Energy Technology Data Exchange (ETDEWEB)
Peters, John W.; Miller, Anne-Frances; Jones, Anne K.; King, Paul W.; Adams, Michael W. W.
2016-04-01
Electron bifurcation is the recently recognized third mechanism of biological energy conservation. It simultaneously couples exergonic and endergonic oxidation-reduction reactions to circumvent thermodynamic barriers and minimize free energy loss. Little is known about the details of how electron bifurcating enzymes function, but specifics are beginning to emerge for several bifurcating enzymes. To date, those characterized contain a collection of redox cofactors including flavins and iron-sulfur clusters. Here we discuss the current understanding of bifurcating enzymes and the mechanistic features required to reversibly partition multiple electrons from a single redox site into exergonic and endergonic electron transfer paths.
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...
Sprinkler Bifurcations and Stability
Sorensen, Jody; Rykken, Elyn
2010-01-01
After discussing common bifurcations of a one-parameter family of single variable functions, we introduce sprinkler bifurcations, in which any number of new fixed points emanate from a single point. Based on observations of these and other bifurcations, we then prove a number of general results about the stabilities of fixed points near a…
About Bifurcational Parametric Simplification
Gol'dshtein, V; Yablonsky, G
2015-01-01
A concept of "critical" simplification was proposed by Yablonsky and Lazman in 1996 for the oxidation of carbon monoxide over a platinum catalyst using a Langmuir-Hinshelwood mechanism. The main observation was a simplification of the mechanism at ignition and extinction points. The critical simplification is an example of a much more general phenomenon that we call \\emph{a bifurcational parametric simplification}. Ignition and extinction points are points of equilibrium multiplicity bifurcations, i.e., they are points of a corresponding bifurcation set for parameters. Any bifurcation produces a dependence between system parameters. This is a mathematical explanation and/or justification of the "parametric simplification". It leads us to a conjecture that "maximal bifurcational parametric simplification" corresponds to the "maximal bifurcation complexity." This conjecture can have practical applications for experimental study, because at points of "maximal bifurcation complexity" the number of independent sys...
Torus Bifurcation Under Discretization
Institute of Scientific and Technical Information of China (English)
邹永魁; 黄明游
2002-01-01
Parameterized dynamical systems with a simple zero eigenvalue and a couple of purely imaginary eigenvalues are considered. It is proved that this type of eigen-structure leads to torns bifurcation under certain nondegenerate conditions. We show that the discrete systems, obtained by discretizing the ODEs using symmetric, eigen-structure preserving schemes, inherit the similar torus bifurcation properties. Fredholm theory in Banach spaces is applied to obtain the global torns bifurcation. Our results complement those on the study of discretization effects of global bifurcation.
Unfolding the Riddling Bifurcation
DEFF Research Database (Denmark)
Maistrenko, Yu.; Popovych, O.; Mosekilde, Erik
1999-01-01
We present analytical conditions for the riddling bifurcation in a system of two symmetrically coupled, identical, smooth one-dimensional maps to be soft or hard and describe a generic scenario for the transformations of the basin of attraction following a soft riddling bifurcation....
Relative Lyapunov Center Bifurcations
DEFF Research Database (Denmark)
Wulff, Claudia; Schilder, Frank
2014-01-01
Relative equilibria (REs) and relative periodic orbits (RPOs) are ubiquitous in symmetric Hamiltonian systems and occur, for example, in celestial mechanics, molecular dynamics, and rigid body motion. REs are equilibria, and RPOs are periodic orbits of the symmetry reduced system. Relative Lyapunov...... center bifurcations are bifurcations of RPOs from REs corresponding to Lyapunov center bifurcations of the symmetry reduced dynamics. In this paper we first prove a relative Lyapunov center theorem by combining recent results on the persistence of RPOs in Hamiltonian systems with a symmetric Lyapunov...... center theorem of Montaldi, Roberts, and Stewart. We then develop numerical methods for the detection of relative Lyapunov center bifurcations along branches of RPOs and for their computation. We apply our methods to Lagrangian REs of the N-body problem....
Bifurcation of hyperbolic planforms
Chossat, Pascal; Faugeras, Olivier
2010-01-01
Motivated by a model for the perception of textures by the visual cortex in primates, we analyse the bifurcation of periodic patterns for nonlinear equations describing the state of a system defined on the space of structure tensors, when these equations are further invariant with respect to the isometries of this space. We show that the problem reduces to a bifurcation problem in the hyperbolic plane D (Poincar\\'e disc). We make use of the concept of periodic lattice in D to further reduce the problem to one on a compact Riemann surface D/T, where T is a cocompact, torsion-free Fuchsian group. The knowledge of the symmetry group of this surface allows to carry out the machinery of equivariant bifurcation theory. Solutions which generically bifurcate are called "H-planforms", by analogy with the "planforms" introduced for pattern formation in Euclidean space. This concept is applied to the case of an octagonal periodic pattern, where we are able to classify all possible H-planforms satisfying the hypotheses o...
Minton, Roland; Pennings, Timothy J.
2007-01-01
When a dog (in this case, Tim Pennings' dog Elvis) is in the water and a ball is thrown downshore, it must choose to swim directly to the ball or first swim to shore. The mathematical analysis of this problem leads to the computation of bifurcation points at which the optimal strategy changes.
Global Bifurcations With Symmetry
Porter, J B
2001-01-01
Symmetry is a ubiquitous feature of physical systems with profound implications for their dynamics. This thesis investigates the role of symmetry in global bifurcations. In particular, the structure imposed by symmetry can encourage the formation of complex solutions such as heteroclinic cycles and chaotic invariant sets. The first study focuses on the dynamics of 1:n steady-state mode interactions in the presence of O(2) symmetry. The normal form equations considered are relevant to a variety of physical problems including Rayleigh-Bénard convection with periodic boundary conditions. In open regions of parameter space these equations contain structurally stable heteroclinic cycles composed of connections between standing wave, pure mode, and trivial solutions. These structurally stable cycles exist between two global bifurcations, the second of which involves an additional mixed mode state and creates as many as four distinct kinds of structurally unstable heteroclinic cycles. The various cycles c...
Noise induced Hopf bifurcation
Shuda, I. A.; Borysov, S S; A.I. Olemskoi
2008-01-01
We consider effect of stochastic sources upon self-organization process being initiated with creation of the limit cycle induced by the Hopf bifurcation. General relations obtained are applied to the stochastic Lorenz system to show that departure from equilibrium steady state can destroy the limit cycle in dependence of relation between characteristic scales of temporal variation of principle variables. Noise induced resonance related to the limit cycle is found to appear if the fastest vari...
Neural Excitability and Singular Bifurcations.
De Maesschalck, Peter; Wechselberger, Martin
2015-12-01
We discuss the notion of excitability in 2D slow/fast neural models from a geometric singular perturbation theory point of view. We focus on the inherent singular nature of slow/fast neural models and define excitability via singular bifurcations. In particular, we show that type I excitability is associated with a novel singular Bogdanov-Takens/SNIC bifurcation while type II excitability is associated with a singular Andronov-Hopf bifurcation. In both cases, canards play an important role in the understanding of the unfolding of these singular bifurcation structures. We also explain the transition between the two excitability types and highlight all bifurcations involved, thus providing a complete analysis of excitability based on geometric singular perturbation theory.
Introduction to bifurcation theory
International Nuclear Information System (INIS)
Bifurcation theory is a subject with classical mathematical origins. The modern development of the subject starts with Poincare and the qualitative theory of differential equations. In recent years, the theory has undergone a tremendous development with the infusion of new ideas and methods from dynamical systems theory, singularity theory, group theory, and computer-assisted studies of dynamics. As a result, it is difficult to draw the boundaries of the theory with any confidence. In this review, the objects in question will be parameterized families of dynamical systems (vector fields or maps). In the sciences these families commonly arise when one formulates equations of motion to model a physical system. We specifically analyze how the time evolution near an equilibrium can change as parameters are varied; for simplicity we consider the case of a single parameter only
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...
DYNAMIC BIFURCATION OF NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
MA TIAN; WANG SHOUHONG
2005-01-01
The authors introduce a notion of dynamic bifurcation for nonlinear evolution equations, which can be called attractor bifurcation. It is proved that as the control parameter crosses certain critical value, the system bifurcates from a trivial steady state solution to an attractor with dimension between m and m + 1, where m + 1 is the number of eigenvalues crossing the imaginary axis. The attractor bifurcation theory presented in this article generalizes the existing steady state bifurcations and the Hopf bifurcations. It provides a unified point of view on dynamic bifurcation and can be applied to many problems in physics and mechanics.
Bifurcation Adds Flavor to Basketball
Min, Byeong June
2016-01-01
We report an emergence of bifurcation in basketball, a single-particle system governed by Newtonian mechanics. When shooting the basketball, the obvious control parameters are the launch speed and the launch angle. We propose to use the three-dimensional velocity phase-space volume associated with the given launch parameters to quantify the difficulty of the shooting. The optimal launch angle that maximizes the associated phase-space volume undergoes a bifurcation as the launch speed is increased, if the shooter is farther than a critical distance away from the hoop. Thus, the bifurcation makes it very important to control the launch speed accurately. If the air resistance is removed, the bifurcation disappears and the phase-space volume distribution becomes dispersionless and shrinks in magnitude.
Bifurcations, instabilities, degradation in geomechanics
Exadaktylos, George
2007-01-01
Leading international researchers and practitioners of bifurcations and instabilities in geomechanics debate the developments and applications which have occurred over the last few decades. The topics covered include modeling of bifurcation, structural failure of geomaterials and geostructures, advanced analytical, numerical and experimental techniques, and application and development of generalised continuum models etc. In addition analytical solutions, numerical methods, experimental techniques, and case histories are presented. Beside fundamental research findings, applications in geotechni
Invariant manifolds and global bifurcations.
Guckenheimer, John; Krauskopf, Bernd; Osinga, Hinke M; Sandstede, Björn
2015-09-01
Invariant manifolds are key objects in describing how trajectories partition the phase spaces of a dynamical system. Examples include stable, unstable, and center manifolds of equilibria and periodic orbits, quasiperiodic invariant tori, and slow manifolds of systems with multiple timescales. Changes in these objects and their intersections with variation of system parameters give rise to global bifurcations. Bifurcation manifolds in the parameter spaces of multi-parameter families of dynamical systems also play a prominent role in dynamical systems theory. Much progress has been made in developing theory and computational methods for invariant manifolds during the past 25 years. This article highlights some of these achievements and remaining open problems.
Controlling hopf bifurcations: Discrete-time systems
Directory of Open Access Journals (Sweden)
Guanrong Chen
2000-01-01
Full Text Available Bifurcation control has attracted increasing attention in recent years. A simple and unified state-feedback methodology is developed in this paper for Hopf bifurcation control for discrete-time systems. The control task can be either shifting an existing Hopf bifurcation or creating a new Hopf bifurcation. Some computer simulations are included to illustrate the methodology and to verify the theoretical results.
Multiple Bifurcations of a Cylindrical Dynamical System
Han Ning; Cao Qingjie
2016-01-01
This paper focuses on multiple bifurcations of a cylindrical dynamical system, which is evolved from a rotating pendulum with SD oscillator. The rotating pendulum system exhibits the coupling dynamics property of the bistable state and conventional pendulum with the ho- moclinic orbits of the first and second type. A double Andronov-Hopf bifurcation, two saddle-node bifurcations of periodic orbits and a pair of homoclinic bifurcations are detected by using analytical analysis and nu- merical ...
Bifurcations associated with sub-synchronous resonance
Mitani, Yasunori; K. Tsuji; M.Varghese; Wu, F. F.; VARAIYA, P
1998-01-01
This paper describes a set of results of detecting nonlinear phenomena appearing in a turbine generator power system with series-capacitor compensation. The analysis was based on the Floquet theory as well as the Hopf bifurcation theorem. After the first Hopf bifurcation, the stable limit cycle bifurcates to a stable torus and an unstable limit cycle which connects to a stable limit cycle by a supercritical torus bifurcation. The stable limit cycle joins with an unstable limit cycle at a cycl...
Thermodynamic geometry and critical aspects of bifurcations.
Mihara, A
2016-07-01
This work presents an exploratory study of the critical aspects of some well-known bifurcations in the context of thermodynamic geometry. For each bifurcation its normal form is regarded as a geodesic equation of some model analogous to a thermodynamic system. From this hypothesis it is possible to calculate the corresponding metric and curvature and analyze the critical behavior of the bifurcation.
Solution and transcritical bifurcation of Burgers equation
Institute of Scientific and Technical Information of China (English)
Tang Jia-Shi; Zhao Ming-Hua; Han Feng; Zhang Liang
2011-01-01
Burgers equation is reduced into a first-order ordinary differential equation by using travelling wave transformation and it has typical bifurcation characteristics. We can obtain many exact solutions of the Burgers equation, discuss its transcritical bifurcation and control dynamical behaviours by extending the stable region. The transcritical bifurcation exists in the (2 + 1)-dimensional Burgers equation.
NEW BIFURCATION PATTERNS IN ELEMENTARY BIFURCATION PROBLEMS WITH SINGLE-SIDE CONSTRAINT
Institute of Scientific and Technical Information of China (English)
吴志强; 陈予恕
2001-01-01
Bifurcations with constraints are open problems appeared in research on periodic bifurcations of nonlinear dynamical systems, but the present singularity theory doesn't contain any analytical methods and results about it. As the complement to singularity theory and the first step to study on constrained bifurcations, here are given the transition sets and persistent perturbed bifurcation diagrams of 10 elementary bifurcation of codimension no more than three.
ROBUST CONTROL OF PERIODIC BIFURCATION SOLUTIONS
Institute of Scientific and Technical Information of China (English)
梁建术; 陈予恕; 梁以德
2004-01-01
The topological bifurcation diagrams and the coefficients of bifurcation equation were obtained by C-L method.According to obtained bifurcation diagrams and combining control theory,the method of robust control of periodic bifurcation was presented,which differs from generic methods of bifurcation control.It can make the existing motion pattern into the goal motion pattern.Because the method does not make strict requirement about parametric values of the controller,it is convenient to design and make it.Numerical simulations verify validity of the method.
Insight into Phenomena of Symmetry Breaking Bifurcation
Institute of Scientific and Technical Information of China (English)
FANG Tong; ZHANG Ying
2008-01-01
@@ We show that symmetry-breaking (SB) bifurcation is just a transition of different forms of symmetry, while still preserving system's symmetry. SB bifurcation always associates with a periodic saddle-node bifurcation, identifiable by a zero maximum of the top Lyapunov exponent of the system. In addition, we show a significant phase portrait of a newly born periodic saddle and its stable and unstable invariant manifolds, together with their neighbouring flow pattern of Poincaré mapping points just after the periodic saddle-node bifurcation, thus gaining an insight into the mechanism of SB bifurcation.
Bifurcations analysis of turbulent energy cascade
Energy Technology Data Exchange (ETDEWEB)
Divitiis, Nicola de, E-mail: n.dedivitiis@gmail.com
2015-03-15
This note studies the mechanism of turbulent energy cascade through an opportune bifurcations analysis of the Navier–Stokes equations, and furnishes explanations on the more significant characteristics of the turbulence. A statistical bifurcations property of the Navier–Stokes equations in fully developed turbulence is proposed, and a spatial representation of the bifurcations is presented, which is based on a proper definition of the fixed points of the velocity field. The analysis first shows that the local deformation can be much more rapid than the fluid state variables, then explains the mechanism of energy cascade through the aforementioned property of the bifurcations, and gives reasonable argumentation of the fact that the bifurcations cascade can be expressed in terms of length scales. Furthermore, the study analyzes the characteristic length scales at the transition through global properties of the bifurcations, and estimates the order of magnitude of the critical Taylor-scale Reynolds number and the number of bifurcations at the onset of turbulence.
Numerical bifurcation of Hamiltonian relative periodic orbits
DEFF Research Database (Denmark)
Wulff, Claudia; Schilder, Frank
2009-01-01
-breaking bifurcations of RPOs in Hamiltonian systems with compact symmetry group and show how they can be detected and computed numerically. These are turning points of RPOs and relative period-doubling and relative period-halving bifurcations along branches of RPOs. In a comoving frame the latter correspond...... to symmetry-breaking/symmetry-increasing pitchfork bifurcations or to period-doubling/period-halving bifurcations. We apply our methods to the family of rotating choreographies which bifurcate from the famous figure eight solution of the three-body problem as angular momentum is varied. We find...... that the family of choreographies rotating around the $e^2$-axis bifurcates to the family of rotating choreographies that connects to the Lagrange relative equilibrium. Moreover, we compute several relative period-doubling bifurcations and a turning point of the family of planar rotating choreographies, which...
Escape statistics for parameter sweeps through bifurcations.
Miller, Nicholas J; Shaw, Steven W
2012-04-01
We consider the dynamics of systems undergoing parameter sweeps through bifurcation points in the presence of noise. Of interest here are local codimension-one bifurcations that result in large excursions away from an operating point that is transitioning from stable to unstable during the sweep, since information about these "escape events" can be used for system identification, sensing, and other applications. The analysis is based on stochastic normal forms for the dynamic saddle-node and subcritical pitchfork bifurcations with a time-varying bifurcation parameter and additive noise. The results include formulation and numerical solution for the distribution of escape events in the general case and analytical approximations for delayed bifurcations for which escape occurs well beyond the corresponding quasistatic bifurcation points. These bifurcations result in amplitude jumps encountered during parameter sweeps and are particularly relevant to nano- and microelectromechanical systems, for which noise can play a significant role.
Evolution and stability of tidal river bifurcations
Kleinhans, M. G.
2011-12-01
At bifurcations, water and sediment are partitioned, so that long-term evolution of fluvial and deltaic channels is determined by the bifurcation stability. Recent work in fluvial environments showed that bifurcations are commonly unstable so that avulsion results. For tidal rivers it could be argued that the discharge fluctuation enhances transport so that it simply closes of faster than in steady flow, but it could also be argued that tidal phase differences between the bifurcates cause a residual flow that counteracts the closing trend and keeps both bifurcates open. A physics-based numerical model (Delft3D) was used to model fixed-bank fork-shaped bifurcations with and without tides, and with short and long length relative to tidal wavelength. In all cases the bifurcations remained as unstable as without tides and ended invariably in avulsion. Tidal bifurcations unbalanced more rapidly than fluvial bifurcations, because of the increased ebb current and nonlinearity of sediment transport. On the other hand, discharge partitioning at the final bifurcation was much less asymmetrical with tides than without. Tidal wave deformation and production of higher harmonics in the longer channels affected sediment partitioning in the unstable phase but seems to have no effect on equilibrium morphology. Significant phase differences between the bifurcates caused a tidal floss effect, which scoured the bifurcation. In conclusion, symmetrical bifurcations affected by tides are unstable, but their final equilibrium is more symmetrical than without tides unless bifurcates have significant tidal phase differences. Furthermore I modelled growing deltas with self-formed distributary channels with and without cohesive sediment and with and without tides. Here, tides cause the flow to be more focussed in fewer and larger channels, whilst the few bifurcations are relatively stable. Combined fluvial discharge and tidal ebb flow in the channels transports more sediment than in fluvial
Bifurcations analysis of oscillating hypercycles.
Guillamon, Antoni; Fontich, Ernest; Sardanyés, Josep
2015-12-21
We investigate the dynamics and transitions to extinction of hypercycles governed by periodic orbits. For a large enough number of hypercycle species (n>4) the existence of a stable periodic orbit has been previously described, showing an apparent coincidence of the vanishing of the periodic orbit with the value of the replication quality factor Q where two unstable (non-zero) equilibrium points collide (named QSS). It has also been reported that, for values below QSS, the system goes to extinction. In this paper, we use a suitable Poincaré map associated to the hypercycle system to analyze the dynamics in the bistability regime, where both oscillatory dynamics and extinction are possible. The stable periodic orbit is identified, together with an unstable periodic orbit. In particular, we are able to unveil the vanishing mechanism of the oscillatory dynamics: a saddle-node bifurcation of periodic orbits as the replication quality factor, Q, undergoes a critical fidelity threshold, QPO. The identified bifurcation involves the asymptotic extinction of all hypercycle members, since the attractor placed at the origin becomes globally stable for values Qbifurcation, these extinction dynamics display a periodic remnant that provides the system with an oscillating delayed transition. Surprisingly, we found that the value of QPO is slightly higher than QSS, thus identifying a gap in the parameter space where the oscillatory dynamics has vanished while the unstable equilibrium points are still present. We also identified a degenerate bifurcation of the unstable periodic orbits for Q=1.
Oscillatory flow in bifurcating tubes
International Nuclear Information System (INIS)
Respiratory fluid mechanics is characterized by flow through bifurcating, Y-shaped, tubes. Steady flow through such geometries has been studied in detail by several authors. However, the recent widespread use of high frequency mechanical assistance of ventilation has generated interest in unsteady flows. A symmetric, singly branching pipe has been constructed, with its bifurcation shaped to model pulmonary conditions. The form of the bifurcation is based on CAT scans of human tracheal carinas. Its features include an area change of the parent tube from circular to roughly elliptical near the junction, a pinch-off effect on the parent tube, smoothly curved outer walls at the junction, and a sharp flow divider. Parent and daughter tubes have an l/d ratio of > 50, so that entrance effects are avoided. In order to better understand the effects of unsteadiness, piston driven, laminar, purely oscillatory flow has been established in the pipe for a variety of Womersley numbers. By appropriate choices of flow frequency and amplitude, fluid viscosity, and pipe diameter, tracheal Reynolds and Womersley numbers have been matched for resting breathing (tidal volume of 600 ml to 0.25 Hz), high frequency breathing (50 ml at 5 Hz), and intermediate breathing levels
BIFURCATIONS OF AIRFOIL IN INCOMPRESSIBLE FLOW
Institute of Scientific and Technical Information of China (English)
LiuFei; YangYiren
2005-01-01
Bifurcations of an airfoil with nonlinear pitching stiffness in incompressible flow are investigated. The pitching spring is regarded as a spring with cubic stiffness. The motion equations of the airfoil are written as the four dimensional one order differential equations. Taking air speed and the linear part of pitching stiffness as the parameters, the analytic solutions of the critical boundaries of pitchfork bifurcations and Hopf bifurcations are obtained in 2 dimensional parameter plane. The stabilities of the equilibrium points and the limit cycles in different regions of 2 dimensional parameter plane are analyzed. By means of harmonic balance method, the approximate critical boundaries of 2-multiple semi-stable limit cycle bifurcations are obtained, and the bifurcation points of supercritical or subcritical Hopf bifurcation are found. Some numerical simulation results are given.
Einstein's Field Equations as a Fold Bifurcation
Kohli, Ikjyot Singh
2016-01-01
It is shown that Einstein's field equations for \\emph{all} perfect-fluid $k=0$ FLRW cosmologies have the same form as the topological normal form of a fold bifurcation. In particular, we assume that the cosmological constant is a bifurcation parameter, and as such, fold bifurcation behaviour is shown to occur in a neighbourhood of Minkowski spacetime in the phase space. We show that as this cosmological constant parameter is varied, an expanding and contracting de Sitter universe \\emph{emerge} via this bifurcation.
Bifurcation and instability problems in vortex wakes
DEFF Research Database (Denmark)
Aref, Hassan; Brøns, Morten; Stremler, Mark A.
2007-01-01
A number of instability and bifurcation problems related to the dynamics of vortex wake flows are addressed using various analytical tools and approaches. We discuss the bifurcations of the streamline pattern behind a bluff body as a vortex wake is produced, a theory of the universal Strouhal......-Reynolds number relation for vortex wakes, the bifurcation diagram for "exotic" wake patterns behind an oscillating cylinder first determined experimentally by Williamson & Roshko, and the bifurcations in topology of the streamlines pattern in point vortex streets. The Hamiltonian dynamics of point vortices...
Perturbed bifurcations in the BCS gap equation
DEFF Research Database (Denmark)
Spathis, P. N.; Sørensen, Mads Peter; Lazarides, Nickos
1992-01-01
. The transitions from d- or s- to mixed s- and d-wave solutions result from pitchfork bifurcations. In the case of slightly different pairing strength in the x and y directions, perturbed pitchfork bifurcations emerge, leading to a dramatic change in the physical properties of the superconducting state....
