro through 2D PIV measurements. Flow characteristics are first established in the model resembling a symmetric AAA with a straight outlet tube. The influence of aorto-iliac bifurcation and iliac stenosis on AAA flow dynamics is then explored through a comparison of the nature of flow patterns, vorticity evolution, vortex core trajectory and hemodynamic factors against the reference configuration. Specifically, wall shear stress and oscillatory shear index in the bulge portion of the models are of interest. The results of this investigation indicate overall phenomenological similarity in AAA flow patterns across the models. The pattern is characterized by a central jet and wall-bounded vortices whose strength increases during the deceleration phase as it moves forward. The central jet impacts the wall of AAA at its distal end. In the presence of an aorto-iliac bifurcation as well as iliac stenosis, the flow patterns show diminished strength, expanse and speed of propagation of the primary vortices. The positions of the instantaneous vortex cores, determined using the Q -function, correlate with flow separation in the bulge, flow resistance due to a bifurcation, and the break in symmetry introduced by a stenosis in one of the legs of the model. Time-averaged WSS in a healthy aorta is around 0.70 N m{sup −2} and is lowered to the range ±0.2 N m{sup −2} in the presence of the downstream bifurcation with a stenosed common iliac artery. The consequence of changes in the flow pattern within the aneurysm on disease progression is discussed. (paper)
Zhao, Huiqiang; Banerjee, Subhash; Chen, Hui; Li, Hongwei
2018-05-01
Recent studies have shown sheathless guide catheters (GCs) to be safe and effective during complex lesions such as bifurcations, chronic total occlusion (CTO), and/or calcified lesions. We investigated the feasibility and safety of using 7.5-Fr sheathless GC for transradial percutaneous coronary intervention (PCI) to treat left main bifurcation lesions.A total of 82 patients were consecutively enrolled from March 2013 to February 2016. They underwent transradial PCI for left main bifurcation lesions using the 7.5-Fr sheathless GC.The mean syntax score was 28.1 ± 6.1, and the majority (n = 55, 67.1%) was intermediate scores (23∼32). The unprotected LM disease was present in 67 of 82 patients (81.7%), and true bifurcation (Medina 1, 1, 1) was present in 46 of 82 patients (56.1%). The 2-stent technique was used in 62 of 82 patients (75.6%). The 2-stent technique included 31 cases (37.8%) of "Crush," 18 cases (22.0%) of "Cullote," and 13 (15.8%) cases of "T stent and modified T stent" (T stent). Immediate angiographic success rate was 100% (82/82), and procedural success rate was 97.6% (80/82). The vascular complications occurred in 3 patients (3/82, 3.7%).The use of 7.5-Fr sheathless GC is safe and allows PCI for complex bifurcation lesions located in the distal of left main to be performed transradially with a high success rate.
On control of Hopf bifurcation in time-delayed neural network system
Zhou Shangbo; Liao Xiaofeng; Yu Juebang; Wong Kwokwo
2005-01-01
The control of Hopf bifurcations in neural network systems is studied in this Letter. The asymptotic stability theorem and the relevant corollary for linearized nonlinear dynamical systems are proven. In particular, a novel method for analyzing the local stability of a dynamical system with time-delay is suggested. For the time-delayed system consisting of one or two neurons, a washout filter based control model is proposed and analyzed. By employing the stability theorems derived, we investigate the stability of a control system and state the relevant theorems for choosing the parameters of the stabilized control system
Experimental bifurcation analysis of an impact oscillator - Tuning a non-invasive control scheme
Bureau, Emil; Schilder, Frank; Santos, Ilmar
2013-01-01
We investigate a non-invasive, locally stabilizing control scheme necessary for an experimental bifurcation analysis. Our test-rig comprises a harmonically forced impact oscillator with hardening spring nonlinearity controlled by electromagnetic actuators, and serves as a prototype...... for electromagnetic bearings and other machinery with build-in actuators. We propose a sequence of experiments that allows one to choose optimal control-gains, filter parameters and settings for a continuation method without a priori study of a model. Depending on the algorithm for estimating the Jacobian required...
Eckhaus and Benjamin-Feir instabilities near a weakly inverted bifurcation
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
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
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.
The selection pressures induced non-smooth infectious disease model and bifurcation analysis
Qin, Wenjie; Tang, Sanyi
2014-01-01
Highlights: • A non-smooth infectious disease model to describe selection pressure is developed. • The effect of selection pressure on infectious disease transmission is addressed. • The key factors which are related to the threshold value are determined. • The stabilities and bifurcations of model have been revealed in more detail. • Strategies for the prevention of emerging infectious disease are proposed. - Abstract: Mathematical models can assist in the design strategies to control emerging infectious disease. This paper deduces a non-smooth infectious disease model induced by selection pressures. Analysis of this model reveals rich dynamics including local, global stability of equilibria and local sliding bifurcations. Model solutions ultimately stabilize at either one real equilibrium or the pseudo-equilibrium on the switching surface of the present model, depending on the threshold value determined by some related parameters. Our main results show that reducing the threshold value to a appropriate level could contribute to the efficacy on prevention and treatment of emerging infectious disease, which indicates that the selection pressures can be beneficial to prevent the emerging infectious disease under medical resource limitation
Verma, Dinkar, E-mail: dinkar@iitk.ac.in [Nuclear Engineering and Technology Program, Indian Institute of Technology Kanpur, Kanpur 208 016 (India); Kalra, Manjeet Singh, E-mail: drmanjeet.singh@dituniversity.edu.in [DIT University, Dehradun 248 009 (India); Wahi, Pankaj, E-mail: wahi@iitk.ac.in [Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208 016 (India)
2017-04-15
Highlights: • A simplified model with nonlinear void reactivity feedback is studied. • Method of multiple scales for nonlinear analysis and oscillation characteristics. • Second order void reactivity dominates in determining system dynamics. • Opposing signs of linear and quadratic void reactivity enhances global safety. - Abstract: In the present work, the effect of nonlinear void reactivity on the dynamics of a simplified lumped-parameter model for a boiling water reactor (BWR) is investigated. A mathematical model of five differential equations comprising of neutronics and thermal-hydraulics encompassing the nonlinearities associated with both the reactivity feedbacks and the heat transfer process has been used. To this end, we have considered parameters relevant to RBMK for which the void reactivity is known to be nonlinear. A nonlinear analysis of the model exploiting the method of multiple time scales (MMTS) predicts the occurrence of the two types of Hopf bifurcation, namely subcritical and supercritical, leading to the evolution of limit cycles for a range of parameters. Numerical simulations have been performed to verify the analytical results obtained by MMTS. The study shows that the nonlinear reactivity has a significant influence on the system dynamics. A parametric study with varying nominal reactor power and operating conditions in coolant channel has also been performed which shows the effect of change in concerned parameter on the boundary between regions of sub- and super-critical Hopf bifurcations in the space constituted by the two coefficients of reactivities viz. the void and the Doppler coefficient of reactivities. In particular, we find that introduction of a negative quadratic term in the void reactivity feedback significantly increases the supercritical region and dominates in determining the system dynamics.
An Investigation of Determinants Global Entrepreneurship: Multi-Country Panel Studies
Riznaldi Akbar
2016-06-01
Full Text Available This study examines the validity of governmental supports and policies; and financing for entrepreneurs in the context of global entrepreneurial activities. Our studies are based on the rich datasets of the Global Entrepreneurship Monitor (GEM database covering 108 countries from 2001 to 2014. In this study, we examine whether countries with more favorable policies and supports towards entrepreneurship and availability of financing for entrepreneurs would result in the higher country’s entrepreneurial activities. We use total early-stage entrepreneurial activity (TEA, a percentage of 18 - 64 year old population who are either a nascent entrepreneur or an owner manager of a new business, as our dependent variable to represent country’s entrepreneurial activities. There are two main explanatory variables used in the study: governmental supports and financing for entrepreneurs. The governmental supports represents the extent to which public policies support entrepreneurship as a relevant economic issue, while financing for entrepreneurs indicates the availability of financial resources for small and medium enterprises (SMEs including grants and subsidies. We also include three control variables of basic school entrepreneurial education and training; physical and services infrastructure; and cultural and social norms to test the significance of these factors to the country’s entrepreneurial activities. This study adopts panel regression model augmented with control variables. We favor Random Effect model as opposed to Fixed Effect or Pooled OLS model as Hausman and Breusch–Pagan test suggest. Our results suggest that there is no evident that government supports have significant contribution to country’s entrepreneurial activities. In other words, entrepreneurial activities are more flourished in a country that has not set entrepreneurship as relevant economic issues as it might be the case for many emerging countries. The availability of
Bakasov, A.A.; Govorkov, B.B. Jr.
1990-08-01
The critical case in stability theory is the case when it is impossible to study the stability of solutions over the linear part of ordinary differential equations. This situation is usual at the bifurcation points. There exists a powerful and constructive approach to investigate the stability - the theory of critical cases created by Lyapunov. The famous Lorenz model is used in this article as an illustration of the power of the method (new results). (author). 27 refs
Bifurcation and chaos in simple jerk dynamical systems
In recent years, it is observed that the third-order explicit autonomous differential equation, named as jerk equation, represents an interesting sub-class of dynamical systems that can exhibit many major features of the regular and chaotic motion. In this paper, we investigate the global dynamics of a special family of jerk ...
Bifurcation and chaos in simple jerk dynamical systems
- ferential equation, named as jerk equation, represents an interesting sub-class of dynam- ical systems that can exhibit many major features of the regular and chaotic motion. In this paper, we investigate the global dynamics of a special family ...
Quantifying the role of noise on droplet decisions in bifurcating microchannels
Norouzi Darabad, Masoud; Vaughn, Mark; Vanapalli, Siva
2017-11-01
While many aspects of path selection of droplets flowing through a bifurcating microchannel have been studied, there are still unaddressed issues in predicting and controlling droplet traffic. One of the more important is understanding origin of aperiodic patterns. As a new tool to investigate this phenomena we propose monitoring the continuous time response of pressure fluctuations at different locations. Then we use time-series analysis to investigate the dynamics of the system. We suggest that natural system noise is the cause of irregularity in the traffic patterns. Using a mathematical model, we investigate the effect of noise on droplet decisions at the junction. Noise can be derived from different sources including droplet size variation, droplet spacing, and pump induced velocity fluctuation. By analyzing different situations we explain system behavior. We also investigate the ``memory'' of a microfluidic system in terms of the resistance to perturbations that quantify the allowable deviation in operating condition before the system changes state.