BIFURCATION IN PRESCRIBED MEAN CURVATURE PROBLEM
Institute of Scientific and Technical Information of China (English)
马力
2002-01-01
This paper discusses the existence problem in the study of some partial differential equations. The author gets some bifurcation on the prescribed mean curvature problem on the unit ball, the scalar curvature problem on the n-sphere, and some field equations. The author gives some natural conditions such that the standard bifurcation or Thom-Mather theory can be used.
Crisis bifurcations in plane Poiseuille flow.
Zammert, Stefan; Eckhardt, Bruno
2015-04-01
Many shear flows follow a route to turbulence that has striking similarities to bifurcation scenarios in low-dimensional dynamical systems. Among the bifurcations that appear, crisis bifurcations are important because they cause global transitions between open and closed attractors, or indicate drastic increases in the range of the state space that is covered by the dynamics. We here study exterior and interior crisis bifurcations in direct numerical simulations of transitional plane Poiseuille flow in a mirror-symmetric subspace. We trace the state space dynamics from the appearance of the first three-dimensional exact coherent structures to the transition from an attractor to a chaotic saddle in an exterior crisis. For intermediate Reynolds numbers, the attractor undergoes several interior crises, in which new states appear and intermittent behavior can be observed. The bifurcations contribute to increasing the complexity of the dynamics and to a more dense coverage of state space.
Voltage stability, bifurcation parameters and continuation methods
Energy Technology Data Exchange (ETDEWEB)
Alvarado, F.L. [Wisconsin Univ., Madison, WI (United States)
1994-12-31
This paper considers the importance of the choice of bifurcation parameter in the determination of the voltage stability limit and the maximum power load ability of a system. When the bifurcation parameter is power demand, the two limits are equivalent. However, when other types of load models and bifurcation parameters are considered, the two concepts differ. The continuation method is considered as a method for determination of voltage stability margins. Three variants of the continuation method are described: the continuation parameter is the bifurcation parameter the continuation parameter is initially the bifurcation parameter, but is free to change, and the continuation parameter is a new `arc length` parameter. Implementations of voltage stability software using continuation methods are described. (author) 23 refs., 9 figs.
Multiple Bifurcations in the Periodic Orbit around Eros
Ni, Yanshuo; Baoyin, Hexi
2016-01-01
We investigate the multiple bifurcations in periodic orbit families in the potential field of a highly irregular-shaped celestial body. Topological cases of periodic orbits and four kinds of basic bifurcations in periodic orbit families are studied. Multiple bifurcations in periodic orbit families consist of four kinds of basic bifurcations. We found both binary period-doubling bifurcations and binary tangent bifurcations in periodic orbit families around asteroid 433 Eros. The periodic orbit family with binary period-doubling bifurcations is nearly circular, with almost zero inclination, and is reversed relative to the body of the asteroid 433 Eros. This implies that there are two stable regions separated by one unstable region for the motion around this asteroid. In addition, we found triple bifurcations which consist of two real saddle bifurcations and one period-doubling bifurcation. A periodic orbit family generated from an equilibrium point of asteroid 433 Eros has five bifurcations, which are one real ...
Hero's journey in bifurcation diagram
Monteiro, L. H. A.; Mustaro, P. N.
2012-06-01
The hero's journey is a narrative structure identified by several authors in comparative studies on folklore and mythology. This storytelling template presents the stages of inner metamorphosis undergone by the protagonist after being called to an adventure. In a simplified version, this journey is divided into three acts separated by two crucial moments. Here we propose a discrete-time dynamical system for representing the protagonist's evolution. The suffering along the journey is taken as the control parameter of this system. The bifurcation diagram exhibits stationary, periodic and chaotic behaviors. In this diagram, there are transition from fixed point to chaos and transition from limit cycle to fixed point. We found that the values of the control parameter corresponding to these two transitions are in quantitative agreement with the two critical moments of the three-act hero's journey identified in 10 movies appearing in the list of the 200 worldwide highest-grossing films.
Equilibrium-torus bifurcation in nonsmooth systems
DEFF Research Database (Denmark)
Zhusubahyev, Z.T.; Mosekilde, Erik
2008-01-01
Considering a set of two coupled nonautonomous differential equations with discontinuous right-hand sides describing the behavior of a DC/DC power converter, we discuss a border-collision bifurcation that can lead to the birth of a two-dimensional invariant torus from a stable node equilibrium...... linear approximation to our system in the neighbourhood of the border. We determine the functional relationships between the parameters of the normal form map and the actual system and illustrate how the normal form theory can predict the bifurcation behaviour along the border-collision equilibrium......-torus bifurcation curve....
EFFECTS OF CONSTANT EXCITATION ON LOCAL BIFURCATION
Institute of Scientific and Technical Information of China (English)
WU Zhi-qiang; CHEN Yu-shu
2006-01-01
The effects of the constant excitation on the local bifurcation of the periodic solutions in the 1:2 internal resonant systems were analyzed based on the singularity theory. It is shown that the constant excitation make influence only when there exist some nonlinear terms, in the oscillator with lower frequency. Besides acting as main bifurcation parameter, the constant excitation, together with coefficients of some nonlinear terms,may change the values of unfolding parameters and the type of the bifurcation. Under the non-degenerate cases, the effect of the third order terms can be neglected.
Attractivity and bifurcation for nonautonomous dynamical systems
Rasmussen, Martin
2007-01-01
Although, bifurcation theory of equations with autonomous and periodic time dependence is a major object of research in the study of dynamical systems since decades, the notion of a nonautonomous bifurcation is not yet established. In this book, two different approaches are developed which are based on special definitions of local attractivity and repulsivity. It is shown that these notions lead to nonautonomous Morse decompositions, which are useful to describe the global asymptotic behavior of systems on compact phase spaces. Furthermore, methods from the qualitative theory for linear and nonlinear systems are derived, and nonautonomous counterparts of the classical one-dimensional autonomous bifurcation patterns are developed.
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.
Backward Bifurcation in Simple SIS Model
Institute of Scientific and Technical Information of China (English)
Zhan-wei Wang
2009-01-01
We describe and analyze a simple SIS model with treatment.In particular,we give a completely qualitative analysis by means of the theory of asymptotically autonomous system.It is found that a backward bifurcation occurs if the adequate contact rate or the capacity is small.It is also found that there exists bistable endemic equilibria.In the case of disease-induced death,it is shown that the backward bifurcation also occurs.Moreover,there is no limit cycle under some conditions,and the subcritical Hopf bifurcation occurs under another conditions.
Cellular Cell Bifurcation of Cylindrical Detonations
Institute of Scientific and Technical Information of China (English)
HAN Gui-Lai; JIANG Zong-Lin; WANG Chun; ZHANG Fan
2008-01-01
Cellular cell pattern evolution of cylindrically-diverging detonations is numerically simulated successfully by solving two-dimensional Euler equations implemented with an improved two-step chemical kinetic model. From the simulation, three cell bifurcation modes are observed during the evolution and referred to as concave front focusing, kinked and wrinkled wave front instability, and self-merging of cellular cells. Numerical research demonstrates that the wave front expansion resulted from detonation front diverging plays a major role in the cellular cell bifurcation, which can disturb the nonlinearly self-sustained mechanism of detonations and finally lead to cell bifurcations.
BIFURCATION OF PERIODIC ORBITS OF A THREE-DIMENSIONAL SYSTEM
Institute of Scientific and Technical Information of China (English)
LIU XUANLIANG; HAN MAOAN
2005-01-01
Consider a three-dimensional system having an invariant surface. By using bifurcation techniques and analyzing the solutions of bifurcation equations, the authors study the spacial bifurcation phenomena of a k multiple closed orbit in the invariant surface.The sufficient conditions of the existence of many closed orbits bifurcate from the k multiple closed orbit are obtained.
Bifurcation of non-negative solutions for an elliptic system
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
In the paper,we consider a nonlinear elliptic system coming from the predator-prey model with diffusion.Predator growth-rate is treated as bifurcation parameter.The range of parameter is found for which there exists nontrivial solution via the theory of bifurcation from infinity,local bifurcation and global bifurcation.
Singular analysis of two-dimensional bifurcation system
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Bifurcation properties of two-dimensional bifurcation system are studied in this paper.Universal unfolding and transition sets of the bifurcation equations are obtained.The whole parametric plane is divided into several different persistent regions according to the type of motion,and the different qualitative bifurcation diagrams in different persistent regions are given.The bifurcation properties of the two-dimensional bifurcation system are compared with its reduced one-dimensional system.It is found that the system which is reduced to one dimension has lost many bifurcation properties.
The Bifurcation Behavior of CO Coupling Reactor
Institute of Scientific and Technical Information of China (English)
徐艳; 马新宾; 许根慧
2005-01-01
The bifurcation behavior of the CO coupling reactor was examined based on the one-dimensional pseudohomogeneous axial dispersion dynamic model. The method of finite difference was used for solving the boundary value problem; the continuation technique and the direct method were applied to determine the bifurcation diagram.The effects of dimensionless adiabatic temperature rise, Damkoehler number, activation energy, heat transfer coefficient and feed ratio on the bifurcation behavior were investigated. It was shown that there existed static bifurcation and the oscillations did not occur in the reactor. The result also revealed that the reactor exhibited at most 1-3-1 multiplilicity patterns within the range of practical possible parameters and the measures, such as weakening the axial dispersion of reactor, enhancing heat transfer, decreasing the concentration of ethyl nitrite, were efficient for avoiding the possible risk of multiple steady states.
Torus bifurcations in multilevel converter systems
DEFF Research Database (Denmark)
Zhusubaliyev, Zhanybai T.; Mosekilde, Erik; Yanochkina, Olga O.
2011-01-01
This paper considers the processes of torus formation and reconstruction through smooth and nonsmooth bifurcations in a pulse-width modulated DC/DC converter with multilevel control. When operating in a regime of high corrector gain, converters of this type can generate structures of stable tori....... 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....
Cavitated Bifurcation for Incompressible Hyperelastic Material
Institute of Scientific and Technical Information of China (English)
任九生; 程昌钧
2002-01-01
The spherical cavitated bifurcation for a hyperelastic solid sphere made of the incompressible Valanis-Landel material under boundary dead-loading is examined. The analytic solution for the bifurcation problem is obtained. The catastrophe and concentration of stresses are discussed. The stability of solutions is discussed through the energy comparison.And the growth of a pre-existing micro-void is also observed.
Bifurcations and Chaos in Duffing Equation
Institute of Scientific and Technical Information of China (English)
2007-01-01
The Duffing equation with even-odd asymmetrical nonlinear-restoring force and one external forcing is investigated. The conditions of existence of primary resonance, second-order, third-order subharmonics, m-order subharmonics and chaos are given by using the second-averaging method, the Melnikov method and bifurcation theory. Numerical simulations including bifurcation diagram, bifurcation surfaces and phase portraits show the consistence with the theoretical analysis. The numerical results also exhibit new dynamical behaviors including onset of chaos, chaos suddenly disappearing to periodic orbit, cascades of inverse period-doubling bifurcations, period-doubling bifurcation, symmetry period-doubling bifurcations of period-3 orbit, symmetry-breaking of periodic orbits, interleaving occurrence of chaotic behaviors and period-one orbit, a great abundance of periodic windows in transient chaotic regions with interior crises and boundary crisis and varied chaotic attractors. Our results show that many dynamical behaviors are strictly departure from the behaviors of the Duffing equation with odd-nonlinear restoring force.
Multiple bifurcations in the periodic orbit around Eros
Ni, Yanshuo; Jiang, Yu; Baoyin, Hexi
2016-05-01
We investigate the multiple bifurcations in periodic orbit families in the potential field of a highly irregular-shaped celestial body. Topological cases of periodic orbits and four kinds of basic bifurcations in periodic orbit families are studied. Multiple bifurcations in periodic orbit families consist of four kinds of basic bifurcations. We found both binary period-doubling bifurcations and binary tangent bifurcations in periodic orbit families around asteroid 433 Eros. The periodic orbit family with binary period-doubling bifurcations is nearly circular, with almost zero inclination, and is reversed relative to the body of the asteroid 433 Eros. This implies that there are two stable regions separated by one unstable region for the motion around this asteroid. In addition, we found triple bifurcations which consist of two real saddle bifurcations and one period-doubling bifurcation. A periodic orbit family generated from an equilibrium point of asteroid 433 Eros has five bifurcations, which are one real saddle bifurcation, two tangent bifurcations, and two period-doubling bifurcations.
Parameterized center manifold for unfolding bifurcations with an eigenvalue +1 in n-dimensional maps
Wen, Guilin; Yin, Shan; Xu, Huidong; Zhang, Sijin; Lv, Zengyao
2016-10-01
For the fold bifurcation with an eigenvalue +1, there are three types of potential solutions from saddle-node bifurcation, transcritical bifurcation and pitchfork bifurcation. In the existing analysis methods for high maps, there is a problem that for the fold bifurcation, saddle-node bifurcation and transcritical bifurcation cannot be distinguished by the center manifold without bifurcation parameter. In this paper, a parameterized center manifold has been derived to unfold the solutions of the fold bifurcation with an eigenvalue +1, which is used to reduce a general n-dimensional map to one-dimensional map. On the basis of the reduced map, the conditions of the fold bifurcations including saddle-node bifurcation, transcritical bifurcation and pitchfork bifurcation are established for general maps, respectively. We show the applications of the proposed bifurcation conditions by three four-dimensional map examples to distinguish saddle-node bifurcation, transcritical bifurcation and pitchfork bifurcation.
Directory of Open Access Journals (Sweden)
Yan Zhang
2014-01-01
Full Text Available We revisit a homogeneous reaction-diffusion Turing model subject to the Neumann boundary conditions in the one-dimensional spatial domain. With the help of the Hopf bifurcation theory applicable to the reaction-diffusion equations, we are capable of proving the existence of Hopf bifurcations, which suggests the existence of spatially homogeneous and nonhomogeneous periodic solutions of this particular system. In particular, we also prove that the spatial homogeneous periodic solutions bifurcating from the smallest Hopf bifurcation point of the system are always unstable. This together with the instability results of the spatially nonhomogeneous periodic solutions by Yi et al., 2009, indicates that, in this model, all the oscillatory patterns from Hopf bifurcations are unstable.
Local bifurcation analysis of a four-dimensional hyperchaotic system
Institute of Scientific and Technical Information of China (English)
Wu Wen-Juan; Chen Zeng-Qiang; Yuan Zhu-Zhi
2008-01-01
Local bifurcation phenomena in a four-dimensional continuous hyperchaotic system, which has rich and complex dynamical behaviours, are analysed. The local bifurcations of the system are investigated by utilizing the bifurcation theory and the centre manifold theorem, and thus the conditions of the existence of pitchfork bifurcation and Hopf bifurcation are derived in detail. Numerical simulations are presented to verify the theoretical analysis, and they show some interesting dynamics, including stable periodic orbits emerging from the new fixed points generated by pitchfork bifurcation, coexistence of a stable limit cycle and a chaotic attractor, as well as chaos within quite a wide parameter region.
Asymptotic Bifurcation Solutions for Perturbed Kuramoto-Sivashinsky Equation
Institute of Scientific and Technical Information of China (English)
HUANG Qiong-Wei; TANG Jia-Shi
2011-01-01
Stability and dynamic bifurcation in the perturbed Kuramoto-Sivashinsky (KS) equation with Dirichlet boundary condition are investigated by using central manifold reduction procedure.The result shows, as the bifurcation parameter crosses a critical value, the system undergoes a pitchfork bifurcation to produce two asymptotically stable solutions.Furthermore, when the distance from bifurcation is of comparable order ∈2 (｜∈｜ (≤) 1), the first two terms in e-expansions for the new asymptotic bifurcation solutions are derived by multiscale expansion method.Such information is useful to the bifurcation control.
Bifurcations of Tumor-Immune Competition Systems with Delay
Directory of Open Access Journals (Sweden)
Ping Bi
2014-01-01
Full Text Available A tumor-immune competition model with delay is considered, which consists of two-dimensional nonlinear differential equation. The conditions for the linear stability of the equilibria are obtained by analyzing the distribution of eigenvalues. General formulas for the direction, period, and stability of the bifurcated periodic solutions are given for codimension one and codimension two bifurcations, including Hopf bifurcation, steady-state bifurcation, and B-T bifurcation. Numerical examples and simulations are given to illustrate the bifurcations analysis and obtained results.
Alternate Pacing of Border-Collision Period-Doubling Bifurcations.
Zhao, Xiaopeng; Schaeffer, David G
2007-11-01
Unlike classical bifurcations, border-collision bifurcations occur when, for example, a fixed point of a continuous, piecewise C1 map crosses a boundary in state space. Although classical bifurcations have been much studied, border-collision bifurcations are not well understood. This paper considers a particular class of border-collision bifurcations, i.e., border-collision period-doubling bifurcations. We apply a subharmonic perturbation to the bifurcation parameter, which is also known as alternate pacing, and we investigate the response under such pacing near the original bifurcation point. The resulting behavior is characterized quantitatively by a gain, which is the ratio of the response amplitude to the applied perturbation amplitude. The gain in a border-collision period-doubling bifurcation has a qualitatively different dependence on parameters from that of a classical period-doubling bifurcation. Perhaps surprisingly, the differences are more readily apparent if the gain is plotted vs. the perturbation amplitude (with the bifurcation parameter fixed) than if plotted vs. the bifurcation parameter (with the perturbation amplitude fixed). When this observation is exploited, the gain under alternate pacing provides a useful experimental tool to identify a border-collision period-doubling bifurcation.
Oxygen transfer in human carotid artery bifurcation
Institute of Scientific and Technical Information of China (English)
Z.G.Zhang; Y.B.Fan; X.Y.Deng
2007-01-01
Arterial bifurcations are places where blood flow may be disturbed and slow recirculation flow may occur.To reveal the correlation between local oxygen transfer and atherogenesis, a finite element method was employed to simulate the blood flow and the oxygen transfer in the human carotid artery bifurcation. Under steady-state flow conditions, the numerical simulation demonstrated a variation in local oxygen transfer at the bifurcation, showing that the convective condition in the disturbed flow region may produce uneven local oxygen transfer at the blood/wall interface.The disturbed blood flow with formation of slow eddies in the carotid sinus resulted in a depression in oxygen supply to the arterial wall at the entry of the sinus, which in turn may lead to an atherogenic response of the arterial wall, and contribute to the development of atherosclerotic stenosis there.
Emergence of Network Bifurcation Triggered by Entanglement
Yong, Xi; Gao, Xun; Li, Angsheng
2016-01-01
In many non-linear systems, such as plasma oscillation, boson condensation, chemical reaction, and even predatory-prey oscillation, the coarse-grained dynamics are governed by an equation containing anti-symmetric transitions, known as the anti-symmetric Lotka-Volterra (ALV) equations. In this work, we prove the existence of a novel bifurcation mechanism for the ALV equations, where the equilibrium state can be drastically changed by flipping the stability of a pair of fixed points. As an application, we focus on the implications of the bifurcation mechanism for evolutionary networks; we found that the bifurcation point can be determined quantitatively by the quantum entanglement in the microscopic interactions. The equilibrium state can be critically changed from one type of global demographic condensation to another state that supports global cooperation for homogeneous networks. In other words, our results indicate that there exist a class of many-body systems where the macroscopic properties are, to some ...
Stochastic bifurcations in a prototypical thermoacoustic system.
Gopalakrishnan, E A; Tony, J; Sreelekha, E; Sujith, R I
2016-08-01
We study the influence of noise in a prototypical thermoacoustic system, which represents a nonlinear self-excited bistable oscillator. We analyze the time series of unsteady pressure obtained from a horizontal Rijke tube and a mathematical model to identify the effect of noise. We report the occurrence of stochastic bifurcations in a thermoacoustic system by tracking the changes in the stationary amplitude distribution. We observe a complete suppression of a bistable zone in the presence of high intensity noise. We find that the complete suppression of the bistable zone corresponds to the nonexistence of phenomenological (P) bifurcations. This is a study in thermoacoustics to identify the parameter regimes pertinent to P bifurcation using the stationary amplitude distribution obtained by solving the Fokker-Planck equation.
Stochastic bifurcations in a prototypical thermoacoustic system
Gopalakrishnan, E. A.; Tony, J.; Sreelekha, E.; Sujith, R. I.
2016-08-01
We study the influence of noise in a prototypical thermoacoustic system, which represents a nonlinear self-excited bistable oscillator. We analyze the time series of unsteady pressure obtained from a horizontal Rijke tube and a mathematical model to identify the effect of noise. We report the occurrence of stochastic bifurcations in a thermoacoustic system by tracking the changes in the stationary amplitude distribution. We observe a complete suppression of a bistable zone in the presence of high intensity noise. We find that the complete suppression of the bistable zone corresponds to the nonexistence of phenomenological (P) bifurcations. This is a study in thermoacoustics to identify the parameter regimes pertinent to P bifurcation using the stationary amplitude distribution obtained by solving the Fokker-Planck equation.
Crisis bifurcations in plane Poiseuille flow
Zammert, Stefan
2015-01-01
Direct numerical simulations of transitional plane Poiseuille flow in a mirror-symmetric subspace reveal several interior and exterior crisis bifurcations. They appear in the upper branch that emerges in a saddle-node bifurcation near $Re_{SN}=641$ and then undergoes several bifurcations into a chaotic attractor. Near $Re_{XC}=785.95$ the attractor collides with the lower-branch state and turns into a chaotic saddle in a exterior crisis, with a characteristic $(Re-Re_{XC})^{-\\delta}$ variation in lifetimes. For intermediate Reynolds numbers, the attractor undergoes several interior crises, in which new states appear and intermittent behavior can be observed. They contribute to increasing the complexity of the dynamics and to a more dense coverage of state space. The exterior crisis marks the onset of transient turbulence in this subspace of plane Poiseuille flow.
Periodic orbits near a bifurcating slow manifold
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall
2015-01-01
This paper studies a class of $1\\frac12$-degree-of-freedom Hamiltonian systems with a slowly varying phase that unfolds a Hamiltonian pitchfork bifurcation. The main result of the paper is that there exists an order of $\\ln^2\\epsilon^{-1}$-many periodic orbits that all stay within an $\\mathcal O......(\\epsilon^{1/3})$-distance from the union of the normally elliptic slow manifolds that occur as a result of the bifurcation. Here $\\epsilon\\ll 1$ measures the time scale separation. These periodic orbits are predominantly unstable. The proof is based on averaging of two blowup systems, allowing one to estimate...
Bifurcation of Jovian magnetotail current sheet
Directory of Open Access Journals (Sweden)
P. L. Israelevich
2006-07-01
Full Text Available Multiple crossings of the magnetotail current sheet by a single spacecraft give the possibility to distinguish between two types of electric current density distribution: single-peaked (Harris type current layer and double-peaked (bifurcated current sheet. Magnetic field measurements in the Jovian magnetic tail by Voyager-2 reveal bifurcation of the tail current sheet. The electric current density possesses a minimum at the point of the B_{x}-component reversal and two maxima at the distance where the magnetic field strength reaches 50% of its value in the tail lobe.
CAVITATION BIFURCATION FOR COMPRESSIBLE ANISOTROPIC HYPERELASTIC MATERIALS
Institute of Scientific and Technical Information of China (English)
ChengChangjun; RenJiusheng
2004-01-01
The effect of material anisotropy on the bifurcation for void tormation in anisotropic compressible hyperelastic materials is examined. Numerical solutions are obtained in an anisotropic sphere, whose material is transversely isotropic in the radial direction. It is shown that the bifurcation may occur either to the right or to the left, depending on the degree of material anisotropy. The deformation and stress contribution in the sphere before cavitation are different from those after cavitation. The stability of solutions is discussed through a comparison of energy.
Hopf Bifurcation in a Nonlinear Wave System
Institute of Scientific and Technical Information of China (English)
HE Kai-Fen
2004-01-01
@@ Bifurcation behaviour of a nonlinear wave system is studied by utilizing the data in solving the nonlinear wave equation. By shifting to the steady wave frame and taking into account the Doppler effect, the nonlinear wave can be transformed into a set of coupled oscillators with its (stable or unstable) steady wave as the fixed point.It is found that in the chosen parameter regime, both mode amplitudes and phases of the wave can bifurcate to limit cycles attributed to the Hopf instability. It is emphasized that the investigation is carried out in a pure nonlinear wave framework, and the method can be used for the further exploring routes to turbulence.