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
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.
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.
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
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.
Bifurcations and Crises in a Shape Memory Oscillator
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.
Limit cycles bifurcating from a perturbed quartic center
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}.
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.
Fully developed turbulence via Feigenbaum's period-doubling bifurcations
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
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
[Sciatic nerve block "out-of-plane" distal to the bifurcation: effective and safe].
Geiser, T; Apel, J; Vicent, O; Büttner, J
2017-03-01
Ultrasound guided distal sciatic nerve block (DSB) at bifurcation level shows fast onset and provides excellent success rates. However, its safe performance might be difficult for the unexperienced physician. Just slightly distal to the bifurcation, the tibial nerve (TN) and common fibular nerve (CFN) can be shown clearly separated from each other. Therefore, we investigated if a block done here would provide similar quality results compared to the DSB proximally to the division, with a potentially lower risk of nerve damage. In this randomized, prospective trial, 56 patients per group received either a DSB distal to the bifurcation "out-of-plane" (dist.) or proximally "in-plane" (prox.) with 30 ml of Mepivacaine 1% each. Success was tested by a blinded examiner after 15 and 30 min respectively (sensory and motor block of TN and CFN: 0 = none, 2 = complete, change of skin temperature). Videos of the blocks were inspected by an independent expert retrospectively with regard to the spread of the local anesthetic (LA) and accidental intraneural injection. Cumulative single nerve measurements and temperature changes revealed significant shorter onset and better efficacy (dist/prox: 15 min: 3.13 ± 1.86/1.82 ± 1.62; 30 min: 5.73 ± 1.92/3.21 ± 1.88; T 15 min : 30.3 ± 3.48/28.0 ± 3.67, T 30 min . 33.0 ± 2.46/30.6 ± 3.86; MV/SD; ANOVA; p safe application of the LA, so an effective block can be done with just one injection. DSB slightly distal to the bifurcation, in an out-of-plane technique between the TN and CFN, can be done fast, effectively and safe.
Structural bifurcation of microwave helium jet discharge at atmospheric pressure
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
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
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
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
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
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.
Streamline topology: Patterns in fluid flows and their bifurcations
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....
Application of the bifurcation method to the modified Boussinesq equation
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.
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.
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.
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.
Observation of bifurcation phenomena in an electron beam plasma system
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
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
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)
Ida, K.; Inagaki, S.; Yoshinuma, M.; Narushima, Y.; Itoh, K.; Kobuchi, T.; Watanabe, K. Y.; Funaba, H.; Sakakibara, S.; Morisaki, T.; LHD Experimental Group
2008-01-01
Three states of a magnetic island are observed when the magnetic shear at the rational surface is modified using inductive current associated with the neutral beam current drive in the Large Helical Device. One state is the healed magnetic island with a zero island width. The second state is the saturated magnetic island with partial flattening of the T e profile. The third state is characterized by the global flattening of the T e profile in the core region. As the plasma assumes each of the three states consecutively through a bifurcation process a clear hysteresis in the relation between the size of the magnetic island and the magnetic shear is observed
PROMESS 1: Past Global Changes Investigated by Drilling Mediterranean Continental Margins
Berne, S.
2004-12-01
Between June, 24th and July, 22nd, 2004, a team of European scientists embarked from Brindisi (Italy) to Barcelona (Spain) onboard the Russian vessel "Bavenit", operated by the Dutch geotechnical company FUGRO, for a drilling expedition in the Adriatic Sea and the NW Mediterranean Sea. The purpose of this cruise was to collect long sediment sections and in situ measurements from two deltaic margins where the history of global changes during the last ca. 400 kyr is particularly well preserved. In the Adriatic, two boreholes were drilled at site PRAD1 (water depth 184 m), where the objective was to study the record of the last 4 glacial cycles. A pilot hole was first drilled for assessing the risk of shallow gases, a downhole logging was carried out in this borehole. A second site allowed continuous coring to the targeted depth (71m below sea-floor) with excellent recovery (better than 95%). Very preliminary interpretation indicates that seismic sequences previously identified correspond to 100 kyr glacial cycles. Downhole logging and physical properties of cores allow to identify magnetic events, and tephras. Site PRAD2 was devoted to the study of the recent most sediments (last 12,000 yrs) near the coastline, at a water depth of 56m. The targeted depth was 32 m below sea floor, sufficient to obtain a good record for the last ca 12,000 years. All together, six boreholes were drilled at PRAD2, including a pilot hole, one for continuous sediment recovery, and additional holes for in situ geotechnical tests and sampling. One of the objectives of these tests is to determine whether the wavy features shaping the sedimentary sequences are caused by near-bottom currents or result from liquefaction of unstable sediments triggered by earthquakes or storms. Site PRGL1 in the Gulf of Lion is at 298 m water depth, and the targeted depth below sea floor was 300 m, allowing to reach an expected age of about 430 kyr BP. A pilot hole was drilled down to 310 mbsf, and logged. Two
Reich, Felix A.; Rickert, Wilhelm; Müller, Wolfgang H.
2018-03-01
This study investigates the implications of various electromagnetic force models in macroscopic situations. There is an ongoing academic discussion which model is "correct," i.e., generally applicable. Often, gedankenexperiments with light waves or photons are used in order to motivate certain models. In this work, three problems with bodies at the macroscopic scale are used for computing theoretical model-dependent predictions. Two aspects are considered, total forces between bodies and local deformations. By comparing with experimental data, insight is gained regarding the applicability of the models. First, the total force between two cylindrical magnets is computed. Then a spherical magnetostriction problem is considered to show different deformation predictions. As a third example focusing on local deformations, a droplet of silicone oil in castor oil is considered, placed in a homogeneous electric field. By using experimental data, some conclusions are drawn and further work is motivated.
Chatthong, B. [Department of Physics, Faculty of Science, Prince of Songkla University, Hat Yai, Songkla (Thailand); Onjun, T. [School of Manufacturing Systems and Mechanical Engineering, Sirindhorn International Institute of Technology, Thammasat University, Pathum Thani (Thailand)
2016-08-15
The hysteresis behaviour at the L-H-L transitions in tokamak plasma is investigated based on bifurcation concept. The formation of an edge transport barrier (ETB) is modeled via thermal and particle transport equations with the flow shear suppression effect on anomalous transport included. The anomalous transport is modeled based on critical gradients threshold and the flow shear is calculated from the force balance equation, couples the two transport equations leading to a non-linear behaviour. Analytical investigation reveals that the fluxes versus gradients space exhibits bifurcation behaviour with s -curve soft bifurcation type. Apparently, the backward H-L transition occurs at lower values than that of the forward L-H transition, illustrating hysteresis behaviour. The hysteresis properties, i.e. locations of threshold fluxes, gradients and their ratios are analyzed as a function of neoclassical and anomalous transport values and critical gradients. It is found that the minimum heat flux for maintaining H -mode depends on several plasma parameters including the strength of anomalous transport and neoclassical transport. In particular, the hysteresis depth becomes larger when neoclassical transport decreases or anomalous transport increases. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Bondarenko, Vladimir E.; Cymbalyuk, Gennady S.; Patel, Girish; DeWeerth, Stephen P.; Calabrese, Ronald L.
2004-01-01
Oscillatory activity in the central nervous system is associated with various functions, like motor control, memory formation, binding, and attention. Quasiperiodic oscillations are rarely discussed in the neurophysiological literature yet they may play a role in the nervous system both during normal function and disease. Here we use a physical system and a model to explore scenarios for how quasiperiodic oscillations might arise in neuronal networks. An oscillatory system of two mutually inhibitory neuronal units is a ubiquitous network module found in nervous systems and is called a half-center oscillator. Previously we created a half-center oscillator of two identical oscillatory silicon (analog Very Large Scale Integration) neurons and developed a mathematical model describing its dynamics. In the mathematical model, we have shown that an in-phase limit cycle becomes unstable through a subcritical torus bifurcation. However, the existence of this torus bifurcation in experimental silicon two-neuron system was not rigorously demonstrated or investigated. Here we demonstrate the torus predicted by the model for the silicon implementation of a half-center oscillator using complex time series analysis, including bifurcation diagrams, mapping techniques, correlation functions, amplitude spectra, and correlation dimensions, and we investigate how the properties of the quasiperiodic oscillations depend on the strengths of coupling between the silicon neurons. The potential advantages and disadvantages of quasiperiodic oscillations (torus) for biological neural systems and artificial neural networks are discussed
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
Investigating Global Ion and Neutral Atom Populations with IBEX and Voyager
Florinski, Vladimir
2016-01-01
The main objective of this project was to investigate pickup ion (PUI) production in the solar wind and heliosheath (the region between the termination shock and the heliopause) and compute the distributed energetic neutral atom fluxes throughout the helioshpere. The simulations were constrained by comparing the model output against observations from Ulysses, New Horizons, Voyager 1 and 2, and IBEX space probes. As evidenced by the number of peer reviewed journal publications resulting from the project (13 plus three submitted) and their citation rate (156 citations over three years), the project has made a lasting contribution to the field. The outcome is a significant improvement of our understanding of the pickup ion production and distribution in the distant heliosphere. The team has accomplished the entire set of tasks A-H set forth in the proposal. Namely, the transport modeling framework has been augmented with two populations of pickup ions (PUIs), the boundary conditions for the plasma and interstellar neutral hydrogen were verified against Ulysses and New Horizons PUI and an optimal set of velocity diffusion parameters established. The multi-component fluxes of PUIs were computed and isotropic velocity distributions generated for each cell in the computer simulation that covered the heliosphere from 1.5 AU to the heliopause. The distributions were carefully compared with in situ measurements at 3 AU (Ulysses), 12 AU (New Horizons), and 80-90 AU (Voyager 1 and 2) as well as those inferred from ENA fluxes measured by Cassini and IBEX (Wu et al., 2016). Some examples of modeldata comparison are shown in Figure 1. We have used coupled MHD-plasma and kinetic-neutral code to investigate the likely range of plasma and magnetic field parameters in the local interstellar medium (LISM), based on the assumption that the shape of the IBEX ribbon could be used to determine the orientation of the interstellar magnetic field. While the magnetic field is believed to be
Fonti, Patrick; von Arx, Georg; García-González, Ignacio; Eilmann, Britta; Sass-Klaassen, Ute; Gärtner, Holger; Eckstein, Dieter
2010-01-01
Variability in xylem anatomy is of interest to plant scientists because of the role water transport plays in plant performance and survival. Insights into plant adjustments to changing environmental conditions have mainly been obtained through structural and functional comparative studies between taxa or within taxa on contrasting sites or along environmental gradients. Yet, a gap exists regarding the study of hydraulic adjustments in response to environmental changes over the lifetimes of plants. In trees, dated tree-ring series are often exploited to reconstruct dynamics in ecological conditions, and recent work in which wood-anatomical variables have been used in dendrochronology has produced promising results. Environmental signals identified in water-conducting cells carry novel information reflecting changes in regional conditions and are mostly related to short, sub-annual intervals. Although the idea of investigating environmental signals through wood anatomical time series goes back to the 1960s, it is only recently that low-cost computerized image-analysis systems have enabled increased scientific output in this field. We believe that the study of tree-ring anatomy is emerging as a promising approach in tree biology and climate change research, particularly if complemented by physiological and ecological studies. This contribution presents the rationale, the potential, and the methodological challenges of this innovative approach.