Splitting rivers at their seams: bifurcations and avulsion
Kleinhans, M.G.; Ferguson, R.I.; Lane, S.N.; Hardy, R.J.
2012-01-01
River bifurcations are critical but poorly understood elements of many geomorphological systems. They are integralelements of alluvial fans, braided rivers, fluvial lowland plains, and deltas and control the partitioning of water and sediment throughthese systems. Bifurcations are commonly unstable
Homoclinic Bifurcation Properties near Eight－figure Homoclinic Orbit
Institute of Scientific and Technical Information of China (English)
邹永魁; 佘彦
2002-01-01
In this paper paper we investigate the homoclinic bifurcation properties near an eight-figure homoclinic orbit of co-dimension two of a planar dynamical system.The corresponding local bifurcation diagram is also illustrated by numerical computation.
Codimension-2 bifurcations of the Kaldor model of business cycle
International Nuclear Information System (INIS)
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.
Bifurcation Analysis of a Discrete Logistic System with Feedback Control
Institute of Scientific and Technical Information of China (English)
WU Dai-yong
2015-01-01
The paper studies the dynamical behaviors of a discrete Logistic system with feedback control. The system undergoes Flip bifurcation and Hopf bifurcation by using the center manifold theorem and the bifurcation theory. Numerical simulations not only illustrate our results, but also exhibit the complex dynamical behaviors of the system, such as the period-doubling bifurcation in periods 2, 4, 8 and 16, and quasi-periodic orbits and chaotic sets.
Delay-induced multistability near a global bifurcation
Hizanidis, J.; Aust, R.; Schoell, E.
2007-01-01
We study the effect of a time-delayed feedback within a generic model for a saddle-node bifurcation on a limit cycle. Without delay the only attractor below this global bifurcation is a stable node. Delay renders the phase space infinite-dimensional and creates multistability of periodic orbits and the fixed point. Homoclinic bifurcations, period-doubling and saddle-node bifurcations of limit cycles are found in accordance with Shilnikov's theorems.
Two degenerate boundary equilibrium bifurcations in planar Filippov systems
Dercole, F.; Della Rossa, F.; Colombo, A.; Kuznetsov, Yuri
2011-01-01
We contribute to the analysis of codimension-two bifurcations in discontinuous systems by studying all equilibrium bifurcations of 2D Filippov systems that involve a sliding limit cycle. There are only two such local bifurcations: (1) a degenerate boundary focus, which we call the homoclinic boundar
NUMERICAL HOPF BIFURCATION OF DELAY-DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper we consider the numerical solution of some delay differential equations undergoing a Hopf bifurcation. We prove that if the delay differential equations have a Hopf bifurcation point atλ=λ*, then the numerical solution of the equation also has a Hopf bifurcation point atλh =λ* + O(h).
CLASSIFICATION OF BIFURCATIONS FOR NONLINEAR DYNAMICAL PROBLEMS WITH CONSTRAINTS
Institute of Scientific and Technical Information of China (English)
吴志强; 陈予恕
2002-01-01
Bifurcation of periodic solutions widely existed in nonlinear dynamical systems isa kind of constrained one in intrinsic quality because its amplitude is always non-negative.Classification of the bifurcations with the type of constraint was discussed. All its six typesof transition sets are derived, in which three types are newly found and a method isproposed for analyzing the constrained bifurcation.
Chaos and reverse bifurcation in a RCL circuit
Cascais, J.; Dilão, R.; da Costa, A. Noronha
1983-01-01
The bifurcation diagram and attractor of a driven non-linear oscillator are directly obtained. The system exhibits not only period doubling, chaotic band merging and noise-free windows like the logistic map, but also reverse flip bifurcations, i.e. period halving. A negative schwartzian derivative map is found also possessing reverse bifurcations.
The Bifurcations of Traveling Wave Solutions of the Kundu Equation
Yating Yi; Zhengrong Liu
2013-01-01
We use the bifurcation method of dynamical systems to study the bifurcations of traveling wave solutions for the Kundu equation. Various explicit traveling wave solutions and their bifurcations are obtained. Via some special phase orbits, we obtain some new explicit traveling wave solutions. Our work extends some previous results.
The recognition of equivariant bifurcation problems
Institute of Scientific and Technical Information of China (English)
李养成
1996-01-01
The orbit of an equivariant bifurcation problem with multiparameter is characterized under the action of the group of unipotent equivalences. When the unipotent tangent space is invariant under unipotent equivalences, the recognition problem can be solved by just using linear algebra. Sufficient conditions for a subspace to be intrinsic subspace under unipotent equivalences are given.
HOMOCLINIC TWIST BIFURCATIONS WITH Z(2) SYMMETRY
ARONSON, DG; VANGILS, SA; KRUPA, M
1994-01-01
We analyze bifurcations occurring in the vicinity of a homoclinic twist point for a generic two-parameter family of Z2 equivariant ODEs in four dimensions. The results are compared with numerical results for a system of two coupled Josephson junctions with pure capacitive load.
Sex differences in intracranial arterial bifurcations
DEFF Research Database (Denmark)
Lindekleiv, Haakon M; Valen-Sendstad, Kristian; Morgan, Michael K;
2010-01-01
Subarachnoid hemorrhage (SAH) is a serious condition, occurring more frequently in females than in males. SAH is mainly caused by rupture of an intracranial aneurysm, which is formed by localized dilation of the intracranial arterial vessel wall, usually at the apex of the arterial bifurcation...
Bifurcation structure of an optical ring cavity
DEFF Research Database (Denmark)
Kubstrup, C.; Mosekilde, Erik
1996-01-01
One- and two-dimensional continuation techniques are applied to determine the basic bifurcation structure for an optical ring cavity with a nonlinear absorbing element (the Ikeda Map). By virtue of the periodic structure of the map, families of similar solutions develop in parameter space. Within...
Bifurcations in dynamical systems with parametric excitation
Fatimah, Siti
2002-01-01
This thesis is a collection of studies on coupled nonconservative oscillator systems which contain an oscillator with parametric excitation. The emphasis this study will, on the one hand, be on the bifurcations of the simple solutions such as fixed points and periodic orbits, and on the other hand o
Bifurcation structure of successive torus doubling
Energy Technology Data Exchange (ETDEWEB)
Sekikawa, Munehisa [Department of Information Science, Faculty of Engineering, Utsunomiya University (Japan)]. E-mail: muse@aihara.jst.go.jp; Inaba, Naohiko [Department of Information Science, Faculty of Engineering, Utsunomiya University (Japan)]. E-mail: inaba@is.utsunomiya-u.ac.jp; Yoshinaga, Tetsuya [Department of Radiologic Science and Engineering, School of Health Sciences, The University of Tokushima (Japan)]. E-mail: yosinaga@medsci.tokushima-u.ac.jp; Tsubouchi, Takashi [Institute of Engineering Mechanics and Systems, University of Tsukuba (Japan)]. E-mail: tsubo@esys.tsukuba.ac.jp
2006-01-02
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.
DEFF Research Database (Denmark)
Behan, Miles W; Holm, Niels R; 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.......001). Procedure duration, contrast, and x-ray dose favored the simple approach. Subgroup analysis revealed similar composite end point results for true bifurcations (n=657, simple 9.2% versus complex 17.3%; hazard ratio 1.90 [95% confidence interval 1.22 to 2.94], P=0.004), wide-angled bifurcations >60 to 70° (n.......57). Conclusions— For bifurcation lesions, a provisional single-stent approach is superior to systematic dual stenting techniques in terms of safety and efficacy. A complex approach does not appear to be beneficial in more anatomically complicated lesions....
Complex Dynamics Caused by Torus Bifurcation in Power Systems
Institute of Scientific and Technical Information of China (English)
YU Xiaodan; JIA Hongjie; DONG Cun
2006-01-01
Torus bifurcation is a relatively complicated bifurcation caused by a pair of complex conjuployed to reveal the relationship between torus bifurcation and some complex dynamics.Based on theoretical analysis and simulation studies, it is found that torus bifurcation is a typical route to chaos in power system.Some complex dynamics usually occur after a torus bifurcation, such as self-organization, deep bifurcations, exquisite structure, coexistence of chaos and divergence.It is also found that chaos has close relationship with various instability scenarios of power systems.Studies of this paper are helpful to understand the mechanism of torus bifurcation in power system and relationship of chaos and power system instabilities.
BIFURCATION ANALYSIS OF EQUILIBRIUM POINT IN TWO NODE POWER SYSTEM
Directory of Open Access Journals (Sweden)
Halima Aloui
2014-01-01
Full Text Available This study presents a study of bifurcation in a dynamic power system model. It becomes one of the major precautions for electricity suppliers and these systems must maintain a steady state in the neighborhood of the operating points. We study in this study the dynamic stability of two node power systems theory and the stability of limit cycles emerging from a subcritical or supercritical Hopf bifurcation by computing the first Lyapunov coefficient. The MATCONT package of MATLAB was used for this study and detailed numerical simulations presented to illustrate the types of dynamic behavior. Results have proved the analyses for the model exhibit dynamical bifurcations, including Hopf bifurcations, Limit point bifurcations, Zero Hopf bifurcations and Bagdanov-taknes bifurcations.
Perturbed period-doubling bifurcation. I. Theory
DEFF Research Database (Denmark)
Svensmark, Henrik; Samuelsen, Mogens Rugholm
1990-01-01
The influence of perturbations (a small, near-resonant signal and noise) on a driven dissipative dynamical system that is close to undergoing a period-doubling bifurcation is investigated. It is found that the system is very sensitive, and that periodic perturbations change its stability in a wel...... of a microwave-driven Josephson junction confirm the theory. Results should be of interest in parametric-amplification studies....
Shape optimization of the carotid artery bifurcation
Bressloff, N. W.; Forrester, A.I.J.; Banks, J.; Bhaskar, K.V.
2004-01-01
A parametric CAD model of the human carotid artery bifurcation is employed in an initial exploration of the response of shear stress to the variation of the angle of the internal carotid artery and the width of the sinus bulb. Design of experiment and response surface technologies are harnessed for the first time in such an application with the aim of developing a better understanding of the relationship between geometry (anatomy) and sites of arterial disease.
Sex differences in intracranial arterial bifurcations
DEFF Research Database (Denmark)
Lindekleiv, Haakon M; Valen-Sendstad, Kristian; Morgan, Michael K;
2010-01-01
Subarachnoid hemorrhage (SAH) is a serious condition, occurring more frequently in females than in males. SAH is mainly caused by rupture of an intracranial aneurysm, which is formed by localized dilation of the intracranial arterial vessel wall, usually at the apex of the arterial bifurcation. T....... The female preponderance is usually explained by systemic factors (hormonal influences and intrinsic wall weakness); however, the uneven sex distribution of intracranial aneurysms suggests a possible physiologic factor-a local sex difference in the intracranial arteries....
Multiparametric bifurcations of an epidemiological model with strong Allee effect.
Cai, Linlin; Chen, Guoting; Xiao, Dongmei
2013-08-01
In this paper we completely study bifurcations of an epidemic model with five parameters introduced by Hilker et al. (Am Nat 173:72-88, 2009), which describes the joint interplay of a strong Allee effect and infectious diseases in a single population. Existence of multiple positive equilibria and all kinds of bifurcation are examined as well as related dynamical behavior. It is shown that the model undergoes a series of bifurcations such as saddle-node bifurcation, pitchfork bifurcation, Bogdanov-Takens bifurcation, degenerate Hopf bifurcation of codimension two and degenerate elliptic type Bogdanov-Takens bifurcation of codimension three. Respective bifurcation surfaces in five-dimensional parameter spaces and related dynamical behavior are obtained. These theoretical conclusions confirm their numerical simulations and conjectures by Hilker et al., and reveal some new bifurcation phenomena which are not observed in Hilker et al. (Am Nat 173:72-88, 2009). The rich and complicated dynamics exhibit that the model is very sensitive to parameter perturbations, which has important implications for disease control of endangered species.
Codimension two bifurcation of a vibro-bounce system
Institute of Scientific and Technical Information of China (English)
Guanwei Luo; Yandong Chu; Yanlong Zhang; Jianhua Xie
2005-01-01
A three-degree-of-freedom vibro-bounce system is considered. The disturbed map of period one single-impact motion is derived analytically. A center manifold theorem dimensional one, and the normal form map associated with Hopf-flip bifurcation is obtained. Dynamical behavior of the system, near the point of codimension two bifurcation, is investigated by using qualitative analysis and numerical simulation. It is found that near the point of Hopf-flip bifurcation there exists not only Hopf bifurcation of period one singleimpact motion, but also Hopf bifurcation of period two double-impact motion. The results from simulation show that there exists an interesting torus doubling bifurcation near the codimension two bifurcation. The torus doubling bifurcation makes the quasi-periodic attractor associated with period one single-impact motion transform to the other quasi-periodic attractor represented by two attracting closed circles. The torus bifurcation is qualitatively different from the typical torus doubling bifurcation occurring in the vibro-impact systems. Different routes from period one single-impact motion to chaos are observed by numerical simulation.
Bifurcations and safe regions in open Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Barrio, R; Serrano, S [GME, Dpto Matematica Aplicada and IUMA, Universidad de Zaragoza, E-50009 Zaragoza (Spain); Blesa, F [GME, Dpto Fisica Aplicada, Universidad de Zaragoza, E-50009 Zaragoza (Spain)], E-mail: rbarrio@unizar.es, E-mail: fblesa@unizar.es, E-mail: sserrano@unizar.es
2009-05-15
By using different recent state-of-the-art numerical techniques, such as the OFLI2 chaos indicator and a systematic search of symmetric periodic orbits, we get an insight into the dynamics of open Hamiltonians. We have found that this kind of system has safe bounded regular regions inside the escape region that have significant size and that can be located with precision. Therefore, it is possible to find regions of nonzero measure with stable periodic or quasi-periodic orbits far from the last KAM tori and far from the escape energy. This finding has been possible after a careful combination of a precise 'skeleton' of periodic orbits and a 2D plate of the OFLI2 chaos indicator to locate saddle-node bifurcations and the regular regions near them. Besides, these two techniques permit one to classify the different kinds of orbits that appear in Hamiltonian systems with escapes and provide information about the bifurcations of the families of periodic orbits, obtaining special cases of bifurcations for the different symmetries of the systems. Moreover, the skeleton of periodic orbits also gives the organizing set of the escape basin's geometry. As a paradigmatic example, we study in detail the Henon-Heiles Hamiltonian, and more briefly the Barbanis potential and a galactic Hamiltonian.
Bifurcations and safe regions in open Hamiltonians
Barrio, R.; Blesa, F.; Serrano, S.
2009-05-01
By using different recent state-of-the-art numerical techniques, such as the OFLI2 chaos indicator and a systematic search of symmetric periodic orbits, we get an insight into the dynamics of open Hamiltonians. We have found that this kind of system has safe bounded regular regions inside the escape region that have significant size and that can be located with precision. Therefore, it is possible to find regions of nonzero measure with stable periodic or quasi-periodic orbits far from the last KAM tori and far from the escape energy. This finding has been possible after a careful combination of a precise 'skeleton' of periodic orbits and a 2D plate of the OFLI2 chaos indicator to locate saddle-node bifurcations and the regular regions near them. Besides, these two techniques permit one to classify the different kinds of orbits that appear in Hamiltonian systems with escapes and provide information about the bifurcations of the families of periodic orbits, obtaining special cases of bifurcations for the different symmetries of the systems. Moreover, the skeleton of periodic orbits also gives the organizing set of the escape basin's geometry. As a paradigmatic example, we study in detail the Hénon-Heiles Hamiltonian, and more briefly the Barbanis potential and a galactic Hamiltonian.
Classification of solitary wave bifurcations in generalized nonlinear Schr\\"odinger equations
Yang, Jianke
2012-01-01
Bifurcations of solitary waves are classified for the generalized nonlinear Schr\\"odinger equations with arbitrary nonlinearities and external potentials in arbitrary spatial dimensions. Analytical conditions are derived for three major types of solitary wave bifurcations, namely saddle-node bifurcations, pitchfork bifurcations and transcritical bifurcations. Shapes of power diagrams near these bifurcations are also obtained. It is shown that for pitchfork and transcritical bifurcations, their power diagrams look differently from their familiar solution-bifurcation diagrams. Numerical examples for these three types of bifurcations are given as well. Of these numerical examples, one shows a transcritical bifurcation, which is the first report of transcritical bifurcations in the generalized nonlinear Schr\\"odinger equations. Another shows a power loop phenomenon which contains several saddle-node bifurcations, and a third example shows double pitchfork bifurcations. These numerical examples are in good agreeme...
Bifurcation property and persistence of configurations for parallel mechanisms
Institute of Scientific and Technical Information of China (English)
王玉新; 王仪明; 刘学深
2003-01-01
The configuration of parallel mechanisms at the singularity position is uncertain. How to control the mechanism through the singularity position with a given configuration is one of the key problems of the robot controlling. In this paper the bifurcation property and persistence of configurations at the singularity position is investigated for 3-DOF parallel mechanisms. The dimension of the bifurcation equations is reduced by Liapunov-Schmidt reduction method. According to the strong equivalence condition, the normal form which is consistent with the bifurcation condition of the original equation is selected. Through universal unfolding of the bifurcation equation, the influences of the disturbance factors, such as the influence of length of the input component on the configuration persistence at the bifurcation position, are analyzed. Using this method we can obtain the bifurcation curve in which the configuration will be held when the mechanism passes through the singularity position. Therefore, the configuration is under control in this way.
Simplest Normal Forms of Generalized Neimark-Sacker Bifurcation
Institute of Scientific and Technical Information of China (English)
DING Yumei; ZHANG Qichang
2009-01-01
The normal forms of generalized Neimark-Sacker bifurcation are extensively studied using normal form theory of dynamic system. It is well known that if the normal forms of the generalized Neimark-Sacker bifurcation are expressed in polar coordinates, then all odd order terms must, in general, remain in the normal forms. In this paper, five theorems are presented to show that the conventional Neimark-Sacker bifurcation can be further simpli-fied. The simplest normal forms of generalized Neimark-Sacker bifurcation are calculated. Based on the conven-tional normal form, using appropriate nonlinear transformations, it is found that the generalized Neimark-Sacker bifurcation has at most two nonlinear terms remaining in the amplitude equations of the simplest normal forms up to any order. There are two kinds of simplest normal forms. Their algebraic expression formulas of the simplest nor-mal forms in terms of the coefficients of the generalized Neimark-Sacker bifurcation systems are given.
Nonlinear instability and dynamic bifurcation of a planeinterface during solidification
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
By taking average over the curvature, the temperature and its gradient, the solute con-centration and its gradient at the flange of planar interface perturbed by sinusoidal ripple during solidifi-cation, the nonlinear dynamic equations of the sinusoidal perturbation wave have been set up. Analysisof the nonlinear instability and the behaviors of dynamic bifurcation of the solutions of these equationsshows that (i) the way of dynamic bifurcation of the flat-to-cellular interface transition vades with differ-ent thermal gradients. The quasi-subcritical-lag bifurcation occurs in the small interface thermal gradientscope, the supercritical-lag bifurcation in the medium thermal gradient scope and the supercritical bifur-cation in the large thermal gradient scope. (ii) The transition of cellular-to-flat interface is realizedthrough supercritical inverse bifurcation in the rapid solidification area.
Codimension 2 reversible heteroclinic bifurcations with inclination flips
Institute of Scientific and Technical Information of China (English)
2009-01-01
In this paper, the heteroclinic bifurcation problem with real eigenvalues and two incli- nation-flips is investigated in a four-dimensional reversible system. We perform a detailed study of this case by using the method originally established in the papers "Problems in Homoclinic Bifurcation with Higher Dimensions" and "Bifurcation of Heteroclinic Loops," and obtain fruitful results, such as the existence and coexistence of R-symmetric homoclinic orbit and R-symmetric heteroclinic loops, R-symmetric homoclinic orbit and R-symmetric periodic orbit. The double R-symmetric homoclinic bifurcation (i.e., two-fold R-symmetric homoclinic bifurcation) for reversible heteroclinic loops is found, and the existence of infinitely many R-symmetric periodic orbits accumulating onto a homoclinic orbit is demonstrated. The relevant bifurcation surfaces and the existence regions are also located.
Bifurcation structure of a model of bursting pancreatic cells
DEFF Research Database (Denmark)
Mosekilde, Erik; Lading, B.; Yanchuk, S.;
2001-01-01
One- and two-dimensional bifurcation studies of a prototypic model of bursting oscillations in pancreatic P-cells reveal a squid-formed area of chaotic dynamics in the parameter plane, with period-doubling bifurcations on one side of the arms and saddle-node bifurcations on the other....... The 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....
Defining universality classes for three different local bifurcations
Leonel, Edson D.
2016-10-01
The convergence to the fixed point at a bifurcation and near it is characterized via scaling formalism for three different types of local bifurcations of fixed points in differential equations, namely: (i) saddle-node; (ii) transcritical; and (iii) supercritical pitchfork. At the bifurcation, the convergence is described by a homogeneous function with three critical exponents α, β and z. A scaling law is derived hence relating the three exponents. Near the bifurcation the evolution towards the fixed point is given by an exponential function whose relaxation time is marked by a power law of the distance of the bifurcation point with an exponent δ. The four exponents α, β, z and δ can be used to defined classes of universality for the local bifurcations of fixed points in differential equations.
Codimension 2 reversible heteroclinic bifurcations with inclination flips
Institute of Scientific and Technical Information of China (English)
XU YanCong; ZHU DeMing; DENG GuiFeng
2009-01-01
In this paper,the heteroclinic bifurcation problem with real eigenvalues and two inclination-flips is investigated in a four-dimensional reversible system.We perform a detailed study of this case by using the method originally established in the papers "Problems in Homoclinic Bifurcation with Higher Dimensions" and "Bifurcation of Heteroclinic Loops," and obtain fruitful results,such as the existence and coexistence of R-symmetric homoclinic orbit and R-symmetric heteroclinic loops,R-symmetric homoclinic orbit and R-symmetric periodic orbit.The double R-symmetric homoclinic bifurcation (i.e.,two-fold R-symmetric homoclinic bifurcation) for reversible heteroclinic loops is found,and the existence of infinitely many R-symmetric periodic orbits accumulating onto a homoclinic orbit is demonstrated.The relevant bifurcation surfaces and the existence regions are also located.
Global Bifurcation of a Novel Computer Virus Propagation Model
Directory of Open Access Journals (Sweden)
Jianguo Ren
2014-01-01
Full Text Available In a recent paper by J. Ren et al. (2012, a novel computer virus propagation model under the effect of the antivirus ability in a real network is established. The analysis there only partially uncovers the dynamics behaviors of virus spread over the network in the case where around bifurcation is local. In the present paper, by mathematical analysis, it is further shown that, under appropriate parameter values, the model may undergo a global B-T bifurcation, and the curves of saddle-node bifurcation, Hopf bifurcation, and homoclinic bifurcation are obtained to illustrate the qualitative behaviors of virus propagation. On this basis, a collection of policies is recommended to prohibit the virus prevalence. To our knowledge, this is the first time the global bifurcation has been explored for the computer virus propagation. Theoretical results and corresponding suggestions may help us suppress or eliminate virus propagation in the network.
Characterization of static bifurcations for n-dimensional flows in the frequency domain
Institute of Scientific and Technical Information of China (English)
Li ZENG; Yi ZHAO
2006-01-01
In this paper n-dimensional flows (described by continuous-time system) with static bifurcations are considered with the aim of classification of different elementary bifurcations using the frequency domain formalism. Based on frequency domain approach, we prove some criterions for the saddle-node bifurcation, transcritical bifurcation and pitchfork bifurcation, and give an example to illustrate the efficiency of the result obtained.
Bifurcation analysis in single-species population model with delay
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
A single-species population model is investigated in this paper.Firstly,we study the existence of Hopf bifurcation at the positive equilibrium.Furthermore,an explicit algorithm for determining the direction of the Hopf bifurcation and stability of the bifurcation periodic solutions are derived by using the normal form and the center manifold theory.At last,numerical simulations to support the analytical conclusions are carried out.