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.
Modal bifurcation in a high-T{sub c} superconducting levitation system
Taguchi, D; Fujiwara, S; Sugiura, T, E-mail: sugiura@mech.keio.ac.jp [Department of Mechanical Engineering, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, kohoku-ku, Yokohama 223-8522 (Japan)
2011-05-15
This paper deals with modal bifurcation of a multi-degree-of-freedom high-T{sub c} superconducting levitation system. As modeling of large-scale high-T{sub 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{sub 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{sub c} superconducting levitation systems.
Even distribution/dividing of single-phase fluids by symmetric bifurcation of flow channels
Liu, Hong; Li, Peiwen
2013-01-01
Highlights: ► We addressed an issue of distributing a flow to a number of flow channels uniformly. ► The flow distribution is accomplished through bifurcation of channels. ► Some key parameters to the flow distribution uniformity have been identified. ► Flow uniformity was studied for several versions of flow distributor designs. ► A novel fluid packaging device of high efficiency was provided. -- Abstract: This study addresses a fundamental issue of distributing a single-phase fluid flow into a number of flow channels uniformly. A basic mechanism of flow distribution is accomplished through bifurcation of channels that symmetrically split one flow channel into two downstream channels. Applying the basic mechanism, cascades flow distributions are designed to split one flow into a large number of downstream flows uniformly. Some key parameters decisive to the flow distribution uniformity in such a system have been identified, and the flow distribution uniformity of air was studied for several versions of flow distributor designs using CFD analysis. The effect of the key parameters of the flow channel designs to the flow distribution uniformity was investigated. As an example of industrial application, a novel fluid packaging device of high efficiency was proposed and some CFD analysis results for the device were provided. The optimized flow distributor makes a very good uniform flow distribution which will significantly improve the efficiency of fluid packaging. The technology is expected to be of great significance to many industrial devices that require high uniformity of flow distribution
Codimension-two bifurcation analysis on firing activities in Chay neuron model
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 on firing activities in Chay neuron model
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.
Global Stability of an Eco-Epidemiological Model with Time Delay and Saturation Incidence
Shuxue Mao
2011-01-01
Full Text Available We investigate a delayed eco-epidemiological model with disease in predator and saturation incidence. First, by comparison arguments, the permanence of the model is discussed. Then, we study the local stability of each equilibrium of the model by analyzing the corresponding characteristic equations and find that Hopf bifurcation occurs when the delay τ passes through a sequence of critical values. Next, by means of an iteration technique, sufficient conditions are derived for the global stability of the disease-free planar equilibrium and the positive equilibrium. Numerical examples are carried out to illustrate the analytical results.
Stability and Hopf Bifurcation in a Delayed SEIRS Worm Model in Computer Network
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.
Period-doubling bifurcation and chaos control in a discrete-time mosquito model
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.
Degenerate ground states and multiple bifurcations in a two-dimensional q-state quantum Potts model.
Dai, Yan-Wei; Cho, Sam Young; Batchelor, Murray T; Zhou, Huan-Qiang
2014-06-01
We numerically investigate the two-dimensional q-state quantum Potts model on the infinite square lattice by using the infinite projected entangled-pair state (iPEPS) algorithm. We show that the quantum fidelity, defined as an overlap measurement between an arbitrary reference state and the iPEPS ground state of the system, can detect q-fold degenerate ground states for the Z_{q} broken-symmetry phase. Accordingly, a multiple bifurcation of the quantum ground-state fidelity is shown to occur as the transverse magnetic field varies from the symmetry phase to the broken-symmetry phase, which means that a multiple-bifurcation point corresponds to a critical point. A (dis)continuous behavior of quantum fidelity at phase transition points characterizes a (dis)continuous phase transition. Similar to the characteristic behavior of the quantum fidelity, the magnetizations, as order parameters, obtained from the degenerate ground states exhibit multiple bifurcation at critical points. Each order parameter is also explicitly demonstrated to transform under the Z_{q} subgroup of the symmetry group of the Hamiltonian. We find that the q-state quantum Potts model on the square lattice undergoes a discontinuous (first-order) phase transition for q=3 and q=4 and a continuous phase transition for q=2 (the two-dimensional quantum transverse Ising model).