Singularly perturbed bifurcation subsystem and its application in power systems
Institute of Scientific and Technical Information of China (English)
An Yichun; Zhang Qingling; Zhu Yukun; Zhang Yan
2008-01-01
The singularly perturbed bifurcation subsystem is described,and the test conditions of subsystem persistence are deduced.By use of fast and slow reduced subsystem model,the result does not require performing nonlinear transformation.Moreover,it is shown and proved that the persistence of the periodic orbits for Hopf bifurcation in the reduced model through center manifold.Van der Pol oscillator circuit is given to illustrate the persistence of bifurcation subsystems with the full dynamic system.
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
Hopf bifurcation in the Clarida, Gali, and Gertler model
Barnett, William A.; Eryilmaz, Unal
2012-01-01
We explore bifurcation phenomena in the open-economy New Keynesian model developed by Clarida, Gali and Gertler (2002). We find that the open economy framework can bring about more complex dynamics, along with a wider variety of qualitative behaviors and policy responses. Introducing parameters related to the open economy structure affects the values of bifurcation parameters and changes the location of bifurcation boundaries. As a result, the stratification of the confidence region, as previ...
Identification of Bifurcations from Observations of Noisy Biological Oscillators
Salvi, Joshua D; Hudspeth, A J
2016-01-01
Hair bundles are biological oscillators that actively transduce mechanical stimuli into electrical signals in the auditory, vestibular, and lateral-line systems of vertebrates. A bundle's function can be explained in part by its operation near a particular type of bifurcation, a qualitative change in behavior. By operating near different varieties of bifurcation, the bundle responds best to disparate classes of stimuli. We show how to determine the identity of and proximity to distinct bifurcations despite the presence of substantial environmental noise.
Periodic solutions and flip bifurcation in a linear impulsive system
Institute of Scientific and Technical Information of China (English)
Jiang Gui-Rong; Yang Qi-Gui
2008-01-01
In this paper,the dynamical behaviour of a linear impulsive system is discussed both theoretically and numerically.The existence and the stability of period-one solution are discussed by using a discrete map.The conditions of existence for flip bifurcation are derived by using the centre manifold theorem and bifurcation theorem.The bifurcation analysis shows that chaotic solutions appear via a cascade of period-doubling in some interval of parameters.Moreover,the periodic solutions,the bifurcation diagram,and the chaotic attractor,which show their consistence with the theoretical analyses,are given in an example.中图分类:O547
Bifurcations in two coupled Rössler systems
DEFF Research Database (Denmark)
Rasmussen, J; Mosekilde, Erik; Reick, C.
1996-01-01
The paper presents a detailed bifurcation analysis of two symmetrically coupled Rössler systems. The symmetry in the coupling does not allow any one direction to become preferred, and the coupled system is therefore an example of a dissipative system that cannot be considered as effectively one......-dimensional. The results are presented in terms of one- and two-parmeter bifurcation diagrams. A particularly interesting finding is the replacement of some of the period-doubling bifurcations by torus bifurcations. By virtue of this replacement, instead of a Feigenbaum transition to chaos a transition via torus...
Hopf bifurcation for tumor-immune competition systems with delay
Directory of Open Access Journals (Sweden)
Ping Bi
2014-01-01
Full Text Available In this article, a immune response system with delay is considered, which consists of two-dimensional nonlinear differential equations. The main purpose of this paper is to explore the Hopf bifurcation of a immune response system with delay. The general formula of the direction, the estimation formula of period and stability of bifurcated periodic solution are also given. Especially, the conditions of the global existence of periodic solutions bifurcating from Hopf bifurcations are given. Numerical simulations are carried out to illustrate the the theoretical analysis and the obtained results.
Diffusion-driven instability and Hopf bifurcation in Brusselator system
Institute of Scientific and Technical Information of China (English)
LI Bo; WANG Ming-xin
2008-01-01
The Hopf bifurcation for the Brusselator ordinary-differential-equation (ODE)model and the corresponding partial-differential-equation(PDE)model are investigated by using the Hopf bifurcation theorem.The stability of the Hopf bifurcation periodic solution is di8cu88ed by applying the normal form theory and the center manifold theorem.When parameters satisfy some conditions,the spatial homogenous equilibrium solution and the spatial homogenous periodic solution become unstable.Our results show that if parameters are properly chosen,Hopf bifurcation does not occur for the ODE system,but occurs for the PDE system.
High-codimensional static bifurcations of strongly nonlinear oscillator
Institute of Scientific and Technical Information of China (English)
Zhang Qi-Chang; Wang Wei; Liu Fu-Hao
2008-01-01
The static bifurcation of the parametrically excited strongly nonlinear oscillator is studied.We consider the averaged equations of a system subject to Duffing-van der Pol and quintic strong nonlinearity by introducing the undetermined fundamental frequency into the computation in the complex normal form.To discuss the static bifurcation,the bifurcation problem is described as a 3-codimensional unfolding with Z2 symmetry on the basis of singularity theory.The transition set and bifurcation diagrams for the singularity are presented,while the stability of the zero solution is studied by using the eigenvalues in various parameter regions.
Oscillatory Activities in Regulatory Biological Networks and Hopf Bifurcation
Institute of Scientific and Technical Information of China (English)
YAN Shi-Wei; WANG Qi; XIE Bai-Song; ZHANG Feng-Shou
2007-01-01
Exploiting the nonlinear dynamics in the negative feedback loop, we propose a statistical signal-response model to describe the different oscillatory behaviour in a biological network motif. By choosing the delay as a bifurcation parameter, we discuss the existence of Hopf bifurcation and the stability of the periodic solutions of model equations with the centre manifold theorem and the normal form theory. It is shown that a periodic solution is born in a Hopf bifurcation beyond a critical time delay, and thus the bifurcation phenomenon may be important to elucidate the mechanism of oscillatory activities in regulatory biological networks.
Bifurcation Analysis for Neural Networks in Neutral Form
Chen, Hong-Bing; Sun, Xiao-Ke
2016-06-01
In this paper, a system of neural networks in neutral form with time delay is investigated. Further, by introducing delay τ as a bifurcation parameter, it is found that Hopf bifurcation occurs when τ is across some critical values. The direction of the Hopf bifurcations and the stability are determined by using normal form method and center manifold theory. Next, the global existence of periodic solution is established by using a global Hopf bifurcation result. Finally, an example is given to support the theoretical predictions.
The Branching Bifurcation of Adaptive Dynamics
Della Rossa, Fabio; Dercole, Fabio; Landi, Pietro
2015-06-01
We unfold the bifurcation involving the loss of evolutionary stability of an equilibrium of the canonical equation of Adaptive Dynamics (AD). The equation deterministically describes the expected long-term evolution of inheritable traits — phenotypes or strategies — of coevolving populations, in the limit of rare and small mutations. In the vicinity of a stable equilibrium of the AD canonical equation, a mutant type can invade and coexist with the present — resident — types, whereas the fittest always win far from equilibrium. After coexistence, residents and mutants effectively diversify, according to the enlarged canonical equation, only if natural selection favors outer rather than intermediate traits — the equilibrium being evolutionarily unstable, rather than stable. Though the conditions for evolutionary branching — the joint effect of resident-mutant coexistence and evolutionary instability — have been known for long, the unfolding of the bifurcation has remained a missing tile of AD, the reason being related to the nonsmoothness of the mutant invasion fitness after branching. In this paper, we develop a methodology that allows the approximation of the invasion fitness after branching in terms of the expansion of the (smooth) fitness before branching. We then derive a canonical model for the branching bifurcation and perform its unfolding around the loss of evolutionary stability. We cast our analysis in the simplest (but classical) setting of asexual, unstructured populations living in an isolated, homogeneous, and constant abiotic environment; individual traits are one-dimensional; intra- as well as inter-specific ecological interactions are described in the vicinity of a stationary regime.
Burzotta, Francesco; Cook, Brian; Iaizzo, Paul A; Singh, Jasvindar; Louvard, Yves; Latib, Azeem
2015-01-01
The Visible Heart® Laboratory is an original experimental laboratory in which harvested animal hearts are resuscitated and connected to a support machine in order to beat outside the animal body. Resuscitated animal hearts may be exposed to various types of endovascular intervention under full, multimodality inspection. This unique experimental setting allows the performance of percutaneous coronary intervention (PCI) in a setting which resembles a standard catheterisation laboratory set-up, and contemporaneously allows unique multimodality imaging. For these reasons, the performance of PCI on bifurcations in the Visible Heart® Laboratory may improve the knowledge of the dynamic stent deformations and stent-vessel wall interactions associated with the different steps of the various techniques for bifurcation stenting. Furthermore, the collected images may also serve as a novel educative resource for physicians. The performance of bifurcation stenting in the Visible Heart® Laboratory is a promising experimental setting to gain novel information regarding any existing or future PCI technique to treat coronary bifurcations.
Burzotta, Francesco; Cook, Brian; Iaizzo, Paul A; Singh, Jasvindar; Louvard, Yves; Latib, Azeem
2015-01-01
The Visible Heart® Laboratory is an original experimental laboratory in which harvested animal hearts are resuscitated and connected to a support machine in order to beat outside the animal body. Resuscitated animal hearts may be exposed to various types of endovascular intervention under full, multimodality inspection. This unique experimental setting allows the performance of percutaneous coronary intervention (PCI) in a setting which resembles a standard catheterisation laboratory set-up, and contemporaneously allows unique multimodality imaging. For these reasons, the performance of PCI on bifurcations in the Visible Heart® Laboratory may improve the knowledge of the dynamic stent deformations and stent-vessel wall interactions associated with the different steps of the various techniques for bifurcation stenting. Furthermore, the collected images may also serve as a novel educative resource for physicians. The performance of bifurcation stenting in the Visible Heart® Laboratory is a promising experimental setting to gain novel information regarding any existing or future PCI technique to treat coronary bifurcations. PMID:25983169
On the application of Newton's and Chord methods to bifurcation problems
Directory of Open Access Journals (Sweden)
M. B. M. Elgindi
1994-01-01
Full Text Available This paper is concerned with the applications of Newton's and chord methods in the computations of the bifurcation solutions in a neighborhood of a simple bifurcation point for prescribed values of the bifurcation parameter.
Homoclinic bifurcation in Chua’s circuit
Indian Academy of Sciences (India)
S K Dana; S Chakraborty; G Ananthakrishna
2005-03-01
We report our experimental observations of the Shil’nikov-type homoclinic chaos in asymmetry-induced Chua’s oscillator. The asymmetry plays a crucial role in the related homoclinic bifurcations. The asymmetry is introduced in the circuit by forcing a DC voltage. For a selected asymmetry, when a system parameter is controlled, we observed transition from large amplitude limit cycle to homoclinic chaos via a sequence of periodic mixed-mode oscillations interspersed by chaotic states. Moreover, we observed two intermediate bursting regimes. Experimental evidences of homoclinic chaos are verified with PSPICE simulations.
Longitudinal stent deformation during coronary bifurcation stenting.
Vijayvergiya, Rajesh; Sharma, Prafull; Gupta, Ankush; Goyal, Praveg; Panda, Prashant
2016-03-01
A distortion of implanted coronary stent along its longitudinal axis during coronary intervention is known as longitudinal stent deformation (LSD). LSD is frequently seen with newer drug eluting stents (DES), specifically with PROMUS Element stent. It is usually caused by impact of guide catheter tip, or following passage of catheters like balloon catheter, IVUS catheter, guideliner, etc. We hereby report a case of LSD during coronary bifurcation lesion intervention, using two-stents technique. Patient had acute stent thrombosis as a complication of LSD, which was successfully managed. PMID:26811144
Bifurcation Control, Manufacturing Planning and Formation Control
Institute of Scientific and Technical Information of China (English)
Wei Kang; Mumin Song; Ning Xi
2005-01-01
The paper consists of three topics on control theory and engineering applications, namely bifurcation control, manufacturing planning, and formation control. For each topic, we summarize the control problem to be addressed and some key ideas used in our recent research. Interested readers are referred to related publications for more details. Each of the three topics in this paper is technically independent from the other ones. However, all three parts together reflect the recent research activities of the first author, jointly with other researchers in different fields.
Bifurcation analysis of a preloaded Jeffcott rotor
International Nuclear Information System (INIS)
A model of two-degrees-of-freedom Jeffcott rotor system with bearing clearance subjected of an out-of-balance excitation is considered. The influence of preloading and viscous damping of the snubber ring is introduced in the mathematical description. A programme of numerical simulations is conducted to show how the preloading and viscous damping change the dynamics of the rotor system. Bifurcation diagrams and Lyapunov exponents are constructed to explore stability. It is shown that dynamics of the rotor system can be effectively controlled by varying the preloading and the damping both of the rotor and the snubber ring. In the most considered cases preloading stabilises the dynamic responses
Bifurcation analysis of a preloaded Jeffcott rotor
Energy Technology Data Exchange (ETDEWEB)
Karpenko, Evgueni V.; Pavlovskaia, Ekaterina E.; Wiercigroch, Marian E-mail: m.wiercigroch@eng.abdn.ac.uk
2003-01-01
A model of two-degrees-of-freedom Jeffcott rotor system with bearing clearance subjected of an out-of-balance excitation is considered. The influence of preloading and viscous damping of the snubber ring is introduced in the mathematical description. A programme of numerical simulations is conducted to show how the preloading and viscous damping change the dynamics of the rotor system. Bifurcation diagrams and Lyapunov exponents are constructed to explore stability. It is shown that dynamics of the rotor system can be effectively controlled by varying the preloading and the damping both of the rotor and the snubber ring. In the most considered cases preloading stabilises the dynamic responses.
Characteristics of Period-Adding Bursting Bifurcation Without Chaos in the Chay Neuron Model
Institute of Scientific and Technical Information of China (English)
YANG Zhuo-Qin; LU Qi-Shao
2004-01-01
@@ A period-adding bursting sequence without bursting-chaos in the Chay neuron model is studied by bifurcation analysis. The genesis of each periodic bursting is separately evoked by the corresponding periodic spiking patterns through two period-doubling bifurcations, except for the period-1 bursting occurring via Hopf bifurcation. Hence,it is concluded that this period-adding bursting bifurcation without chaos has a compound bifurcation structure closely related to period-doubling bifurcations of periodic spiking in essence.
Inversion of hematocrit partition at microfluidic bifurcations.
Shen, Zaiyi; Coupier, Gwennou; Kaoui, Badr; Polack, Benoît; Harting, Jens; Misbah, Chaouqi; Podgorski, Thomas
2016-05-01
Partitioning of red blood cells (RBCs) at the level of bifurcations in the microcirculatory system affects many physiological functions yet it remains poorly understood. We address this problem by using T-shaped microfluidic bifurcations as a model. Our computer simulations and in vitro experiments reveal that the hematocrit (ϕ0) partition depends strongly on RBC deformability, as long as ϕ0<20% (within the normal range in microcirculation), and can even lead to complete deprivation of RBCs in a child branch. Furthermore, we discover a deviation from the Zweifach-Fung effect which states that the child branch with lower flow rate recruits less RBCs than the higher flow rate child branch. At small enough ϕ0, we get the inverse scenario, and the hematocrit in the lower flow rate child branch is even higher than in the parent vessel. We explain this result by an intricate up-stream RBC organization and we highlight the extreme dependence of RBC transport on geometrical and cell mechanical properties. These parameters can lead to unexpected behaviors with consequences on the microcirculatory function and oxygen delivery in healthy and pathological conditions.
Inversion of hematocrit partition at microfluidic bifurcations
Shen, Zaiyi; Kaoui, Badr; Polack, Benoît; Harting, Jens; Misbah, Chaouqi; Podgorski, Thomas
2016-01-01
Partitioning of red blood cells (RBCs) at the level of bifurcations in the microcirculatory system affects many physiological functions yet it remains poorly understood. We address this problem by using T-shaped microfluidic bifurcations as a model. Our computer simulations and in vitro experiments reveal that the hematocrit ($\\phi_0$) partition depends strongly on RBC deformability, as long as $\\phi_0 <20$% (within the normal range in microcirculation), and can even lead to complete deprivation of RBCs in a child branch. Furthermore, we discover a deviation from the Zweifach-Fung effect which states that the child branch with lower flow rate recruits less RBCs than the higher flow rate child branch. At small enough $\\phi_0$, we get the inverse scenario, and the hematocrit in the lower flow rate child branch is even higher than in the parent vessel. We explain this result by an intricate up-stream RBC organization and we highlight the extreme dependence of RBC transport on geometrical and cell mechanical p...
Hopf Bifurcations of a Chemostat System with Bi-parameters
Institute of Scientific and Technical Information of China (English)
李晓月; 千美华; 杨建平; 黄启昌
2004-01-01
We study a chemostat system with two parameters, S0-initial density and D-flow-speed of the solution. At first, a generalization of the traditional Hopf bifurcation theorem is given. Then, an existence theorem for the Hopf bifurcation of the chemostat system is presented.
Degenerate Orbit Flip Homoclinic Bifurcations with Higher Dimensions
Institute of Scientific and Technical Information of China (English)
Ran Chao WU; Jian Hua SUN
2006-01-01
Bifurcations of a degenerate homoclinic orbit with orbit flip in high dimensional system are existence and uniqueness of 1-homoclinic orbit and 1-periodic orbit are given. Also considered is the existence of 2-homoclinic orbit and 2-periodic orbit. In additon, the corresponding bifurcation surfaces are given.
Influence of perturbations on period-doubling bifurcation
DEFF Research Database (Denmark)
Svensmark, Henrik; Samuelsen, Mogens Rugholm
1987-01-01
The influence of noise and resonant perturbation on a dynamical system in the vicinity of a period-doubling bifurcation is investigated. It is found that the qualitative dynamics can be revealed by simple considerations of the Poincaré map. These considerations lead to a shift of the bifurcation...
Splitting rivers at their seams: bifurcations and avulsion
Kleinhans, M.G.; Ferguson, R.I.; Lane, S.N.; Hardy, R.J.
2012-01-01
River bifurcations are critical but poorly understood elements of many geomorphological systems. They are integral elements of alluvial fans, braided rivers, fluvial lowland plains, and deltas and control the partitioning of water and sediment through these systems. Bifurcations are commonly unstabl
Identification of Bifurcations from Observations of Noisy Biological Oscillators.
Salvi, Joshua D; Ó Maoiléidigh, Dáibhid; Hudspeth, A J
2016-08-23
Hair bundles are biological oscillators that actively transduce mechanical stimuli into electrical signals in the auditory, vestibular, and lateral-line systems of vertebrates. A bundle's function can be explained in part by its operation near a particular type of bifurcation, a qualitative change in behavior. By operating near different varieties of bifurcation, the bundle responds best to disparate classes of stimuli. We show how to determine the identity of and proximity to distinct bifurcations despite the presence of substantial environmental noise. Using an improved mechanical-load clamp to coerce a hair bundle to traverse different bifurcations, we find that a bundle operates within at least two functional regimes. When coupled to a high-stiffness load, a bundle functions near a supercritical Hopf bifurcation, in which case it responds best to sinusoidal stimuli such as those detected by an auditory organ. When the load stiffness is low, a bundle instead resides close to a subcritical Hopf bifurcation and achieves a graded frequency response-a continuous change in the rate, but not the amplitude, of spiking in response to changes in the offset force-a behavior that is useful in a vestibular organ. The mechanical load in vivo might therefore control a hair bundle's responsiveness for effective operation in a particular receptor organ. Our results provide direct experimental evidence for the existence of distinct bifurcations associated with a noisy biological oscillator, and demonstrate a general strategy for bifurcation analysis based on observations of any noisy system.
THE UNFOLDING OF EQUIVARIANT BIFURCATION PROBLEMS WITH PARAMETERS SYMMETRY
Institute of Scientific and Technical Information of China (English)
高守平; 李养成
2004-01-01
In this paper versal unfolding theorem of multiparameter equivariant bifurcation problem with parameter symmetry is given. The necessary and sufficient condition that unfolding of multiparameter equivariant bifurcation problem with parameter symmetry factors through another is given. The corresponding results in [1]-[6] are generalized.
Identification of Bifurcations from Observations of Noisy Biological Oscillators.
Salvi, Joshua D; Ó Maoiléidigh, Dáibhid; Hudspeth, A J
2016-08-23
Hair bundles are biological oscillators that actively transduce mechanical stimuli into electrical signals in the auditory, vestibular, and lateral-line systems of vertebrates. A bundle's function can be explained in part by its operation near a particular type of bifurcation, a qualitative change in behavior. By operating near different varieties of bifurcation, the bundle responds best to disparate classes of stimuli. We show how to determine the identity of and proximity to distinct bifurcations despite the presence of substantial environmental noise. Using an improved mechanical-load clamp to coerce a hair bundle to traverse different bifurcations, we find that a bundle operates within at least two functional regimes. When coupled to a high-stiffness load, a bundle functions near a supercritical Hopf bifurcation, in which case it responds best to sinusoidal stimuli such as those detected by an auditory organ. When the load stiffness is low, a bundle instead resides close to a subcritical Hopf bifurcation and achieves a graded frequency response-a continuous change in the rate, but not the amplitude, of spiking in response to changes in the offset force-a behavior that is useful in a vestibular organ. The mechanical load in vivo might therefore control a hair bundle's responsiveness for effective operation in a particular receptor organ. Our results provide direct experimental evidence for the existence of distinct bifurcations associated with a noisy biological oscillator, and demonstrate a general strategy for bifurcation analysis based on observations of any noisy system. PMID:27558723
Effects of Hard Limits on Bifurcation, Chaos and Stability
Institute of Scientific and Technical Information of China (English)
Rui-qi Wang; Ji-cai Huang
2004-01-01
An SMIB model in the power systems,especially that concering the effects of hard limits on bifurcations, chaos and stability is studied.Parameter conditions for bifurcations and chaos in the absence of hard limits are compared with those in the presence of hard limits.It has been proved that hard limits can affect system stability.We find that (1)hard limits can change unstable equilibrium into stable one;(2)hard limits can change stability of limit cycles induced by Hopf bifurcation;(3)persistence of hard limits can stabilize divergent trajectory to a stable equilibrium or limit cycle;(4)Hopf bifurcation occurs before SN bifurcation,so the system collapse can be controlled before Hopf bifurcation occurs.We also find that suitable limiting values of hard limits can enlarge the feasibility region.These results are based on theoretical analysis and numerical simulations, such as condition for SNB and Hopf bifurcation,bifurcation diagram,trajectories,Lyapunov exponent,Floquet multipliers,dimension of attractor and so on.
Bifurcation Analysis in a Delayed Diffusive Leslie-Gower Model
Directory of Open Access Journals (Sweden)
Shuling Yan
2013-01-01
Full Text Available We investigate a modified delayed Leslie-Gower model under homogeneous Neumann boundary conditions. We give the stability analysis of the equilibria of the model and show the existence of Hopf bifurcation at the positive equilibrium under some conditions. Furthermore, we investigate the stability and direction of bifurcating periodic orbits by using normal form theorem and the center manifold theorem.
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 tida
Views on the Hopf bifurcation with respect to voltage instabilities
Energy Technology Data Exchange (ETDEWEB)
Roa-Sepulveda, C.A. [Universidad de Concepcion, Concepcion (Chile). Dept. de Ingenieria Electrica; Knight, U.G. [Imperial Coll. of Science and Technology, London (United Kingdom). Dept. of Electrical and Electronic Engineering
1994-12-31
This paper presents a sensitivity study of the Hopf bifurcation phenomenon which can in theory appear in power systems, with reference to the dynamics of the process and the impact of demand characteristics. Conclusions are drawn regarding power levels at which these bifurcations could appear and concern the concept of the imaginary axis as a `hard` limit eigenvalue analyses. (author) 20 refs., 31 figs.
Bifurcation of the femur with tibial agenesis and additional anomalies
van der Smagt, JJ; Bos, CFA; van Haeringen, A; Hogendoorn, PCW; Breuning, MH
2005-01-01
Bifurcation of the femur and tibial agenesis are rare anomalies and have been described in both the Gollop-Wolfgang Complex and the tibial agenesis-ectrodactyly syndrome. We report on two patients with bifurcation of the femur and tibial agenesis. Hand ectrodactyly was seen in one of these patients.