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.
Yi, Sun; Nelson, Patrick W; Ulsoy, A Galip
2007-04-01
In a turning process modeled using delay differential equations (DDEs), we investigate the stability of the regenerative machine tool chatter problem. An approach using the matrix Lambert W function for the analytical solution to systems of delay differential equations is applied to this problem and compared with the result obtained using a bifurcation analysis. The Lambert W function, known to be useful for solving scalar first-order DDEs, has recently been extended to a matrix Lambert W function approach to solve systems of DDEs. The essential advantages of the matrix Lambert W approach are not only the similarity to the concept of the state transition matrix in lin ear ordinary differential equations, enabling its use for general classes of linear delay differential equations, but also the observation that we need only the principal branch among an infinite number of roots to determine the stability of a system of DDEs. The bifurcation method combined with Sturm sequences provides an algorithm for determining the stability of DDEs without restrictive geometric analysis. With this approach, one can obtain the critical values of delay, which determine the stability of a system and hence the preferred operating spindle speed without chatter. We apply both the matrix Lambert W function and the bifurcation analysis approach to the problem of chatter stability in turning, and compare the results obtained to existing methods. The two new approaches show excellent accuracy and certain other advantages, when compared to traditional graphical, computational and approximate methods.
Souayeh Saoussen
2014-01-01
Full Text Available The collective nonlinear dynamics of a coupled array of nanocantilevers is investigated while taking into account the main sources of nonlinearities. The amplitude and phase equations of this device, subject to parametric and internal resonances, are analytically derived by means of a multi-modal Galerkin discretization coupled with a multiscale analysis. Based on the steady-state solutions of these equations, the frequency responses are numerically computed for a two-beam array. The effects of different parameters are investigated and several dynamical aspects are confirmed by numerical simulations. Particularly, we have demonstrated that the bifurcation topology transfer is imposed by the first nanocantilever and it can be general to the collective nonlinear dynamics of the NEMS array.
Rogers, W
2002-01-01
This report describes an investigation to determine the relative importance of various sources of error in the two global-scale models of wind-generated surface waves used operationally by the U.S. Navy...
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.
A numerical study of crack initiation in a bcc iron system based on dynamic bifurcation theory
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
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.
Park, K.; Mak, J. E.; Emmons, L. K.
2008-12-01
Carbon monoxide is not only an important component for determining the atmospheric oxidizing capacity but also a key trace gas in the atmospheric chemistry of the Earth's background environment. The global CO cycle and its change are closely related to both the change of CO mixing ratio and the change of source strength. Previously, to estimate the global CO budget, most top-down estimation techniques have been applied the concentrations of CO solely. Since CO from certain sources has a unique isotopic signature, its isotopes provide additional information to constrain its sources. Thus, coupling the concentration and isotope fraction information enables to tightly constrain CO flux by its sources and allows better estimations on the global CO budget. MOZART4 (Model for Ozone And Related chemical Tracers), a 3-D global chemical transport model developed at NCAR, MPI for meteorology and NOAA/GFDL and is used to simulate the global CO concentration and its isotopic signature. Also, a tracer version of MOZART4 which tagged for C16O and C18O from each region and each source was developed to see their contributions to the atmosphere efficiently. Based on the nine-year-simulation results we analyze the influences of each source of CO to the isotopic signature and the concentration. Especially, the evaluations are focused on the oxygen isotope of CO (δ18O), which has not been extensively studied yet. To validate the model performance, CO concentrations and isotopic signatures measured from MPI, NIWA and our lab are compared to the modeled results. The MOZART4 reproduced observational data fairly well; especially in mid to high latitude northern hemisphere. Bayesian inversion techniques have been used to estimate the global CO budget with combining observed and modeled CO concentration. However, previous studies show significant differences in their estimations on CO source strengths. Because, in addition to the CO mixing ratio, isotopic signatures are independent tracers
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
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.
Square-lattice random Potts model: criticality and pitchfork bifurcation
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.
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
R. Alfaro-Contreras
2016-01-01
Full Text Available Seven and a half years (June 2006 to November 2013 of Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP aerosol and cloud layer products are compared with collocated Ozone Monitoring Instrument (OMI aerosol index (AI data and Aqua Moderate Resolution Imaging Spectroradiometer (MODIS cloud products in order to investigate variability in estimates of biannual and monthly above-cloud aerosol (ACA events globally. The active- (CALIOP and passive-based (OMI-MODIS techniques have their advantages and caveats for ACA detection, and thus both are used to derive a thorough and robust comparison of daytime cloudy-sky ACA distribution and climatology. For the first time, baseline above-cloud aerosol optical depth (ACAOD and AI thresholds are derived and examined (AI = 1.0, ACAOD = 0.015 for each sensor. Both OMI-MODIS and CALIOP-based daytime spatial distributions of ACA events show similar patterns during both study periods (December–May and (June–November. Divergence exists in some regions, however, such as Southeast Asia during June through November, where daytime cloudy-sky ACA frequencies of up to 10 % are found from CALIOP yet are non-existent from the OMI-based method. Conversely, annual cloudy-sky ACA frequencies of 20–30 % are reported over northern Africa from the OMI-based method yet are largely undetected by the CALIOP-based method. Using a collocated OMI-MODIS-CALIOP data set, our study suggests that the cloudy-sky ACA frequency differences between the OMI-MODIS- and CALIOP-based methods are mostly due to differences in cloud detection capability between MODIS and CALIOP as well as QA flags used. An increasing interannual variability of ∼ 0.3–0.4 % per year (since 2009 in global monthly cloudy-sky ACA daytime frequency of occurrence is found using the OMI-MODIS-based method. Yet, CALIOP-based global daytime ACA frequencies exhibit a near-zero interannual variability. Further analysis suggests
Global optimization and sensitivity analysis
Cacuci, D.G.