Magnetic navigation system assisted stenting of coronary bifurcation lesions
C. Simsek (Cihan); M. Magro (Michael); M.S. Patterson (Mark); Y. Onuma (Yosinobu); I. Ciampichetti (Isabella); S. van Weenen (Sander); R.T. van Domburg (Ron); P.W.J.C. Serruys (Patrick); H. Boersma (Eric); R.J.M. van Geuns (Robert Jan)
2011-01-01
textabstractAims: Magnetic guidewire assisted percutaneous coronary interventions (MPCI) could have certain advantages in coronary bifurcation lesions. We aimed to report the angiographic characteristics of the bifurcation lesions, as well as the procedural and clinical outcomes of the MPCI patients
Streamline topologies and their bifurcations for mixed convective peristaltic flow
Directory of Open Access Journals (Sweden)
Z. Asghar
2015-09-01
Full Text Available In this work our focus is on streamlines patterns and their bifurcations for mixed convective peristaltic flow of Newtonian fluid with heat transfer. The flow is considered in a two dimensional symmetric channel and the governing equations are simplified under widely taken assumptions of large wavelength and low Reynolds number in a wave frame of reference. In order to study the streamlines patterns, a system of nonlinear autonomous differential equations are established and dynamical systems approach is used to discuss the local bifurcations and their topological changes. We have discussed all types of bifurcations and their topological changes are presented graphically. We found that the vortices contract along the vertical direction whereas they expand along horizontal direction. A global bifurcations diagram is used to summarize the bifurcations. The trapping and backward flow regions are mainly affected by increasing Grashof number and constant heat source parameter in such a way that trapping region increases whereas backward flow region shrinks.
Critical bifurcation surfaces of 3D discrete dynamics
Directory of Open Access Journals (Sweden)
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.
Coronary bifurcation lesions treated with simple or complex stenting
DEFF Research Database (Denmark)
Behan, Miles W; Holm, Niels R; de Belder, Adam J;
2016-01-01
AIMS: Randomized trials of coronary bifurcation stenting have shown better outcomes from a simple (provisional) strategy rather than a complex (planned two-stent) strategy in terms of short-term efficacy and safety. Here, we report the 5-year all-cause mortality based on pooled patient-level data...... from two large bifurcation coronary stenting trials with similar methodology: the Nordic Bifurcation Study (NORDIC I) and the British Bifurcation Coronary Study: old, new, and evolving strategies (BBC ONE). METHODS AND RESULTS: Both multicentre randomized trials compared simple (provisional T...... groups were similar in terms of patient and lesion characteristics. Five-year mortality was lower among patients who underwent a simple strategy rather than a complex strategy [17 patients (3.8%) vs. 31 patients (7.0%); P = 0.04]. CONCLUSION: For coronary bifurcation lesions, a provisional single...
Symmetric/asymmetric bifurcation behaviours of a bogie system
DEFF Research Database (Denmark)
Xue-jun, Gao; Ying-hui, Li; Yuan, Yue;
2013-01-01
Based on the bifurcation and stability theory of dynamical systems, the symmetric/asymmetric bifurcation behaviours and chaotic motions of a railway bogie system under a complex nonlinear wheel–rail contact relation are investigated in detail by the ‘resultant bifurcation diagram’ method...... with slowly increasing and decreasing speed. It is found that the stationary equilibrium solution and the periodic motions coexist due to the sub-critical Hopf bifurcation in the railway bogie system. It is also found that multiple solutions coexist in many speed ranges. The coexistence of multiple solutions...... may result in a jump and hysteresis of the oscillating amplitude for different kinds of disturbances. It should be avoided in the normal operation. Furthermore, it is found that symmetry-breaking of the system through a pitchfork bifurcation leads to asymmetric chaotic motions in the railway bogie...
Bifurcation behaviours of peak current controlled PFC boost converter
Institute of Scientific and Technical Information of China (English)
Ren Hai-Peng; Liu Ding
2005-01-01
Bifurcation behaviours of the peak current controlled power-factor-correction (PFC) boost converter, including fast-scale instability and low-frequency bifurcation, are investigated in this paper. Conventionally, the PFC converter is analysed in continuous conduction mode (CCM). This prevents us from recognizing the overall dynamics of the converter. It has been pointed out that the discontinuous conduction mode (DCM) can occur in the PFC boost converter, especially in the light load condition. Therefore, the DCM model is employed to analyse the PFC converter to cover the possible DCM operation. By this way, the low-frequency bifurcation diagram is derived, which makes the route from period-double bifurcation to chaos clear. The bifurcation diagrams versus the load resistance and the output capacitance also indicate the stable operation boundary of the converter, which is useful for converter design.
Bifurcations of emerging patterns in the presence of additive noise.
Agez, Gonzague; Clerc, Marcel G; Louvergneaux, Eric; Rojas, René G
2013-04-01
A universal description of the effects of additive noise on super- and subcritical spatial bifurcations in one-dimensional systems is theoretically, numerically, and experimentally studied. The probability density of the critical spatial mode amplitude is derived. From this generalized Rayleigh distribution we predict the shape of noisy bifurcations by means of the most probable value of the critical mode amplitude. Comparisons with numerical simulations are in quite good agreement for cubic or quintic amplitude equations accounting for stochastic supercritical bifurcation and for cubic-quintic amplitude equation accounting for stochastic subcritical bifurcation. Experimental results obtained in a one-dimensional Kerr-like slice subjected to optical feedback confirm the analytical expression prediction for the supercritical bifurcation shape.
Comments on the Bifurcation Structure of 1D Maps
DEFF Research Database (Denmark)
Belykh, V.N.; Mosekilde, Erik
1997-01-01
The paper presents a complementary view on some of the phenomena related to the bifurcation structure of unimodal maps. An approximate renormalization theory for the period-doubling cascade is developed, and a mapping procedure is established that accounts directly for the box-within-a-box struct......The paper presents a complementary view on some of the phenomena related to the bifurcation structure of unimodal maps. An approximate renormalization theory for the period-doubling cascade is developed, and a mapping procedure is established that accounts directly for the box......-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...
Bifurcations and Stability Boundary of a Power System
Institute of Scientific and Technical Information of China (English)
Ying-hui Gao
2004-01-01
A single-axis ux decay model including an excitation control model proposed in [12,14,16] is studied. As the bifurcation parameter P m (input power to the generator) varies, the system exhibits dynamics emerging from static and dynamic bifurcations which link with system collapse. We show that the equilibrium point of the system undergoes three bifurcations: one saddle-node bifurcation and two Hopf bifurcations. The state variables dominating system collapse are different for different critical points, and the excitative control may play an important role in delaying system from collapsing. Simulations are presented to illustrate the dynamical behavior associated with the power system stability and collapse. Moreover, by computing the local quadratic approximation of the 5-dimensional stable manifold at an order 5 saddle point, an analytical expression for the approximate stability boundary is worked out.
Bifurcation of transition paths induced by coupled bistable systems
Tian, Chengzhe; Mitarai, Namiko
2016-06-01
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.
Bifurcation behaviours of peak current controlled PFC boost converter
Ren, Hai-Peng; Liu, Ding
2005-07-01
Bifurcation behaviours of the peak current controlled power-factor-correction (PFC) boost converter, including fast-scale instability and low-frequency bifurcation, are investigated in this paper. Conventionally, the PFC converter is analysed in continuous conduction mode (CCM). This prevents us from recognizing the overall dynamics of the converter. It has been pointed out that the discontinuous conduction mode (DCM) can occur in the PFC boost converter, especially in the light load condition. Therefore, the DCM model is employed to analyse the PFC converter to cover the possible DCM operation. By this way, the low-frequency bifurcation diagram is derived, which makes the route from period-double bifurcation to chaos clear. The bifurcation diagrams versus the load resistance and the output capacitance also indicate the stable operation boundary of the converter, which is useful for converter design.
Ecological consequences of global bifurcations in some food chain models.
van Voorn, George A K; Kooi, Bob W; Boer, Martin P
2010-08-01
Food chain models of ordinary differential equations (ode's) are often used in ecology to gain insight in the dynamics of populations of species, and the interactions of these species with each other and their environment. One powerful analysis technique is bifurcation analysis, focusing on the changes in long-term (asymptotic) behaviour under parameter variation. For the detection of local bifurcations there exists standardised software, but until quite recently most software did not include any capabilities for the detection and continuation of global bifurcations. We focus here on the occurrence of global bifurcations in four food chain models, and discuss the implications of their occurrence. In two stoichiometric models (one piecewise continuous, one smooth) there exists a homoclinic bifurcation, that results in the disappearance of a limit cycle attractor. Instead, a stable positive equilibrium becomes the global attractor. The models are also capable of bistability. In two three-dimensional models a Shil'nikov homoclinic bifurcation functions as the organising centre of chaos, while tangencies of homoclinic cycle-to-cycle connections 'cut' the chaotic attractors, which is associated with boundary crises. In one model this leads to extinction of the top predator, while in the other model hysteresis occurs. The types of ecological events occurring because of a global bifurcation will be categorized. Global bifurcations are always catastrophic, leading to the disappearance or merging of attractors. However, there is no 1-on-1 coupling between global bifurcation type and the possible ecological consequences. This only emphasizes the importance of including global bifurcations in the analysis of food chain models.
Ecological consequences of global bifurcations in some food chain models.
van Voorn, George A K; Kooi, Bob W; Boer, Martin P
2010-08-01
Food chain models of ordinary differential equations (ode's) are often used in ecology to gain insight in the dynamics of populations of species, and the interactions of these species with each other and their environment. One powerful analysis technique is bifurcation analysis, focusing on the changes in long-term (asymptotic) behaviour under parameter variation. For the detection of local bifurcations there exists standardised software, but until quite recently most software did not include any capabilities for the detection and continuation of global bifurcations. We focus here on the occurrence of global bifurcations in four food chain models, and discuss the implications of their occurrence. In two stoichiometric models (one piecewise continuous, one smooth) there exists a homoclinic bifurcation, that results in the disappearance of a limit cycle attractor. Instead, a stable positive equilibrium becomes the global attractor. The models are also capable of bistability. In two three-dimensional models a Shil'nikov homoclinic bifurcation functions as the organising centre of chaos, while tangencies of homoclinic cycle-to-cycle connections 'cut' the chaotic attractors, which is associated with boundary crises. In one model this leads to extinction of the top predator, while in the other model hysteresis occurs. The types of ecological events occurring because of a global bifurcation will be categorized. Global bifurcations are always catastrophic, leading to the disappearance or merging of attractors. However, there is no 1-on-1 coupling between global bifurcation type and the possible ecological consequences. This only emphasizes the importance of including global bifurcations in the analysis of food chain models. PMID:20447411
Climate bifurcation during the last deglaciation?
Directory of Open Access Journals (Sweden)
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
Bifurcated SEN with Fluid Flow Conditioners
Directory of Open Access Journals (Sweden)
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.
Chua Corsage Memristor Oscillator via Hopf Bifurcation
Mannan, Zubaer Ibna; Choi, Hyuncheol; Kim, Hyongsuk
This paper demonstrates that the Chua Corsage Memristor, when connected in series with an inductor and a battery, oscillates about a locally-active operating point located on the memristor’s DC V-I curve. On the operating point, a small-signal equivalent circuit is derived via a Taylor series expansion. The small-signal admittance Y (s,V ) is derived from the small-signal equivalent circuit and the value of inductance is determined at a frequency where the real part of the admittance ReY (iω) of the small-signal equivalent circuit of Chua Corsage Memristor is zero. Oscillation of the circuit is analyzed via an in-depth application of the theory of Local Activity, Edge of Chaos and the Hopf-bifurcation.
Bifurcations and Patterns in Nonlinear Dissipative Systems
Energy Technology Data Exchange (ETDEWEB)
Guenter Ahlers
2005-05-27
This project consists of experimental investigations of heat transport, pattern formation, and bifurcation phenomena in non-linear non-equilibrium fluid-mechanical systems. These issues are studies in Rayleigh-B\\'enard convection, using both pure and multicomponent fluids. They are of fundamental scientific interest, but also play an important role in engineering, materials science, ecology, meteorology, geophysics, and astrophysics. For instance, various forms of convection are important in such diverse phenomena as crystal growth from a melt with or without impurities, energy production in solar ponds, flow in the earth's mantle and outer core, geo-thermal stratifications, and various oceanographic and atmospheric phenomena. Our work utilizes computer-enhanced shadowgraph imaging of flow patterns, sophisticated digital image analysis, and high-resolution heat transport measurements.
The Persistence of a Slow Manifold with Bifurcation
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall; Palmer, P.; Robert, M.
2012-01-01
his paper considers the persistence of a slow manifold with bifurcation in a slow-fast two degree of freedom Hamiltonian system. In particular, we consider a system with a supercritical pitchfork bifurcation in the fast space which is unfolded by the slow coordinate. The model system is motivated...... by tethered satellites. It is shown that an almost full measure subset of a neighborhood of the slow manifold's normally elliptic branches persists in an adiabatic sense. We prove this using averaging and a blow-up near the bifurcation....
Synchronization and Bifurcation of General Complex Dynamical Networks
Institute of Scientific and Technical Information of China (English)
SUN Wei-Gang; XU Cong-Xiang; LI Chang-Pin; FANG Jin-Qing
2007-01-01
In the present paper, synchronization and bifurcation of general complex dynamical networks are investigated. We mainly focus on networks with a somewhat general coupling matrix, i.e., the sum of each row equals a nonzero constant u. We derive a result that the networks can reach a new synchronous state, which is not the asymptotic limit set determined by the node equation. At the synchronous state, the networks appear bifurcation if we regard the constant u as a bifurcation parameter. Numerical examples are given to illustrate our derived conclusions.
Delay Induced Hopf Bifurcation of Small-World Networks
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper, the stability and the Hopf bifurcation of small-world networks with time delay are studied. By analyzing the change of delay, we obtain several sufficient conditions on stable and unstable properties. When the delay passes a critical value, a Hopf bifurcation may appear. Furthermore, the direction and the stability of bifurcating periodic solutions are investigated by the normal form theory and the center manifold reduction. At last, by numerical simulations, we further illustrate the effectiveness of theorems in this paper.
Bifurcation of learning and structure formation in neuronal maps
DEFF Research Database (Denmark)
Marschler, Christian; Faust-Ellsässer, Carmen; Starke, Jens;
2014-01-01
to map formation in the laminar nucleus of the barn owl's auditory system. Using equation-free methods, we perform a bifurcation analysis of spatio-temporal structure formation in the associated synaptic-weight matrix. This enables us to analyze learning as a bifurcation process and follow the unstable...... states as well. A simple time translation of the learning window function shifts the bifurcation point of structure formation and goes along with traveling waves in the map, without changing the animal's sound localization performance....
Systematic experimental exploration of bifurcations with noninvasive control.
Barton, D A W; Sieber, J
2013-05-01
We present a general method for systematically investigating the dynamics and bifurcations of a physical nonlinear experiment. In particular, we show how the odd-number limitation inherent in popular noninvasive control schemes, such as (Pyragas) time-delayed or washout-filtered feedback control, can be overcome for tracking equilibria or forced periodic orbits in experiments. To demonstrate the use of our noninvasive control, we trace out experimentally the resonance surface of a periodically forced mechanical nonlinear oscillator near the onset of instability, around two saddle-node bifurcations (folds) and a cusp bifurcation.
Bifurcation diagrams in relation to synchronization in chaotic systems
Indian Academy of Sciences (India)
Debabrata Dutta; Sagar Chakraborty
2010-06-01
We numerically study some of the three-dimensional dynamical systems which exhibit complete synchronization as well as generalized synchronization to show that these systems can be conveniently partitioned into equivalent classes facilitating the study of bifurcation diagrams within each class. We demonstrate how bifurcation diagrams may be helpful in predicting the nature of the driven system by knowing the bifurcation diagram of driving system and vice versa. The study is extended to include the possible generalized synchronization between elements of two different equivalent classes by taking the Rössler-driven-Lorenz-system as an example.
Optimization Design and Application of Underground Reinforced Concrete Bifurcation Pipe
Directory of Open Access Journals (Sweden)
Chao Su
2015-01-01
Full Text Available Underground reinforced concrete bifurcation pipe is an important part of conveyance structure. During construction, the workload of excavation and concrete pouring can be significantly decreased according to optimized pipe structure, and the engineering quality can be improved. This paper presents an optimization mathematical model of underground reinforced concrete bifurcation pipe structure according to real working status of several common pipe structures from real cases. Then, an optimization design system was developed based on Particle Swarm Optimization algorithm. Furthermore, take the bifurcation pipe of one hydropower station as an example: optimization analysis was conducted, and accuracy and stability of the optimization design system were verified successfully.
FFT Bifurcation Analysis of Routes to Chaos via Quasiperiodic Solutions
Directory of Open Access Journals (Sweden)
L. Borkowski
2015-01-01
Full Text Available The dynamics of a ring of seven unidirectionally coupled nonlinear Duffing oscillators is studied. We show that the FFT analysis presented in form of a bifurcation graph, that is, frequency distribution versus a control parameter, can provide a valuable and helpful complement to the corresponding typical bifurcation diagram and the course of Lyapunov exponents, especially in context of detailed identification of the observed attractors. As an example, bifurcation analysis of routes to chaos via 2-frequency and 3-frequency quasiperiodicity is demonstrated.
Arctic melt ponds and bifurcations in the climate system
Sudakov, Ivan; Golden, Kenneth M
2014-01-01
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 simple 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 nonlinear phase transition model for melt ponds, and bifurcation analysis of a simple climate model with ice - albedo feedback as the key mechanism driving the system to a potential bifurcation point.
Statistical multimoment bifurcations in random-delay coupled swarms
Mier-y-Teran-Romero, Luis; Lindley, Brandon; Schwartz, Ira B.
2012-11-01
We study the effects of discrete, randomly distributed time delays on the dynamics of a coupled system of self-propelling particles. Bifurcation analysis on a mean field approximation of the system reveals that the system possesses patterns with certain universal characteristics that depend on distinguished moments of the time delay distribution. Specifically, we show both theoretically and numerically that although bifurcations of simple patterns, such as translations, change stability only as a function of the first moment of the time delay distribution, more complex patterns arising from Hopf bifurcations depend on all of the moments.
Bifurcations of a parametrically excited oscillator with strong nonlinearity
Institute of Scientific and Technical Information of China (English)
唐驾时; 符文彬; 李克安
2002-01-01
A parametrically excited oscillator with strong nonlinearity, including van der Poi and Duffing types, is studied for static bifurcations. The applicable range of the modified Lindstedt-Poincaré method is extended to 1/2 subharmonic resonance systems. The bifurcation equation of a strongly nonlinear oscillator, which is transformed into a small parameter system, is determined by the multiple scales method. On the basis of the singularity theory, the transition set and the bifurcation diagram in various regions of the parameter plane are analysed.
Seasonal variability of the bifurcation of the North Equatorial Current
Institute of Scientific and Technical Information of China (English)
JU Qiang-chang; JIANG Song; TIAN Ji-wei; KONG Ling-hai; NI Guo-xi
2013-01-01
Seasonal variability of the bifurcation of the North Equatorial Current (NEC) is studied by constructing the analytic solution for the time-dependent horizontal linear shallow water quasi-geostrophic equations.Using the Florida State University wind data from 1961 through 1992,we find that the bifurcation latitude of the NEC changes with seasons.Furthermore,it is shown that the NEC bifurcation is at its southernmost latitude (12.7°N) in June and the northernmost latitude (14.4° N) in November.
Bifurcation control of nonlinear oscillator in primary and secondary resonance
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A weakly nonlinear oscillator was modeled by a sort of differential equation, a saddle-node bifurcation was found in case of primary and secondary resonance. To control the jumping phenomena and the unstable region of the nonlinear oscillator, feedback controllers were designed. Bifurcation control equations were obtained by using the multiple scales method. And through the numerical analysis, good controller could be obtained by changing the feedback control gain. Then a feasible way of further research of saddle-node bifurcation was provided. Finally, an example shows that the feedback control method applied to the hanging bridge system of gas turbine is doable.
Computational simulations in coronary bifurcations: Paving the future of interventional planning.
Collet, Carlos; Serruys, Patrick W
2016-06-01
Anatomical evaluation is of paramount importance in the treatment of bifurcation lesions. Left main coronary artery bifurcation geometry differs from left anterior descending artery/diagonal and circumflex artery/obtuse marginal bifurcations. Individualized approach with pre-procedural planning has the potential to improve outcomes after bifurcation treatment.
Codimension-Two Bifurcation Analysis in Hindmarsh-Rose Model with Two Parameters
Institute of Scientific and Technical Information of China (English)
DUAN Li-Xia; LU Qi-Shao
2005-01-01
@@ Bifurcation phenomena in a Hindmarsh-Rose neuron model are investigated. Special attention is paid to the bifurcation structures off two parameters, where codimension-two generalized-Hopf bifurcation and fold-Hopf bifurcation occur. The classification offiring patterns as well as the transition mechanism in different regions on the parameter plane are obtained.
Supercritical as well as subcritical Hopf bifurcation in nonlinear flutter systems
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
The Hopf bifurcations of an airfoil flutter system with a cubic nonlinearity are investigated,with the flow speed as the bifurcation parameter.The center manifold theory and complex normal form method are used to obtain the bifurcation equation.Interestingly,for a certain linear pitching stiffness the Hopf bifurcation is both supercritical and subcritical.It is found,mathematically,this is caused by the fact that one coefficient in the bifurcation equation does not contain the first power of the bifurcation parameter.The solutions of the bifurcation equation are validated by the equivalent linearization method and incremental harmonic balance method.
Dynamical Analysis of Nonlinear Bifurcation in Current-Controlled Boost Converter
Institute of Scientific and Technical Information of China (English)
Quan-Min Niu; Bo Zhang; Yan-Ling Li
2007-01-01
Based on the bifurcation theory in nonlinear dynamics, this paper analyzes quantitatively period solution dynamic characteristic. In particular, the ones of period1 and period2 solutions are deeply studied. From locus of Jacobian matrix eigenvalue, we conclude that the bifurcations between period1 and period2 solutions are pitchfork bifurcations while the bifurcations between period2 and period3 solutions are border collision bifurcations. The double period bifurcation condition is verified from complex plane locus of eigenvalues,furthermore, the necessary condition occurred pitchfork bifurcation is obtained from the cause of border collisionbifurcation.
Hopf bifurcation and multistability in a system of phase oscillators
Astakhov, Sergey; Fujiwara, Naoya; Gulay, Artem; Tsukamoto, Naofumi; Kurths, Jürgen
2013-09-01
We study the phase reduction of two coupled van der Pol oscillators with asymmetric repulsive coupling under an external harmonic force. We show that the system of two phase oscillators undergoes a Hopf bifurcation and possesses multistability on a 2π-periodic phase plane. We describe the bifurcation mechanisms of formation of multistability in the phase-reduced system and show that the Andronov-Hopf bifurcation in the phase-reduced system is not an artifact of the reduction approach but, indeed, has its prototype in the nonreduced system. The bifurcational mechanisms presented in the paper enable one to describe synchronization effects in a wide class of interacting systems with repulsive coupling e.g., genetic oscillators.
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...
Classification of boundary equilibrium bifurcations in planar Filippov systems.
Glendinning, Paul
2016-01-01
If a family of piecewise smooth systems depending on a real parameter is defined on two different regions of the plane separated by a switching surface, then a boundary equilibrium bifurcation occurs if a stationary point of one of the systems intersects the switching surface at a critical value of the parameter. We derive the leading order terms of a normal form for boundary equilibrium bifurcations of planar systems. This makes it straightforward to derive a complete classification of the bifurcations that can occur. We are thus able to confirm classic results of Filippov [Differential Equations with Discontinuous Right Hand Sides (Kluwer, Dordrecht, 1988)] using different and more transparent methods, and explain why the 'missing' cases of Hogan et al. [Piecewise Smooth Dynamical Systems: The Case of the Missing Boundary Equilibrium Bifurcations (University of Bristol, 2015)] are the only cases omitted in more recent work.
Bifurcation behaviors of catalytic combustion in a micro-channel
Institute of Scientific and Technical Information of China (English)
Wen Zeng; Maozhao Xie; Hongan Maa; Wei Xua
2008-01-01
Bifurcation analysis of ignition and extinction of catalytic combustion in a short micro-channel is carried out with the laminar flow model incorporated as the flow model. The square of transverse Thiele modulus and the realdence time are used as bifurcation parameters. The influences of different parameters on ignition and extinction behavior are investigated. It is shown that all these parameters have great effects on the bifurcation behaviors of ignition and extinction in the short micro-channel. The effects of flow models on bifurcation behaviors of combustion are also analyzed. The results show that in comparison with the fiat velocity profile model, for the case of the laminar flow model, the temperatures of ignition and extinction of combustion ate higher and the unsteady multiple solution region is larger.
Cardiac Alternans Arising from an Unfolded Border-Collision Bifurcation
Zhao, Xiaopeng; Berger, Carolyn M; Krassowska, Wanda; Gauthier, Daniel J
2007-01-01
Following an electrical stimulus, the transmembrane voltage of cardiac tissue rises rapidly and remains at a constant value before returning to the resting value, a phenomenon known as an action potential. When the pacing rate of a periodic train of stimuli is increased above a critical value, the action potential undergoes a period-doubling bifurcation, where the resulting alternation of the action potential duration is known as alternans in the medical literature. Existing cardiac models treat alternans either as a smooth or as a border-collision bifurcation. However, recent experiments in paced cardiac tissue reveal that the bifurcation to alternans exhibits hybrid smooth/nonsmooth behaviors, which can be qualitatively described by a model of so-called unfolded border-collision bifurcation. In this paper, we obtain analytical solutions of the unfolded border-collision model and use it to explore the crossover between smooth and nonsmooth behaviors. Our analysis shows that the hybrid smooth/nonsmooth behavi...
Bifurcation dynamics of the tempered fractional Langevin equation.
Zeng, Caibin; Yang, Qigui; Chen, YangQuan
2016-08-01
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. PMID:27586627
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.
Hopf bifurcation in doubly fed induction generator under vector control
International Nuclear Information System (INIS)
This paper first presents the Hopf bifurcation phenomena of a vector-controlled doubly fed induction generator (DFIG) which is a competitive choice in wind power industry. Using three-phase back-to-back pulse-width-modulated (PWM) converters, DFIG can keep stator frequency constant under variable rotor speed and provide independent control of active and reactive power output. Main results are illustrated by 'exact' cycle-by-cycle simulations. The detailed mathematical model of the closed-loop system is derived and used to analyze the observed bifurcation phenomena. The loci of the Jacobian's eigenvalues are computed and the analysis shows that the system loses stability via a Hopf bifurcation. Moreover, the boundaries of Hopf bifurcation are also given to facilitate the selection of practical parameters for guaranteeing stable operation.
Grazing bifurcation and chaos in response of rubbing rotor
International Nuclear Information System (INIS)
This paper investigates the grazing bifurcation in the nonlinear response of a complex rotor system. For a rotor with overhung disc, step diameter shaft and elastic supports, the motion equations are derived based on the Transition Matrix Method. When the rotor speed increases, the disc will touch the case and lead to rubbing of rotor. When the disc rubs with the case, the elastic force and friction force of the case will make the rotor exhibit nonlinear characteristics. For the piecewise ODEs, the numerical method is applied to obtain its nonlinear response. From the results, the grazing bifurcation, which happens at the moment of touching between disc and case, can be observed frequently. The grazing bifurcation can lead to the jump between periodic orbits. The response can go to chaos from periodic motion under grazing bifurcation. When grazing occurs, response can become quasi-period from period
Bifurcation dynamics of the tempered fractional Langevin equation
Zeng, Caibin; Yang, Qigui; Chen, YangQuan
2016-08-01
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.
2D bifurcations and Newtonian properties of memristive Chua's circuits
Marszalek, W.; Podhaisky, H.
2016-01-01
Two interesting properties of Chua's circuits are presented. First, two-parameter bifurcation diagrams of Chua's oscillatory circuits with memristors are presented. To obtain various 2D bifurcation images a substantial numerical effort, possibly with parallel computations, is needed. The numerical algorithm is described first and its numerical code for 2D bifurcation image creation is available for free downloading. Several color 2D images and the corresponding 1D greyscale bifurcation diagrams are included. Secondly, Chua's circuits are linked to Newton's law φ ''= F(t,φ,φ')/m with φ=\\text{flux} , constant m > 0, and the force term F(t,φ,φ') containing memory terms. Finally, the jounce scalar equations for Chua's circuits are also discussed.
Bifurcation methods of dynamical systems for handling nonlinear wave equations
Indian Academy of Sciences (India)
Dahe Feng; Jibin Li
2007-05-01
By using the bifurcation theory and methods of dynamical systems to construct the exact travelling wave solutions for nonlinear wave equations, some new soliton solutions, kink (anti-kink) solutions and periodic solutions with double period are obtained.
Institute of Scientific and Technical Information of China (English)
Liu Su-Hua; Tang Jia-Shi; Qin Jin-Qi; Yin Xiao-Bo
2008-01-01
Bifurcation characteristics of the Langford system in a general form are systematically analysed,and nonlinear controls of periodic solutions changing into invariant tori in this system are achieved.Analytical relationship between control gain and bifurcation parameter is obtained.Bifurcation diagrams are drawn,showing the results of control for secondary Hopf bifurcation and sequences of bifurcations route to chaos.Numerical simulations of quasi-periodic tori validate analytic predictions.
Institute of Scientific and Technical Information of China (English)
Pengnian CHEN; Huashu QIN; Shengwei MEI
2005-01-01
This paper deals with the problems of bifurcation suppression and bifurcation suppression with stability of nonlinear systems. Necessary conditions and sufficient conditions for bifurcation suppression via dynamic output feedback are presented;Sufficient conditions for bifurcation suppression with stability via dynamic output feedback are obtained. As an application, a dynamic compensator, which guarantees that the bifurcation point of rotating stall in axial flow compressors is stably suppressed, is constructed.
Subcritical dynamo bifurcation in the Taylor Green flow
Ponty, Yannick; Dubrulle, Berengere; Daviaud, François; Pinton, Jean-François
2007-01-01
We report direct numerical simulations of dynamo generation for flow generated using a Taylor-Green forcing. We find that the bifurcation is subcritical, and show its bifurcation diagram. We connect the associated hysteretic behavior with hydrodynamics changes induced by the action of the Lorentz force. We show the geometry of the dynamo magnetic field and discuss how the dynamo transition can be induced when an external field is applied to the flow.
Bifurcations and chaos control in discrete small-world networks
Institute of Scientific and Technical Information of China (English)
Li Ning; Sun Hai-Yi; Zhang Qing-Ling
2012-01-01
An impulsive delayed feedback control strategy to control period-doubling bifurcations and chaos is proposed.The control method is then applied to a discrete small-world network model.Qualitative analyses and simulations show that under a generic condition,the bifurcations and the chaos can be delayed or eliminated completely.In addition,the periodic orbits embedded in the chaotic attractor can be stabilized.
Iterative Controller Tuning for Process with Fold Bifurcations
DEFF Research Database (Denmark)
Huusom, Jakob Kjøbsted; Poulsen, Niels Kjølstad; Jørgensen, Sten Bay
2007-01-01
Processes involving fold bifurcation are notoriously difficult to control in the vicinity of the fold where most often optimal productivity is achieved . In cases with limited process insight a model based control synthesis is not possible. This paper uses a data driven approach with an improved...... version of iterative feedback tuning to optimizing a closed loop performance criterion, as a systematic tool for tuning process with fold bifurcations....
A Bifurcation Monte Carlo Scheme for Rare Event Simulation
Liu, Hongliang
2016-01-01
The bifurcation method is a way to do rare event sampling -- to estimate the probability of events that are too rare to be found by direct simulation. We describe the bifurcation method and use it to estimate the transition rate of a double well potential problem. We show that the associated constrained path sampling problem can be addressed by a combination of Crooks-Chandler sampling and parallel tempering and marginalization.
Experimental Bifurcation Analysis Using Control-Based Continuation
DEFF Research Database (Denmark)
Bureau, Emil; Starke, Jens
The focus of this thesis is developing and implementing techniques for performing experimental bifurcation analysis on nonlinear mechanical systems. The research centers around the newly developed control-based continuation method, which allows to systematically track branches of stable and unsta......The focus of this thesis is developing and implementing techniques for performing experimental bifurcation analysis on nonlinear mechanical systems. The research centers around the newly developed control-based continuation method, which allows to systematically track branches of stable...
Optimization Design and Application of Underground Reinforced Concrete Bifurcation Pipe
Chao Su; Zhenxue Zhu; Yangyang Zhang; Niantang Jiang
2015-01-01
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 optimiza...
Bunch lengthening with bifurcation in electron storage rings
Energy Technology Data Exchange (ETDEWEB)
Kim, Eun-San; Hirata, Kohji [National Lab. for High Energy Physics, Tsukuba, Ibaraki (Japan)
1996-08-01
The mapping which shows equilibrium particle distribution in synchrotron phase space for electron storage rings is discussed with respect to some localized constant wake function based on the Gaussian approximation. This mapping shows multi-periodic states as well as double bifurcation in dynamical states of the equilibrium bunch length. When moving around parameter space, the system shows a transition/bifurcation which is not always reversible. These results derived by mapping are confirmed by multiparticle tracking. (author)
BIFURCATIONS OF ROUGH 3-POINT-LOOP WITH HIGHER DIMENSIONS
Institute of Scientific and Technical Information of China (English)
金银来; 朱德明; 郑庆玉
2003-01-01
The authors study the bifurcation problems of rough heteroclinic loop connecting threesaddle points for the case β1 ＞ 1, β2 ＞ 1, β3 ＜ 1 and β1β2β3 ＜ 1. The existence, number, co-existence and incoexistence of 2-point-loop, 1-homoclinic orbit and 1-periodic orbit are studied.Meanwhile, the bifurcation surfaces and existence regions are given.
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.
Application of Bifurcation Theory to Subsynchronous Resonance in Power Systems
Harb, Ahmad M.
1996-01-01
A bifurcation analysis is used to investigate the complex dynamics of two heavily loaded single-machine-infinite-busbar power systems modeling the characteristics of the BOARDMAN generator with respect to the rest of the North-Western American Power System and the CHOLLA$#$ generator with respect to the SOWARO station. In the BOARDMAN system, we show that there are three Hopf bifurcations at practical co...
Noise Delays Bifurcation in a Positively Coupled Neural Circuit
Gutkin, Boris; Hely, Tim; Jost, Juergen
2000-01-01
We report a noise induced delay of bifurcation in a simple pulse-coupled neural circuit. We study the behavior of two neural oscillators, each individually governed by saddle-node dynamics, with reciprocal excitatory synaptic connections. In the deterministic circuit, the synaptic current amplitude acts as a control parameter to move the circuit from a mono-stable regime through a bifurcation into a bistable regime. In this regime stable sustained anti-phase oscillations in both neurons coexi...
Subcritical dynamo bifurcation in the Taylor Green flow
Ponty, Yannick; Laval, Jean-Phillipe; Dubrulle, Berengere; Daviaud, François; Pinton, Jean-François
2007-01-01
4 pages We report direct numerical simulations of dynamo generation for flow generated using a Taylor-Green forcing. We find that the bifurcation is subcritical, and show its bifurcation diagram. We connect the associated hysteretic behavior with hydrodynamics changes induced by the action of the Lorentz force. We show the geometry of the dynamo magnetic field and discuss how the dynamo transition can be induced when an external field is applied to the flow.
Effects of Bifurcations on Aft-Fan Engine Nacelle Noise
Nark, Douglas M.; Farassat, Fereidoun; Pope, D. Stuart; Vatsa, Veer N.
2004-01-01
Aft-fan engine nacelle noise is a significant factor in the increasingly important issue of aircraft community noise. The ability to predict such noise within complex duct geometries is a valuable tool in studying possible noise attenuation methods. A recent example of code development for such predictions is the ducted fan noise propagation and radiation code CDUCT-LaRC. This work focuses on predicting the effects of geometry changes (i.e. bifurcations, pylons) on aft fan noise propagation. Beginning with simplified geometries, calculations show that bifurcations lead to scattering of acoustic energy into higher order modes. In addition, when circumferential mode number and the number of bifurcations are properly commensurate, bifurcations increase the relative importance of the plane wave mode near the exhaust plane of the bypass duct. This is particularly evident when the bypass duct surfaces include acoustic treatment. Calculations involving more complex geometries further illustrate that bifurcations and pylons clearly affect modal content, in both propagation and radiation calculations. Additionally, results show that consideration of acoustic radiation results may provide further insight into acoustic treatment effectiveness for situations in which modal decomposition may not be straightforward. The ability of CDUCT-LaRC to handle complex (non-axisymmetric) multi-block geometries, as well as axially and circumferentially segmented liners, allows investigation into the effects of geometric elements (bifurcations, pylons).
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...
Prolegomena to a theory of bifurcating universes
International Nuclear Information System (INIS)
We outline a framework for describing the bifurcation of the universe into disconnected pieces, and formulate criteria for a system in which such phenomena occur, to describe local quantum physics in a single connected universe. The formalism is a four-dimensional analog of string field theory which we call Universal Field Theory (UFT). We argue that local dynamics in a single universe is a good approximation to UFT if the universal field is classical and if the vertex for emission of a new connected component of the universe is concentrated on universes of small volume. We show that classical UFT is equivalent to a Wheeler-DeWitt equation for a single connected universe plus a set of nonlocal gap equations for the couplings in the spacetime lagrangian. The effective action must be stationary with respect to the couplings. Nonlocality shows up only at short distances. We solve the equation for the low-energy cosmological constant and show that if the universe undergoes substantial inflation then the cosmological constant is determined to be negative and very small. Its precise value may depend on the fate of nonrelativistic matter in the very late stages of universal expansion. Finally, we argue that corrections to the classical UFT are nonlocal and must be suppressed if the theory is to make sense. This may be the reason that supersymmetric vacua of string theory are not realized in nature. (orig.)
Bifurcation readout of a Josephson phase qubit
International Nuclear Information System (INIS)
The standard method to read out a Josephson phase qubit is using a dc-SQUID to measure the state-dependent magnetic flux of the qubit by switching to the non-superconducting state. This process generates heat directly on the qubit chip and quasi-particles in the circuitry. Both effects require a relatively long cool-down time after each switching event. This, together with the time needed to ramp up the bias current of the SQUID limits the repetition rate of the experiment. In our ongoing experiments we replace the standard readout scheme by a SQUID shunted by a capacitor. This nonlinear resonator is operated close to its bifurcation point between two oscillating states which depend on the qubit flux. The measurement is done by detecting either the resonance amplitude or phase shift of the reflected probe signal. We verified that our SQUID resonator works as linear resonator for low excitation powers and observed the periodic dependence of the resonance frequency on the externally applied magnetic flux. For higher excitation powers the device shows a hysteretic behavior between the two oscillating states. Current experiments are focused on a pulsed rf-readout to measure coherent evolution of the qubit states. We hope to achieve longer coherence times, perform faster measurements, and test non-destructive measurement schemes with Josephson phase qubits.
Stability and bifurcation of quasiparallel Alfven solitons
Hamilton, R. L.; Kennel, C. F.; Mjolhus, E.
1992-01-01
The inverse scattering transformation (IST) is used to study the one-parameter and two-parameter soliton families of the derivative nonlinear Schroedinger (DNLS) equation. The two-parameter soliton family is determined by the discrete complex eigenvalue spectrum of the Kaup-Newell scattering problem and the one-parameter soliton family corresponds to the discrete real eigenvalue spectrum. The structure of the IST is exploited to discuss the existence of discrete real eigenvalues and to prove their structural stability to perturbations of the initial conditions. Also, though the two-parameter soliton is structurally stable in general, it is shown that a perturbation of the initial conditions may change the two-parameter soliton into a degenerate soliton which, in turn, is structurally unstable. This degenerate, or double pole, soliton may bifurcate due to a perturbation of the initial conditions into a pair of one-parameter solitons. If the initial profile is on compact support, then this pair of one-parameter solitons must be compressive and rarefactive respectively. Finally, the Gelfand-Levitan equations appropriate for the double pole soliton are solved.
Yang, Jianke
2012-01-01
Linear stability of both sign-definite (positive) and sign-indefinite solitary waves near pitchfork bifurcations is analyzed for the generalized nonlinear Schroedinger equations with arbitrary forms of nonlinearity and external potentials in arbitrary spatial dimensions. Bifurcations of linear-stability eigenvalues associated with pitchfork bifurcations are analytically calculated. It is shown that the smooth solution branch switches stability at the bifurcation point. In addition, the two bifurcated solution branches and the smooth branch have the opposite (same) stability when their power slopes have the same (opposite) sign. One unusual feature on the stability of these pitchfork bifurcations is that the smooth and bifurcated solution branches can be both stable or both unstable, which contrasts such bifurcations in finite-dimensional dynamical systems where the smooth and bifurcated branches generally have opposite stability. For the special case of positive solitary waves, stronger and more explicit stab...
Morphodynamics of a Bifurcation on the Wax Lake Delta, LA
Slingerland, R. L.; Best, J.; Parsons, D. R.; Edmonds, D. A.
2009-12-01
To better predict the dynamical behavior of fine-grained deltaic distributary networks, we collected integrated morphological, flow, and sediment transport data from a third-order bifurcation (BIF) on the Wax Lake Delta, LA, during July 15-20, 2009. Theory and numerical modeling predicts that over a range of channel aspect ratios, friction factors, and Shields numbers, three functions exist that relate the discharge ratio of the bifurcate arms at equilibrium conditions to the Shields number. One function predicts symmetrical configurations, while the other two predict asymmetrical discharges. To test the theoretical predictions we employed high-resolution multibeam echo sounding (MBES) and acoustic Doppler velocity profiling to map the bifurcation. The arms of the BIF are asymmetric in planform, depth (west arm/east arm = 4.2/3.1 m), discharge (335/140 cumecs), and bedload transport, with two-thirds of the dunes revealed on the MBES survey entering the western bifurcate channel. The bed consists of fine sand (D50 = 0.125 mm) sculpted into dunes, which in these 4 m water depths average 7 meters long and 0.52 m high and provide a form friction factor of about 0.028. Measured cross-sectional mean velocity of the main channel during the survey was ~ 0.23 m/s, which for sand-bed systems yields a low Shields number of θ = 0.093. For this θ theory predicts a stable equilibrium bifurcate discharge ratio of 4.5, which compares unfavorably with the observed value of 2.4. As there is no indication from 30 years of aerial photography that this BIF is morphologically unstable, either the bifurcation is maintained by the higher discharges of the spring flood or the theoretical envelope of stable bifurcation configurations requires re-evaluation.
Directory of Open Access Journals (Sweden)
Omid Arjmandi-Tash
2012-12-01
Full Text Available Introduction: Atherosclerosis is a focal disease that susceptibly forms near bifurcations, anastomotic joints, side branches, and curved vessels along the arterial tree. In this study, pulsatile blood flow in a bifurcation model with a non-planar branch is investigated. Methods: Wall shear stress (WSS distributions along generating lines on vessels for different bifurcation angles are calculated during the pulse cycle. Results: The WSS at the outer side of the bifurcation plane vanishes especially for higher bifurcation angles but by increasing the bifurcation angle low WSS region squeezes. At the systolic phase there is a high possibility of formation of a separation region at the outer side of bifurcation plane for all the cases. WSS peaks exist on the inner side of bifurcation plane near the entry section of daughter vessels and these peaks drop as bifurcation angle is increased. Conclusion: It was found that non-planarity of the daughter vessel lowers the minimum WSS at the outer side of the bifurcation and increases the maximum WSS at the inner side. So it seems that the formation of atherosclerotic plaques at bifurcation region in direction of non-planar daughter vessel is more risky.
Inverse bifurcation analysis: application to simple gene systems
Directory of Open Access Journals (Sweden)
Schuster Peter
2006-07-01
Full Text Available Abstract Background Bifurcation analysis has proven to be a powerful method for understanding the qualitative behavior of gene regulatory networks. In addition to the more traditional forward problem of determining the mapping from parameter space to the space of model behavior, the inverse problem of determining model parameters to result in certain desired properties of the bifurcation diagram provides an attractive methodology for addressing important biological problems. These include understanding how the robustness of qualitative behavior arises from system design as well as providing a way to engineer biological networks with qualitative properties. Results We demonstrate that certain inverse bifurcation problems of biological interest may be cast as optimization problems involving minimal distances of reference parameter sets to bifurcation manifolds. This formulation allows for an iterative solution procedure based on performing a sequence of eigen-system computations and one-parameter continuations of solutions, the latter being a standard capability in existing numerical bifurcation software. As applications of the proposed method, we show that the problem of maximizing regions of a given qualitative behavior as well as the reverse engineering of bistable gene switches can be modelled and efficiently solved.
Research on bifurcation characters of rotor-SMA bearing system
International Nuclear Information System (INIS)
Based on Landau-Devonshire model, the bifurcation characteristic of rotor-shape memory alloy bearings(SMAB) system was investigated in this paper. Heteronomous system was transformed into autonomous system in averaging method and Van der Pol transformation, and the existence of Hopf bifurcation was proved in theory. The concept of broadened set of equilibrium point was introduced to improve centre manifold method to be adapted to heteronomous system. The equation of the flow on the centre manifold of rotor-SMAB system was obtained, and the existence of transcritical bifurcation and supercritical pitchfork bifurcation was proved in theory. Finally the results in centre manifold method and averaging method were compared with each other. The comparison shows that the results of the two methods were both the parts of global dynamic characteristic of rotor-SMAB system, while centre manifold method can be applied to research bifurcation behavior in the case of more dimensions. It means that the two methods both have limitation, and global dynamic characteristic must be obtained in kinds of method
Full system bifurcation analysis of endocrine bursting models.
Tsaneva-Atanasova, Krasimira; Osinga, Hinke M; Riess, Thorsten; Sherman, Arthur
2010-06-21
Plateau bursting is typical of many electrically excitable cells, such as endocrine cells that secrete hormones and some types of neurons that secrete neurotransmitters. Although in many of these cell types the bursting patterns are regulated by the interplay between voltage-gated calcium channels and calcium-sensitive potassium channels, they can be very different. We investigate so-called square-wave and pseudo-plateau bursting patterns found in endocrine cell models that are characterized by a super- or subcritical Hopf bifurcation in the fast subsystem, respectively. By using the polynomial model of Hindmarsh and Rose (Proceedings of the Royal Society of London B 221 (1222) 87-102), which preserves the main properties of the biophysical class of models that we consider, we perform a detailed bifurcation analysis of the full fast-slow system for both bursting patterns. We find that both cases lead to the same possibility of two routes to bursting, that is, the criticality of the Hopf bifurcation is not relevant for characterizing the route to bursting. The actual route depends on the relative location of the full-system's fixed point with respect to a homoclinic bifurcation of the fast subsystem. Our full-system bifurcation analysis reveals properties of endocrine bursting that are not captured by the standard fast-slow analysis. PMID:20307553
High-resolution mapping of bifurcations in nonlinear biochemical circuits.
Genot, A J; Baccouche, A; Sieskind, R; Aubert-Kato, N; Bredeche, N; Bartolo, J F; Taly, V; Fujii, T; Rondelez, Y
2016-08-01
Analog molecular circuits can exploit the nonlinear nature of biochemical reaction networks to compute low-precision outputs with fewer resources than digital circuits. This analog computation is similar to that employed by gene-regulation networks. Although digital systems have a tractable link between structure and function, the nonlinear and continuous nature of analog circuits yields an intricate functional landscape, which makes their design counter-intuitive, their characterization laborious and their analysis delicate. Here, using droplet-based microfluidics, we map with high resolution and dimensionality the bifurcation diagrams of two synthetic, out-of-equilibrium and nonlinear programs: a bistable DNA switch and a predator-prey DNA oscillator. The diagrams delineate where function is optimal, dynamics bifurcates and models fail. Inverse problem solving on these large-scale data sets indicates interference from enzymatic coupling. Additionally, data mining exposes the presence of rare, stochastically bursting oscillators near deterministic bifurcations.
High-resolution mapping of bifurcations in nonlinear biochemical circuits
Genot, A. J.; Baccouche, A.; Sieskind, R.; Aubert-Kato, N.; Bredeche, N.; Bartolo, J. F.; Taly, V.; Fujii, T.; Rondelez, Y.