1990-01-01
A new direction for the analysis of nonlinear models of nuclear systems is suggested to overcome fundamental limitations of sensitivity analysis and optimization methods currently prevalent in nuclear engineering usage. This direction is toward a global analysis of the behavior of the respective system as its design parameters are allowed to vary over their respective design ranges. Presented is a methodology for global analysis that unifies and extends the current scopes of sensitivity analysis and optimization by identifying all the critical points (maxima, minima) and solution bifurcation points together with corresponding sensitivities at any design point of interest. The potential applicability of this methodology is illustrated with test problems involving multiple critical points and bifurcations and comprising both equality and inequality constraints
Gonalez, Jorge E.; Comarazamy, Daniel E.; Luvall, Jeffrey C.; Rickman, Douglas L.; Smith, T.
2010-01-01
The overachieving goal of this project is to gain a better understanding of the climate impacts caused by the combined effects of land cover and land use (LCLU) changes and increasing global concentrations of green house gases (GHG) in tropical coastal areas, regions where global, regional and local climate phenomena converge, taking as the test case the densely populated northeast region of the Caribbean island of Puerto Rico. The research uses an integrated approach of high-resolution remote sensing information linked to a high resolution Regional Atmospheric Modeling System (RAMS), which was employed to perform ensembles of climate simulations (combining 2-LCLU and 2-GHG concentration scenarios). Reconstructed agricultural maps are used to define past LCLU, and combined with reconstructed sea surface temperatures (SST) for the same period form the PAST climate scenario (1951-1956); while the PRESENT scenario (2000-2004) was additionally supported by high resolution remote sensing data (10-m-res). The climate reconstruction approach is validated with available observed climate data from surface weather stations for both periods of time simulated. The selection of the past and present climate scenarios considers large-scale biases (i.e. ENSO/NAO) as reflected in the region of interest. Direct and cross comparison of the results is allowing quantifying single, combined, and competitive effects. Results indicate that global GHG have dominant effects on minimum temperatures (following regional tendencies), while urban sprawl dominates maximum temperatures. To further investigate impacts of land use the Bowen Ratio and the thermal response number (TRN) are analyzed. The Bowen ratio indicates that forestation of past agricultural high areas have an overwhelmingly mitigation effect on increasing temperatures observed in different LCLU scenarios, but when abandoned agricultural lands are located in plains, the resulting shrub/grass lands produce higher surface
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.
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.
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.
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.
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.
Stability and Hopf bifurcation for a business cycle model with expectation and delay
Liu, Xiangdong; Cai, Wenli; Lu, Jiajun; Wang, Yangyang
2015-08-01
According to rational expectation hypothesis, the government will take into account the future capital stock in the process of investment decision. By introducing anticipated capital stock into an economic model with investment delay, we construct a mixed functional differential system including delay and advanced variables. The system is converted to the one containing only delay by variable substitution. The equilibrium point of the system is obtained and its dynamical characteristics such as stability, Hopf bifurcation and its stability and direction are investigated by using the related theories of nonlinear dynamics. We carry out some numerical simulations to confirm these theoretical conclusions. The results indicate that both capital stock's anticipation and investment lag are the certain factors leading to the occurrence of cyclical fluctuations in the macroeconomic system. Moreover, the level of economic fluctuation can be dampened to some extent if investment decisions are made by the reasonable short-term forecast on capital stock.
Chatthong, B.; Onjun, T.; Imbeaux, F.; Sarazin, Y.; Strugarek, A.; Picha, R.; Poolyarat, N.
2011-06-01
Full text: Formation of transport barrier in fusion plasma is studied using a simple one-field bistable S-curve bifurcation model. This model is characterized by an S-line with two stable branches corresponding to the low (L) and high (H) confinement modes, connected by an unstable branch. Assumptions used in this model are such that the reduction in anomalous transport is caused by v E velocity shear effect and also this velocity shear is proportional to pressure gradient. In this study, analytical and numerical approaches are used to obtain necessary conditions for transport barrier formation, i.e. the ratio of anomalous over neoclassical coefficients and heat flux thresholds which must be exceeded. Several profiles of heat sources are considered in this work including constant, Gaussian, and hyperbolic tangent forms. Moreover, the effect of perturbation in heat flux is investigated with respect to transport barrier formation
Locality effects on bifurcation paradigm of L-H transition in tokamak plasmas
Boonyarit Chatthong
2015-12-01
Full Text Available The locality effects on bifurcation paradigm of L-H transition phenomenon in magnetic confinement plasmas are investigated. One dimensional thermal transport equation with both neoclassical and anomalous transports effects included is considered, where a flow shear due to pressure gradient component is included as a transport suppression mechanism. Three different locally driven models for anomalous transport are considered, including a constant transport model, pressure gradient driven transport model, and critical pressure gradient threshold transport model. Local stability analysis shows that the transition occurs at a threshold flux with hysteresis nature only if ratio of anomalous strength over neoclassical transport exceeds a critical value. The depth of the hysteresis loop depends on both neoclassical and anomalous transports, as well as the suppression strength. The reduction of the heat flux required to maintain H-mode can be as low as a factor of two, which is similar to experimental evidence.