2016-08-01
Analog molecular circuits can exploit the nonlinear nature of biochemical reaction networks to compute low-precision outputs with fewer resources than digital circuits. This analog computation is similar to that employed by gene-regulation networks. Although digital systems have a tractable link between structure and function, the nonlinear and continuous nature of analog circuits yields an intricate functional landscape, which makes their design counter-intuitive, their characterization laborious and their analysis delicate. Here, using droplet-based microfluidics, we map with high resolution and dimensionality the bifurcation diagrams of two synthetic, out-of-equilibrium and nonlinear programs: a bistable DNA switch and a predator-prey DNA oscillator. The diagrams delineate where function is optimal, dynamics bifurcates and models fail. Inverse problem solving on these large-scale data sets indicates interference from enzymatic coupling. Additionally, data mining exposes the presence of rare, stochastically bursting oscillators near deterministic bifurcations.
Fluid dynamics in airway bifurcations: II. Secondary currents.
Martonen, T B; Guan, X; Schreck, R M
2001-04-01
As the second component of a systematic investigation on flows in bifurcations reported in this journal, this work focused on secondary currents. The first article addressed primary flows and the third discusses localized conditions (both in this issue). Secondary flow patterns were studied in two lung bifurcation models (Schreck, 1972) using FIDAP with the Cray T90 supercomputer. The currents were examined at different prescribed distances distal to the carina. Effects of inlet conditions, Reynolds numbers, and diameter ratios and orientations of airways were addressed. The secondary currents caused by the presence of the carina and inclination of the daughter tubes exhibited symmetric, multivortex patterns. The intensities of the secondary currents became stronger for larger Reynolds numbers and larger angles of bifurcation.
Adaptive Control of Electromagnetic Suspension System by HOPF Bifurcation
Directory of Open Access Journals (Sweden)
Aming Hao
2013-01-01
Full Text Available EMS-type maglev system is essentially nonlinear and unstable. It is complicated to design a stable controller for maglev system which is under large-scale disturbance and parameter variance. Theory analysis expresses that this phenomenon corresponds to a HOPF bifurcation in mathematical model. An adaptive control law which adjusts the PID control parameters is given in this paper according to HOPF bifurcation theory. Through identification of the levitated mass, the controller adjusts the feedback coefficient to make the system far from the HOPF bifurcation point and maintain the stability of the maglev system. Simulation result indicates that adjusting proportion gain parameter using this method can extend the state stability range of maglev system and avoid the self-excited vibration efficiently.
Transport Bifurcation Induced by Sheared Toroidal Flow in Tokamak Plasmas
Highcock, E G; Parra, F I; Schekochihin, A A; Roach, C M; Cowley, S C
2011-01-01
First-principles numerical simulations are used to describe a transport bifurcation in a differentially rotating tokamak plasma. Such a bifurcation is more probable in a region of zero magnetic shear, where the component of the sheared toroidal flow that is perpendicular to the magnetic field has the strongest suppressing effect on the turbulence, than one of finite magnetic shear. Where the magnetic shear is zero, there are no growing linear eigenmodes at any finite value of flow shear. However, subcritical turbulence can be sustained, owing to the transient growth of modes driven by the ion temperature gradient (ITG) and the parallel velocity gradient (PVG). Nonetheless, in a parameter space containing a wide range of temperature gradients and velocity shears, there is a sizeable window where all turbulence is suppressed. Combined with the relatively low transport of momentum by collisional (neoclassical) mechanisms, this produces the conditions for a bifurcation from low to high temperature and velocity gr...
The bifurcation locus for numbers of bounded type
Carminati, Carlo
2011-01-01
We define a family B(t) of compact subsets of the unit interval which generalizes the sets of numbers whose continued fraction expansion has bounded digits. We study how the set B(t) changes as one moves the parameter t, and see that the family undergoes period-doubling bifurcations and displays the same transition pattern from periodic to chaotic behavior as the usual family of quadratic polynomials. The set E of bifurcation parameters is a fractal set of measure zero. We also show that the Hausdorff dimension of B(t) varies continuously with the parameter, and the dimension of each individual set equals the dimension of a corresponding section of the bifurcation set E.
On noise induced Poincaré-Andronov-Hopf bifurcation.
Samanta, Himadri S; Bhattacharjee, Jayanta K; Bhattacharyay, Arijit; Chakraborty, Sagar
2014-12-01
It has been numerically seen that noise introduces stable well-defined oscillatory state in a system with unstable limit cycles resulting from subcritical Poincaré-Andronov-Hopf (or simply Hopf) bifurcation. This phenomenon is analogous to the well known stochastic resonance in the sense that it effectively converts noise into useful energy. Herein, we clearly explain how noise induced imperfection in the bifurcation is a generic reason for such a phenomenon to occur and provide explicit analytical calculations in order to explain the typical square-root dependence of the oscillations' amplitude on the noise level below a certain threshold value. Also, we argue that the noise can bring forth oscillations in average sense even in the absence of a limit cycle. Thus, we bring forward the inherent general mechanism of the noise induced Hopf bifurcation naturally realisable across disciplines.
On noise induced Poincaré–Andronov–Hopf bifurcation
Energy Technology Data Exchange (ETDEWEB)
Samanta, Himadri S., E-mail: hss@umd.edu [Biophysics Program, Institute For Physical Science and Technology, University of Maryland, College Park, Maryland 20742 (United States); Bhattacharjee, Jayanta K., E-mail: director@hri.res.in [Harish-Chandra Research Institute, Allahabad (India); Bhattacharyay, Arijit, E-mail: a.bhattacharyay@iiserpune.ac.in [Indian Institute of Science Education and Research, Pune (India); Chakraborty, Sagar, E-mail: sagarc@iitk.ac.in [Department of Physics, Indian Institute of Technology Kanpur, Uttar Pradesh 208016 (India); Mechanics and Applied Mathematics Group, Indian Institute of Technology Kanpur, Uttar Pradesh 208016 (India)
2014-12-01
It has been numerically seen that noise introduces stable well-defined oscillatory state in a system with unstable limit cycles resulting from subcritical Poincaré–Andronov–Hopf (or simply Hopf) bifurcation. This phenomenon is analogous to the well known stochastic resonance in the sense that it effectively converts noise into useful energy. Herein, we clearly explain how noise induced imperfection in the bifurcation is a generic reason for such a phenomenon to occur and provide explicit analytical calculations in order to explain the typical square-root dependence of the oscillations' amplitude on the noise level below a certain threshold value. Also, we argue that the noise can bring forth oscillations in average sense even in the absence of a limit cycle. Thus, we bring forward the inherent general mechanism of the noise induced Hopf bifurcation naturally realisable across disciplines.
Bifurcations in the optimal elastic foundation for a buckling column
International Nuclear Information System (INIS)
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; Farr, Robert; Ding, K.; Mao, Yong
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.
Bifurcations in the optimal elastic foundation for a buckling column
Rayneau-Kirkhope, Daniel; 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.
High-resolution mapping of bifurcations in nonlinear biochemical circuits
Genot, A. J.; Baccouche, A.; Sieskind, R.; Aubert-Kato, N.; Bredeche, N.; Bartolo, J. F.; Taly, V.; Fujii, T.; Rondelez, Y.
2016-08-01
Analog molecular circuits can exploit the nonlinear nature of biochemical reaction networks to compute low-precision outputs with fewer resources than digital circuits. This analog computation is similar to that employed by gene-regulation networks. Although digital systems have a tractable link between structure and function, the nonlinear and continuous nature of analog circuits yields an intricate functional landscape, which makes their design counter-intuitive, their characterization laborious and their analysis delicate. Here, using droplet-based microfluidics, we map with high resolution and dimensionality the bifurcation diagrams of two synthetic, out-of-equilibrium and nonlinear programs: a bistable DNA switch and a predator–prey DNA oscillator. The diagrams delineate where function is optimal, dynamics bifurcates and models fail. Inverse problem solving on these large-scale data sets indicates interference from enzymatic coupling. Additionally, data mining exposes the presence of rare, stochastically bursting oscillators near deterministic bifurcations.
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...
EXPERIMENTAL STUDY ON SEDIMENT DISTRIBUTION AT CHANNEL BIFURCATION
Institute of Scientific and Technical Information of China (English)
G.M. Tarekul ISLAM; M.R. KABIR; Ainun NISHAT
2002-01-01
This paper presents the experimental results on the distribution of sediments at channel bifurcation.The experiments have been conducted in a physical model of channel bifurcation. It consists of a straight main channel which bifurcates into two branch channels of different widths. The test rig is a mobile bed with fixed bank. Four different noses have been used to study the phenomenon. For each nose, three upstream discharges viz. 20 l/s, 30 l/s and 40 l/s have been employed. From the measured data, discharges and sediment transport ratios per unit width are calculated in the downstream branches.These data have been set to the general nodal point relation and a set of equations has been developed to describe the distribution of sediments to the downstream branches for different nose angles.
Hopf bifurcation and chaos in macroeconomic models with policy lag
International Nuclear Information System (INIS)
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
Stochastic stability and bifurcation in a macroeconomic model
International Nuclear Information System (INIS)
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
Spanwise bifurcations beneath the bluff-body instability modes
Sau, Amalendu; Peng, Y. F.; Hwang, R. R.
2016-06-01
A new family of bifurcations is detected in a cylinder wake. The simulations reveal the presence of physically significant spanwise wavy flow undulation in the near-wake of a square cylinder which plays an important role in the modal transition. The alternate process of vortex shedding initiates a systematic cross-stream momentum transfer that activates self-sustained spanwise oscillation of the physical wake, leading to the growth of sequence of Hopf bifurcations along the topological cores of von Kármán vortices. The study exhibits how exactly such self-excited spanwise oscillatory fluctuations of pressure, velocity, and KE keep growing along a vortex-core for increased Re and distinctly influence the growth of "Mode A" and "Mode B" instability. It reports existence of two distinct stages of wake undulation over 125 ≤ Re ≤ 240. While the weakly subcritical spanwise-periodic oscillations of pressure, velocity, vorticity, and associated uniform and wider length-scale bifurcations along the von Kármán vortex corelines dominate during "Mode A" instability, the transition to the "Mode B" is prompted following faster and random eruption (and swapping) of significantly smaller but variable length-scaled bifurcations and accompanied low frequency non-uniform fluctuation of flow variables. Such unstable flow perturbations and resulting bifurcations along the von Kármán vortex cores apparently influence generation of longitudinal vortical ribs (Mode A and Mode B) in the wake. The appearance of a slow varying secondary frequency at the bifurcation points seemed crucial for initiating the spanwise flow irregularity and transition to "Mode B."
Communication: Mode bifurcation of droplet motion under stationary laser irradiation.
Takabatake, Fumi; Yoshikawa, Kenichi; Ichikawa, Masatoshi
2014-08-01
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.
Experimental bifurcation analysis of an impact oscillator – Determining stability
DEFF Research Database (Denmark)
Bureau, Emil; Schilder, Frank; Elmegård, Michael;
2014-01-01
We propose and investigate three different methods for assessing stability of dynamical equilibrium states during experimental bifurcation analysis, using a control-based continuation method. The idea is to modify or turn off the control at an equilibrium state and study the resulting behavior......-time Lyapunov exponents. As a special case we study an isolated branch in the bifurcation diagram brought into existence by a 1:3 subharmonic resonance. On this isola it is only possible to determine stability using one of the three methods, which is due to the fact that only this method guarantees...
Universal fractional map and cascade of bifurcations type attractors.
Edelman, M
2013-09-01
We modified the way in which the Universal Map is obtained in the regular dynamics to derive the Universal α-Family of Maps depending on a single parameter α>0, which is the order of the fractional derivative in the nonlinear fractional differential equation describing a system experiencing periodic kicks. We consider two particular α-families corresponding to the Standard and Logistic Maps. For fractional αbifurcations from regular to chaotic motion in regular dynamics corresponding fractional systems demonstrate a new type of attractors--cascade of bifurcations type trajectories.
Bifurcation analysis of nephron pressure and flow regulation
DEFF Research Database (Denmark)
Barfred, Mikael; Mosekilde, Erik; Holstein-Rathlou, N.-H.
1996-01-01
One- and two-dimensional continuation techniques are applied to study the bifurcation structure of a model of renal flow and pressure control. Integrating the main physiological mechanisms by which the individual nephron regulates the incoming blood flow, the model describes the interaction between...... the tubuloglomerular feedback and the response of the afferent arteriole. It is shown how a Hopf bifurcation leads the system to perform self-sustained oscillations if the feedback gain becomes sufficiently strong, and how a further increase of this parameter produces a folded structure of overlapping period...
An Approach to Robust Control of the Hopf Bifurcation
Directory of Open Access Journals (Sweden)
Giacomo Innocenti
2011-01-01
Full Text Available The paper illustrates a novel approach to modify the Hopf bifurcation nature via a nonlinear state feedback control, which leaves the equilibrium properties unchanged. This result is achieved by recurring to linear and nonlinear transformations, which lead the system to locally assume the ordinary differential equation representation. Third-order models are considered, since they can be seen as proper representatives of a larger class of systems. The explicit relationship between the control input and the Hopf bifurcation nature is obtained via a frequency approach, that does not need the computation of the center manifold.
Cellular instability in rapid directional solidification - Bifurcation theory
Braun, R. J.; Davis, S. H.
1992-01-01
Merchant and Davis performed a linear stability analysis on a model for the directional solidification of a dilute binary alloy valid for all speeds. The analysis revealed that nonequilibrium segregation effects modify the Mullins and Sekerka cellular mode, whereas attachment kinetics has no effect on these cells. In this paper, the nonlinear stability of the steady cellular mode is analyzed. A Landau equation is obtained that determines the amplitude of the cells. The Landau coefficient here depends on both nonequilibrium segregation effects and attachment kinetics. This equation gives the ranges of parameters for subcritical bifurcation (jump transition) or supercritical bifurcation (smooth transition) to cells.
Communication: Mode bifurcation of droplet motion under stationary laser irradiation
Energy Technology Data Exchange (ETDEWEB)
Takabatake, Fumi [Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502 (Japan); Department of Bioengineering and Robotics, Graduate School of Engineering, Tohoku University, Sendai, Miyagi 980-8579 (Japan); Yoshikawa, Kenichi [Faculty of Life and Medical Sciences, Doshisha University, Kyotanabe, Kyoto 610-0394 (Japan); Ichikawa, Masatoshi, E-mail: ichi@scphys.kyoto-u.ac.jp [Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502 (Japan)
2014-08-07
The self-propelled motion of a mm-sized oil droplet floating on water, induced by a local temperature gradient generated by CW laser irradiation is reported. The circular droplet exhibits two types of regular periodic motion, reciprocal and circular, around the laser spot under suitable laser power. With an increase in laser power, a mode bifurcation from rectilinear reciprocal motion to circular motion is caused. The essential aspects of this mode bifurcation are discussed in terms of spontaneous symmetry-breaking under temperature-induced interfacial instability, and are theoretically reproduced with simple coupled differential equations.
Bifurcation Analysis for Surface Waves Generated by Wind
Schweizer, Ben
2001-01-01
We study the generation of surface waves on water as a bifurcation phenomenon. For a critical wind-speed there appear traveling wave solutions. While linear waves do not transport mass (in the mean), nonlinear effects create a shear-flow and result in a net mass transport in the direction of the wind. We derive an asymptotic formula for the average tangential velocity along the free surface. Numerical investigations confirm the appearance of the shear-flow and yield results on the bifurcation...
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.
Bifurcation analysis of a forest-grassland ecosystem
Russo, Lucia; Spiliotis, Konstantinos G.
2016-06-01
The nonlinear analysis of a forest-grassland ecosystem is performed as the main system parameters are changed. The model consists of a couple of nonlinear ordinary differential equations which include dynamically the human perceptions of forest/grassland value. The system displays multiple steady states corresponding to different forest densities as well as periodic regimes characterized by oscillations in time. We performed the bifurcation analysis of the system as the parameter relative to the human opinions influence is changed. We found that the main mechanisms which regulate the transitions occurring between different states or the appearance of new steady and dynamic regimes are transcritical, saddle/node and Hopf bifurcations.
Virtual bench testing to study coronary bifurcation stenting.
Migliavacca, Francesco; Chiastra, Claudio; Chatzizisis, Yiannis S; Dubini, Gabriele
2015-01-01
Virtual bench testing is a numerical methodology which has been applied to the study of coronary interventions. It exploits the amazing growth of computer performance for scientific calculation and makes it possible to simulate very different and complex multiphysics environments and processes, including coronary bifurcation stenting. The quality of prediction from any computer model is very sensitive to the quality of the input data and assumptions. This also holds true in stent virtual bench testing. This paper reviews the state of the art in the field of bifurcation stenting modelling and identifies the current advantages and limitations of this methodology.
The Effect of Alternating Bars Migration on River Bifurcation Dynamics
Miori, S.; Bertoldi, W.; Repetto, R.; Zanoni, L.; Tubino, M.
2007-12-01
Recent theoretical analysis, field and laboratory observations pointed out that fluvial bifurcation show an intrinsic instability, leading to the establishment of an unbalanced flow and sediments distribution in the downstream branches. The existence of equilibrium configurations has been proved, which mainly depend on the hydraulic and morphologic conditions of the upstream flow. However, flow and sediment transport in braided networks are highly unsteady, so that the bifurcation can hardly reach an equilibrium configuration. One of the main causes of temporal fluctuations is the migration of alternate bars in the upstream channel, that can affect and control the flow partition in the distributaries. We analysed the bar - bifurcation interactions by experimental and analytical investigations. We performed a set of flume experiments on a Y shaped fixed banks and movable bed bifurcation. Laboratory results show that bar formation in the upstream channel perturbs the discharge distribution with a series of fluctuations strictly related to the period of bar migration. Four different behaviours have been identified, characterised by small perturbations of the equilibrium state (balanced or unbalanced), by the occurrence of large fluctuations or by the closure of one of the distributaries. The character of the bifurcation is controlled by the amplitude and speed of alternate bars that directly influence the amplitude and period of discharge oscillations. Consequently, at large values of the aspect ratio (high bars) and low sediment mobility (slow bars) the bifurcation dynamics is likely to be dominated by bars migration. Extending the one-dimensional model proposed by Bolla Pittaluga et al. (2003), we introduce the effect of bars migrating in the upstream channel. In the present model, the bifurcation is forced with spatial crosswise fluctuations of feeding conditions, in order to reproduce the transverse distribution of sediment and water of an alternate bar pattern as
LOCAL STABILITY AND BIFURCATION IN A THREE—UNIT DELAYED NEURAL NETWORK
Institute of Scientific and Technical Information of China (English)
LINYiping; LIJibin; 等
2003-01-01
A system of three-unit networks with coupled cells is investigated.The general formula for bifurcation direction of Hopf bifurcation is calculated and the estimate formula of period of the periodic solution is given.
BIFURCATION OF LIMIT CYCLES FROM A DOUBLE HOMOCLINIC LOOP WITH A ROUGH SADDLE
Institute of Scientific and Technical Information of China (English)
HAN MAOAN; BI PING
2004-01-01
This paper concerns with the bifurcation of limit cycles from a double bomoclinic loop under multiple parameter perturbations for general planar systems. The existence conditions of 4 homoclinic bifurcation curves and small and large limit cycles are especially investigated.
Dynamical Systems with a Codimension-One Invariant Manifold: The Unfoldings and Its Bifurcations
Saputra, Kie Van Ivanky
2015-06-01
We investigate a dynamical system having a special structure namely a codimension-one invariant manifold that is preserved under the variation of parameters. We derive conditions such that bifurcations of codimension-one and of codimension-two occur in the system. The normal forms of these bifurcations are derived explicitly. Both local and global bifurcations are analyzed and yield the transcritical bifurcation as the codimension-one bifurcation while the saddle-node-transcritical interaction and the Hopf-transcritical interactions as the codimension-two bifurcations. The unfolding of this degeneracy is also analyzed and reveal global bifurcations such as homoclinic and heteroclinic bifurcations. We apply our results to a modified Lotka-Volterra model and to an infection model in HIV diseases.
A bifurcation set associated to the copy phenomenon in the space of gauge fields
International Nuclear Information System (INIS)
It is shown that gauge field copies are associated to a stratified bifurcation set in gauge field space. Such a set is noticed to be locus of other bifurcation phenomena in gauge field theory besides the copy phenomenon. (Author)
Hopf Bifurcation of a Differential-Algebraic Bioeconomic Model with Time Delay
Directory of Open Access Journals (Sweden)
Xiaojian Zhou
2012-01-01
Full Text Available We investigate the dynamics of a differential-algebraic bioeconomic model with two time delays. Regarding time delay as a bifurcation parameter, we show that a sequence of Hopf bifurcations occur at the positive equilibrium as the delay increases. Using the theories of normal form and center manifold, we also give the explicit algorithm for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions. Numerical tests are provided to verify our theoretical analysis.
Stability and Hopf bifurcation in a symmetric Lotka-Volterra predator-prey system with delays
Directory of Open Access Journals (Sweden)
Jing Xia
2013-01-01
Full Text Available This article concerns a symmetrical Lotka-Volterra predator-prey system with delays. By analyzing the associated characteristic equation of the original system at the positive equilibrium and choosing the delay as the bifurcation parameter, the local stability and Hopf bifurcation of the system are investigated. Using the normal form theory, we also establish the direction and stability of the Hopf bifurcation. Numerical simulations suggest an existence of Hopf bifurcation near a critical value of time delay.
Stability and Bifurcation Analysis in a Diffusive Brusselator-Type System
Liao, Maoxin; Wang, Qi-Ru
2016-06-01
In this paper, the dynamic properties for a Brusselator-type system with diffusion are investigated. By employing the theory of Hopf bifurcation for ordinary and partial differential equations, we mainly obtain some conditions of the stability and Hopf bifurcation for the ODE system, diffusion-driven instability of the equilibrium solution, and the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions for the PDE system. Finally, some numerical simulations are presented to verify our results.
STABILITY AND BIFURCATION OF A HUMAN RESPIRATORY SYSTEM MODEL WITH TIME DELAY
Institute of Scientific and Technical Information of China (English)
沈启宏; 魏俊杰
2004-01-01
The stability and bifurcation of the trivial solution in the two-dimensional differential equation of a model describing human respiratory system with time delay were investigated. Formulas about the stability of bifurcating periodic solution and the direction of Hopf bifurcation were exhibited by applying the normal form theory and the center manifold theorem. Furthermore, numerical simulation was carried out.
Stability of the Bifurcation Solutions for a Predator-Prey Model
Institute of Scientific and Technical Information of China (English)
孟义杰; 王一夫
2003-01-01
The bifurcation solution of the nonnegative steady-state of a reaction-diffusion system was investigated. The combination of the sturm-type eigenvalue and the theorem of bifurcation was used to study the local coexistence solutions, and obtain the stability of bifurcation solutions. The system model describes predator-prey interaction in an unstirred chemostat.
Quasi-periodic Bifurcations of Invariant Circles in Low-dimensional Dissipative Dynamical Systems
Vitolo, Renato; Broer, Henk; Simo, Carles
2011-01-01
This paper first summarizes the theory of quasi-periodic bifurcations for dissipative dynamical systems. Then it presents algorithms for the computation and continuation of invariant circles and of their bifurcations. Finally several applications are given for quasiperiodic bifurcations of Hopf, sad
Stability and bifurcations in a nonlocal delayed reaction-diffusion population model
Chen, Shanshan; Yu, Jianshe
2016-01-01
A nonlocal delayed reaction-diffusion equation with Dirichlet boundary condition is considered in this paper. It is shown that a positive spatially nonhomogeneous equilibrium bifurcates from the trivial equilibrium. The stability/instability of the bifurcated positive equilibrium and associated Hopf bifurcation are investigated, providing us with a complete picture of the dynamics.
Equilibrium Point Bifurcation and Singularity Analysis of HH Model with Constraint
2014-01-01
We present the equilibrium point bifurcation and singularity analysis of HH model with constraints. We investigate the effect of constraints and parameters on the type of equilibrium point bifurcation. HH model with constraints has more transition sets. The Matcont toolbox software environment was used for analysis of the bifurcation points in conjunction with Matlab. We also illustrate the stability of the equilibrium points.