Bifurcation behaviors of synchronized regions in logistic map networks with coupling delay
Tang, Longkun; Wu, Xiaoqun; Lu, Jun-an; Lü, Jinhu
2015-01-01
Network synchronized regions play an extremely important role in network synchronization according to the master stability function framework. This paper focuses on network synchronous state stability via studying the effects of nodal dynamics, coupling delay, and coupling way on synchronized regions in Logistic map networks. Theoretical and numerical investigations show that (1) network synchronization is closely associated with its nodal dynamics. Particularly, the synchronized region bifurcation points through which the synchronized region switches from one type to another are in good agreement with those of the uncoupled node system, and chaotic nodal dynamics can greatly impede network synchronization. (2) The coupling delay generally impairs the synchronizability of Logistic map networks, which is also dominated by the parity of delay for some nodal parameters. (3) A simple nonlinear coupling facilitates network synchronization more than the linear one does. The results found in this paper will help to intensify our understanding for the synchronous state stability in discrete-time networks with coupling delay
The integrable case of Adler-van Moerbeke. Discriminant set and bifurcation diagram
Ryabov, Pavel E.; Oshemkov, Andrej A.; Sokolov, Sergei V.
2016-09-01
The Adler-van Moerbeke integrable case of the Euler equations on the Lie algebra so(4) is investigated. For the L- A pair found by Reyman and Semenov-Tian-Shansky for this system, we explicitly present a spectral curve and construct the corresponding discriminant set. The singularities of the Adler-van Moerbeke integrable case and its bifurcation diagram are discussed. We explicitly describe singular points of rank 0, determine their types, and show that the momentum mapping takes them to self-intersection points of the real part of the discriminant set. In particular, the described structure of singularities of the Adler-van Moerbeke integrable case shows that it is topologically different from the other known integrable cases on so(4).
Ravelet, F
2005-09-15
We report experimental studies of the turbulent von Karman flow, inertially stirred between counter-rotating impellers. We first study the flow and its transition from laminar to turbulent regime. We highlight the role of slowly varying large scales, due to the presence of an azimuthal mixing layer. The large scales of this flow can be unstable in turbulent regime. We study the statistics of the transitions between the different mean states. The second part is dedicated to an experiment in liquid sodium, called VKS2. We optimize the time-averaged flow in order to allow kinematic dynamo action. We report the very first results of the experiment, and discuss the role of the large scales temporal non-stationariness. (author)
Dynamics of motion of a clot through an arterial bifurcation: a finite element analysis
Abolfazli, Ehsan; Fatouraee, Nasser [Faculty of Biomedical Engineering, Amirkabir University of Technology, Tehran (Iran, Islamic Republic of); Vahidi, Bahman, E-mail: e.abolfazli@aut.ac.ir, E-mail: nasser@aut.ac.ir, E-mail: bahman_vahidi@ut.ac.ir [Department of Life Science Engineering, Faculty of New Sciences and Technologies, University of Tehran (Iran, Islamic Republic of)
2014-10-01
Although arterial embolism is important as a major cause of brain infarction, little information is available about the hemodynamic factors which govern the path emboli tend to follow. A method which predicts the trajectory of emboli in carotid arteries would be of a great value in understanding ischemic attack mechanisms and eventually devising hemodynamically optimal techniques for prevention of strokes. In this paper, computational models are presented to investigate the motion of a blood clot in a human carotid artery bifurcation. The governing equations for blood flow are the Navier–Stokes formulations. To achieve large structural movements, the arbitrary Lagrangian–Eulerian formulation (ALE) with an adaptive mesh method was employed for the fluid domain. The problem was solved by simultaneous solution of the fluid and the structure equations. In this paper, the phenomenon was simulated under laminar and Newtonian flow conditions. The measured stress–strain curve obtained from ultrasound elasticity imaging of the thrombus was set to a Sussman–Bathe material model representing embolus material properties. Shear stress magnitudes in the inner wall of the internal carotid artery (ICA) were measured. High magnitudes of wall shear stress (WSS) occurred in the areas in which the embolus and arterial are in contact with each other. Stress distribution in the embolus was also calculated and areas prone to rapture were identified. Effects of embolus size and embolus density on its motion velocity were investigated and it was observed that an increase in either embolus size or density led to a reduction in movement velocity of the embolus. Embolus trajectory and shear stress from a simulation of embolus movement in a three-dimensional model with patient-specific carotid artery bifurcation geometry are also presented.