Bifurcation Analysis of Spiral Growth Processes in Plants
DEFF Research Database (Denmark)
Andersen, C.A.; Ernstsen, C.N.; Mosekilde, Erik
1999-01-01
In order to examine the significance of different assumptions about the range of the inhibitory forces, we have performed a series of bifurcation analyses of a simple model that can explain the formation of helical structures in phyllotaxis. Computer simulations are used to illustrate the role...
Streamline topology: Patterns in fluid flows and their bifurcations
DEFF Research Database (Denmark)
Brøns, Morten
2007-01-01
Using dynamical systems theory, we consider structures such as vortices and separation in the streamline patterns of fluid flows. Bifurcation of patterns under variation of external parameters is studied using simplifying normal form transformations. Flows away from boundaries, flows close to fixed...
Evidence and control of bifurcations in a respiratory system
Energy Technology Data Exchange (ETDEWEB)
Goldin, Matías A., E-mail: mgoldin@df.uba.ar; Mindlin, Gabriel B. [Laboratorio de Sistemas Dinámicos, IFIBA y Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón 1, Ciudad Universitaria, Buenos Aires (Argentina)
2013-12-15
We studied the pressure patterns used by domestic canaries in the production of birdsong. Acoustically different sound elements (“syllables”) were generated by qualitatively different pressure gestures. We found that some ubiquitous transitions between syllables can be interpreted as bifurcations of a low dimensional dynamical system. We interpreted these results as evidence supporting a model in which different timescales interact nonlinearly.
Efficient computation of bifurcation diagrams via adaptive ROMs
Energy Technology Data Exchange (ETDEWEB)
Terragni, F [Gregorio Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, E-28911 Leganés (Spain); Vega, J M, E-mail: fterragn@ing.uc3m.es [E.T.S.I. Aeronáuticos, Universidad Politécnica de Madrid, E-28040 Madrid (Spain)
2014-08-01
Various ideas concerning model reduction based on proper orthogonal decomposition are discussed, exploited, and suited to the approximation of complex bifurcations in some dissipative systems. The observation that the most energetic modes involved in these low dimensional descriptions depend only weakly on the actual values of the problem parameters is firstly highlighted and used to develop a simple strategy to capture the transitions occurring over a given bifurcation parameter span. Flexibility of the approach is stressed by means of some numerical experiments. A significant improvement is obtained by introducing a truncation error estimate to detect when the approximation fails. Thus, the considered modes are suitably updated on demand, as the bifurcation parameter is varied, in order to account for possible changes in the phase space of the system that might be missed. A further extension of the method to more complex (quasi-periodic and chaotic) attractors is finally outlined by implementing a control of truncation instabilities, which leads to a general, adaptive reduced order model for the construction of bifurcation diagrams. Illustration of the ideas and methods in the complex Ginzburg–Landau equation (a paradigm of laminar flows on a bounded domain) evidences a fairly good computational efficiency. (paper)
A recent bifurcation in Arctic sea-ice cover
Directory of Open Access Journals (Sweden)
V. N. Livina
2012-07-01
Full Text Available There is ongoing debate over whether Arctic sea-ice has already passed a "tipping point", or whether it will do so in future, with several recent studies arguing that the loss of summer sea ice does not involve a bifurcation because it is highly reversible in models. Recently developed methods can detect and sometimes forewarn of bifurcations in time-series data, hence we applied them to satellite data for Arctic sea-ice cover. Here we show that a new low ice cover state has appeared from 2007 onwards, which is distinct from the normal state of seasonal sea ice variation, suggesting a bifurcation has occurred from one attractor to two. There was no robust early warning signal of critical slowing down prior to this bifurcation, consistent with it representing the appearance of a new ice cover state rather than the loss of stability of the existing state. The new low ice cover state has been sampled predominantly in summer-autumn and seasonal forcing combined with internal climate variability are likely responsible for triggering recent transitions between the two ice cover states. However, all early warning indicators show destabilization of the summer-autumn sea-ice since 2007. This suggests the new low ice cover state may be a transient feature and further abrupt changes in summer-autumn Arctic sea-ice cover could lie ahead; either reversion to the normal state or a yet larger ice loss.
Bifurcation of Pacific North Equatorial Current at the surface
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The grid altimetry data between 1993 and 2006 near the Philippines were analyzed by the method of Empirical Orthogonal Function (EOF) to study the variation of bifurcation of the North Equatorial Current at the surface of the Pacific. The relatively short-term signals with periods of about 6 months, 4 months, 3 months and 2 months are found besides seasonal and interannual variations mentioned in previous studies. Local wind stress curl plays an important role in controlling variation of bifurcation latitude except in the interannual timescale. The bifurcation latitude is about 13.3°N in annual mean state and it lies at the northernmost position (14.0°N) in January, at the southernmost position (12.5°N) in July. The amplitude of variation of bifurcation latitude in a year is 1.5°, which can mainly be explained as the contributions of the signals with periods of about 1 year (1.2°) and 0.5 year (0.3°).
BIFURCATION ANALYSIS OF A MITOTIC MODEL OF FROG EGGS
Institute of Scientific and Technical Information of China (English)
吕金虎; 张子范; 张锁春
2003-01-01
The mitotic model of frog eggs established by Borisuk and Tyson is qualitatively analyzed. The existence and stability of its steady states are further discussed. Furthermore, the bifurcation of above model is further investigated by using theoretical analysis and numerical simulations. At the same time, the numerical results of Tyson are verified by theoretical analysis.
Numerical simulation of magnetic nanoparticles targeting in a bifurcation vessel
Energy Technology Data Exchange (ETDEWEB)
Larimi, M.M.; Ramiar, A., E-mail: aramiar@nit.ac.ir; Ranjbar, A.A.
2014-08-01
Guiding magnetic iron oxide nanoparticles with the help of an external magnetic field to its target is the principle behind the development of super paramagnetic iron oxide nanoparticles (SPIONs) as novel drug delivery vehicles. The present paper is devoted to study on MDT (Magnetic Drug Targeting) technique by particle tracking in the presence of magnetic field in a bifurcation vessel. The blood flow in bifurcation is considered incompressible, unsteady and Newtonian. The flow analysis applies the time dependent, two dimensional, incompressible Navier–Stokes equations for Newtonian fluids. The Lagrangian particle tracking is performed to estimate particle behavior under influence of imposed magnetic field gradients along the bifurcation. According to the results, the magnetic field increased the volume fraction of particle in target region, but in vessels with high Reynolds number, the efficiency of MDT technique is very low. Also the results showed that in the bifurcation vessels with lower angles, wall shear stress is higher and consequently the risk of the vessel wall rupture increases. - Highlights: • Fluid flow and magnetic nanoparticles behavior under influence of external magnetic field are modeled in this study. • Increasing magnetic number increases size and number of recirculation zones. • Increasing Reynolds number reduces the efficiency of magnetic drug targeting. • Number of particles delivered to target region decreases with reducing the diameter of nanoparticles. • Decreasing the ratio of particle diameter to magnetic core diameter (D{sub p}/D{sub m}) will increase magnetic drug targeting efficiency.
Numerical simulation of magnetic nanoparticles targeting in a bifurcation vessel
Larimi, M. M.; Ramiar, A.; Ranjbar, A. A.
2014-08-01
Guiding magnetic iron oxide nanoparticles with the help of an external magnetic field to its target is the principle behind the development of super paramagnetic iron oxide nanoparticles (SPIONs) as novel drug delivery vehicles. The present paper is devoted to study on MDT (Magnetic Drug Targeting) technique by particle tracking in the presence of magnetic field in a bifurcation vessel. The blood flow in bifurcation is considered incompressible, unsteady and Newtonian. The flow analysis applies the time dependent, two dimensional, incompressible Navier-Stokes equations for Newtonian fluids. The Lagrangian particle tracking is performed to estimate particle behavior under influence of imposed magnetic field gradients along the bifurcation. According to the results, the magnetic field increased the volume fraction of particle in target region, but in vessels with high Reynolds number, the efficiency of MDT technique is very low. Also the results showed that in the bifurcation vessels with lower angles, wall shear stress is higher and consequently the risk of the vessel wall rupture increases.
Periodic flow at airway bifurcations. III. Energy dissipation.
Tsuda, A; Savilonis, B J; Kamm, R D; Fredberg, J J
1990-08-01
We measured the energy dissipation associated with large-amplitude periodic flow through airway bifurcation models. Each model consisted of a single asymmetric bifurcation with a different branching angle and area ratio, with each branch terminated into an identical elastic load. Sinusoidal volumetric oscillations were applied at the parent duct so that the upstream Reynolds number (Re) varied from 30 to 77,000 and the Womersley parameter (alpha) from 4 to 30. Pressures were measured continuously at the parent duct and at both terminals, and instantaneous branch flow rates were calculated. Time-averaged energy dissipation in the bifurcation was computed from an energy budget over a control volume integrated over a cycle and was expressed as a friction factor, F. We found that when tidal volume was small [ratio of tidal volume to resident (dead space) volume, VT/VD less than 1], F was independent of branching angle and fell with increasing alpha and VT/VD. When tidal volume was large (VT/VD greater than 1), F increased with increasing branching angle and varied less strongly with alpha and VT/VD. No simple benchmark flow represented the data well over the entire experimental range. This study demonstrates that only two nondimensional parameters, alpha and VT/VD, are necessary and are sufficient to describe time-averaged energy dissipation in a given bifurcation geometry during sinusoidal flow.
Forcing an entire bifurcation diagram: Case studies in chemical oscillators
Kevrekidis, I. G.; Aris, R.; Schmidt, L. D.
1986-12-01
We study the finite amplitude periodic forcing of chemical oscillators. In particular, we examine systems that, when autonomous, (i.e. for zero forcing amplitude) exhibit a single stable oscillation. Using one of the system parameters as a forcing variable by varying it periodically, we show through extensive numerical work how the bifurcation diagram of the autonomous system with respect to this parameter affects the qualitative response of the full forced system. As the forcing variable oscillates around its midpoint, its instantaneous values may cross points (such as Hopf bifurcation poiints) of the autonomous bifurcation diagram so that the characterization of the system as a simple forced oscillator is no longer valid. Such a neighboring Hopf bifurcation of the unforced system is found to set the scene for the interaction of resonance horns and the loss of tori in the full forced system as the amplitude of the forcing grows. Our test case presented here is the Continuous Stirred Tank Reactor (CSTR) with periodically forced coolant temperature.
Limit theorems for bifurcating integer-valued autoregressive processes
Blandin, Vassili
2012-01-01
We study the asymptotic behavior of the weighted least squares estimators of the unknown parameters of bifurcating integer-valued autoregressive processes. Under suitable assumptions on the immigration, we establish the almost sure convergence of our estimators, together with the quadratic strong law and central limit theorems. All our investigation relies on asymptotic results for vector-valued martingales.
Fingerprint pattern recognition from bifurcations: An alternative approach
A. Castañeda-Miranda; R. Castañeda-Miranda; Victor Castano
2015-01-01
A pc-based automatic system for fingerprints recording and classification is described, based on the vector analysis of bifurcations. The system consists of a six-step process: a) acquisition, b) preprocessing, c) fragmentation, d) representation, e) description, and f) recognition. Details of each stage, along with actual examples of fingerprints recognition are provided.
Shells, orbit bifurcations and symmetry restorations in Fermi systems
Magner, A G; Arita, K
2016-01-01
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 the main topics of the fruitful activity of V. G. Solovjov. 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 integrabl...
Preferential adhesion of leukocytes near bifurcations is endothelium independent.
Tousi, Nazanin; Wang, Bin; Pant, Kapil; Kiani, Mohammad F; Prabhakarpandian, Balabhaskar
2010-12-01
Leukocyte-endothelial interactions play central roles in many pathological conditions. However, the in vivo mechanisms responsible for nonuniform spatial distribution of adhering leukocytes to endothelial cells in microvascular networks are not clear. We used a combination of in vitro and in vivo methodologies to explain of this complex phenomenon. A mouse cremaster muscle model was used to study the spatial distribution of leukocyte-endothelial cell interaction in vivo. A PDMS-based synthetic microvascular network (SMN) device was used to study interactions of functionalized microspheres using a receptor-ligand system in a (endothelial) cell-free environment for the in vitro studies. Our in vivo and in vitro findings indicate that both leukocytes in vivo and microspheres in vitro preferentially adhere near bifurcation (within 1-2 diameters from the bifurcation). This adhesion pattern was found to be independent of the diameter of the vessels. These findings support our hypothesis that the fluidic patterns near bifurcations/junctions, and not the presence or cellular aspects of the system (e.g. cell deformation, cell signaling, heterogeneous distribution of adhesion molecules), is the main controlling factor behind the preferential adhesion patterns of leukocytes near bifurcations. PMID:20624406
Bifurcation Analysis and Chaos Control in a Discrete Epidemic System
Directory of Open Access Journals (Sweden)
Wei Tan
2015-01-01
Full Text Available The dynamics of discrete SI epidemic model, which has been obtained by the forward Euler scheme, is investigated in detail. By using the center manifold theorem and bifurcation theorem in the interior R+2, the specific conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation have been derived. Numerical simulation not only presents our theoretical analysis but also exhibits rich and complex dynamical behavior existing in the case of the windows of period-1, period-3, period-5, period-6, period-7, period-9, period-11, period-15, period-19, period-23, period-34, period-42, and period-53 orbits. Meanwhile, there appears the cascade of period-doubling 2, 4, 8 bifurcation and chaos sets from the fixed point. These results show the discrete model has more richer dynamics compared with the continuous model. The computations of the largest Lyapunov exponents more than 0 confirm the chaotic behaviors of the system x→x+δ[rN(1-N/K-βxy/N-(μ+mx], y→y+δ[βxy/N-(μ+dy]. Specifically, the chaotic orbits at an unstable fixed point are stabilized by using the feedback control method.
Ecological consequences of global bifurcations in some food chain models
Voorn, van G.A.K.; Kooi, B.W.; Boer, M.P.
2010-01-01
Food chain models of ordinary differential equations (ode’s) are often used in ecology to gain insight in the dynamics of populations of species, and the interactions of these species with each other and their environment. One powerful analysis technique is bifurcation analysis, focusing on the chan
A recent bifurcation in Arctic sea-ice cover
Livina, Valerie N
2012-01-01
There is ongoing debate over whether Arctic sea-ice has already passed a 'tipping point', or whether it will do so in future, with several recent studies arguing that the loss of summer sea ice does not involve a bifurcation because it is highly reversible in models. Recently developed methods can detect and sometimes forewarn of bifurcations in time-series data, hence we applied them to satellite data for Arctic sea-ice cover. Here we show that a new low ice cover state has appeared from 2007 onwards, which is distinct from the normal state of seasonal sea ice variation, suggesting a bifurcation has occurred from one attractor to two. There was no robust early warning signal of critical slowing down prior to this bifurcation, consistent with it representing the appearance of a new ice cover state rather than the loss of stability of the existing state. The new low ice cover state has been sampled predominantly in summer-autumn and seasonal forcing combined with internal climate variability are likely respons...
Existence and bifurcation of integral manifolds with applications
Institute of Scientific and Technical Information of China (English)
HAN; Mao'an; CHEN; Xianfeng
2005-01-01
In this paper a bifurcation theorem on the existence of integral manifolds is obtained by using contracting principle. As an application, sufficient conditions for a higher dimensional system to have an integral manifold are given. Especially the existence and uniqueness of a 3-dimensional invariant torus appearing in a 4-dimensional autonomous system with singularity of codimension two are proved.
Nonlinear aeroelastic analysis of airfoils: bifurcation and chaos
Lee, B. H. K.; Price, S. J.; Wong, Y. S.
1999-04-01
Different types of structural and aerodynamic nonlinearities commonly encountered in aeronautical engineering are discussed. The equations of motion of a two-dimensional airfoil oscillating in pitch and plunge are derived for a structural nonlinearity using subsonic aerodynamics theory. Three classical nonlinearities, namely, cubic, freeplay and hysteresis are investigated in some detail. The governing equations are reduced to a set of ordinary differential equations suitable for numerical simulations and analytical investigation of the system stability. The onset of Hopf-bifurcation, and amplitudes and frequencies of limit cycle oscillations are investigated, with examples given for a cubic hardening spring. For various geometries of the freeplay, bifurcations and chaos are discussed via the phase plane, Poincaré maps, and Lyapunov spectrum. The route to chaos is investigated from bifurcation diagrams, and for the freeplay nonlinearity it is shown that frequency doubling is the most commonly observed route. Examples of aerodynamic nonlinearities arising from transonic flow and dynamic stall are discussed, and special attention is paid to numerical simulation results for dynamic stall using a time-synthesized method for the unsteady aerodynamics. The assumption of uniform flow is usually not met in practice since perturbations in velocities are encountered in flight. Longitudinal atmospheric turbulence is introduced to show its effect on both the flutter boundary and the onset of Hopf-bifurcation for a cubic restoring force.
Experiments on the bifurcation behaviour of a forced nonlinear pendulum
Beckert, S.; Schock, U.; Schulz, C.-D.; Weidlich, T.; Kaiser, F.
1985-02-01
A mechanical system (forced nonlinear torsion pendulum) is investigated. The state diagram is given as a function of both the external driving frequency and the damping parameter. A bifurcation diagram is measured showing period doubling, chaos and periodic windows. The results are in qualitative agreement with the recent theory.
Topological bifurcations in a model society of reasonable contrarians
Bagnoli, Franco; Rechtman, Raúl
2013-12-01
People are often divided into conformists and contrarians, the former tending to align to the majority opinion in their neighborhood and the latter tending to disagree with that majority. In practice, however, the contrarian tendency is rarely followed when there is an overwhelming majority with a given opinion, which denotes a social norm. Such reasonable contrarian behavior is often considered a mark of independent thought and can be a useful strategy in financial markets. We present the opinion dynamics of a society of reasonable contrarian agents. The model is a cellular automaton of Ising type, with antiferromagnetic pair interactions modeling contrarianism and plaquette terms modeling social norms. We introduce the entropy of the collective variable as a way of comparing deterministic (mean-field) and probabilistic (simulations) bifurcation diagrams. In the mean-field approximation the model exhibits bifurcations and a chaotic phase, interpreted as coherent oscillations of the whole society. However, in a one-dimensional spatial arrangement one observes incoherent oscillations and a constant average. In simulations on Watts-Strogatz networks with a small-world effect the mean-field behavior is recovered, with a bifurcation diagram that resembles the mean-field one but where the rewiring probability is used as the control parameter. Similar bifurcation diagrams are found for scale-free networks, and we are able to compute an effective connectivity for such networks.
BIFURCATION IN A TWO-DIMENSIONAL NEURAL NETWORK MODEL WITH DELAY
Institute of Scientific and Technical Information of China (English)
WEI Jun-jie; ZHANG Chun-rui; LI Xiu-ling
2005-01-01
A kind of 2-dimensional neural network model with delay is considered. By analyzing the distribution of the roots of the characteristic equation associated with the model, a bifurcation diagram was drawn in an appropriate parameter plane. It is found that a line is a pitchfork bifurcation curve. Further more, the stability of each fixed point and existence of Hopf bifurcation were obtained. Finally, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions were determined by using the normal form method and centre manifold theory.
Institute of Scientific and Technical Information of China (English)
LuoGuanwei; XieJianhua
2003-01-01
A two-degrees-of-freedom vibratory system with a clearance or gap is under consideration based on the Poincard map. Stability and local bifurcation of the period-one doubleimpact symmetrical motion of the system are analyzed by using the equation of map. The routes from periodic impact motions to chaos, via pitchfork bifurcation, period-doubling bifurcation and grazing bifurcation, are studied by numerical simulation. Under suitable system parameter conditions, Neimark-Sacker bifurcations associated with periodic impact motion can occur in the two-degrees-of-freedom vibro-impact system.
Bifurcation of piecewise-linear nonlinear vibration system of vehicle suspension
Institute of Scientific and Technical Information of China (English)
Shun ZHONG; Yu-shu CHEN
2009-01-01
A kinetic model of the piecewise-linear nonlinear suspension system that consists of a dominant spring and an assistant spring is established.Bifurcation of the resonance solution to a suspension system with two degrees of freedom is investigated with the singularity theory.Transition sets of the system and 40 groups of bifurcation diagrams are obtained.The local bifurcation is found,and shows the overall characteristics of bifurcation.Based on the relationship between parameters and the topological bifurcation solutions,motion characteristics with different parameters are obtained.The results provides a theoretical basis for the optimal control of vehicle suspension system parameters.
Seo, Jae-Bin; Shin, Dong-Ho; Park, Kyung Woo; Koo, Bon-Kwon; Gwon, Hyeon-Cheol; Jeong, Myung-Ho; Seong, In-Whan; Rha, Seung Woon; Yang, Ju-Young; Park, Seung-Jung; Yoon, Jung Han; Han, Kyoo-Rok; Park, Jong-Sun; Hur, Seung-Ho; Tahk, Seung-Jea; Kim, Hyo-Soo
2016-09-15
The most favored strategy for bifurcation lesion is stenting main vessel with provisional side branch (SB) stenting. This study was performed to elucidate predictors for SB failure during this provisional strategy. The study population was patients from 16 centers in Korea who underwent drug-eluting stent implantation for bifurcation lesions with provisional strategy (1,219 patients and 1,236 lesions). On multivariate analysis, the independent predictors for SB jailing after main vessel stenting were SB calcification, large SB reference diameter, severe stenosis of SB, and not taking clopidogrel. Regarding SB compromise, however, the independent predictors were true bifurcation lesion and small SB reference diameter, whereas possible predictors were parent vessel thrombus and parent vessel total occlusion. In addition, SB predilation helps us to get favorable SB outcome. The diameter of SB ostium after main vessel stenting became similar between severe SB lesions treated with predilation and mild SB lesions not treated with predilation. In conclusion, SB calcification, less clopidogrel use, large SB reference diameter, and high SB diameter stenosis are independent predictors for SB jailing, and true bifurcation and small SB reference diameter are independent predictors for SB compromise after main vessel stenting. PMID:27523437
Multi-Bifurcation Effect of Blood Flow by Lattice Boltzmann Method
Institute of Scientific and Technical Information of China (English)
RAO Yong; NI Yu-Shan; LIU Chao-Feng
2008-01-01
The multi-bifurcation effect of blood flow is investigated by lattice Boltzmann method at Re = 200 with six different bifurcation angles α, which are 22.5°, 25°, 28°, 30°, 33°, 35°, respectively. The velocities and ratios of average velocity at various bifurcations are discussed. It is indicated that the maximum velocity at the section near the first divider increases and shifts towards the walls of branch with the increase of α. At the first bifurcation, the average horizontal velocities increase with the increase of α. The average horizontal velocities of outer branches at the secondary bifurcation decrease at 22.5°≤α≤30° and increase at 30°≤α≤35°, whereas those of inner branches at the secondary bifurcation have the opposite variation, as the same as the above variations of the ratios of average horizontal velocities at various bifurcations. The ratios of average vertical velocities of branch at first bifurcation to that of outer branches at the secondary bifurcation increase at 22.5°≤α≤30° and decrease at 30°≤α≤35°, whereas the ratios of average vertical velocities of branch at first bifurcation to that of inner branches at the secondary bifurcation always decrease.
Deterministic and stochastic bifurcations in the Hindmarsh-Rose neuronal model.
Dtchetgnia Djeundam, S R; Yamapi, R; Kofane, T C; Aziz-Alaoui, M A
2013-09-01
We analyze the bifurcations occurring in the 3D Hindmarsh-Rose neuronal model with and without random signal. When under a sufficient stimulus, the neuron activity takes place; we observe various types of bifurcations that lead to chaotic transitions. Beside the equilibrium solutions and their stability, we also investigate the deterministic bifurcation. It appears that the neuronal activity consists of chaotic transitions between two periodic phases called bursting and spiking solutions. The stochastic bifurcation, defined as a sudden change in character of a stochastic attractor when the bifurcation parameter of the system passes through a critical value, or under certain condition as the collision of a stochastic attractor with a stochastic saddle, occurs when a random Gaussian signal is added. Our study reveals two kinds of stochastic bifurcation: the phenomenological bifurcation (P-bifurcations) and the dynamical bifurcation (D-bifurcations). The asymptotical method is used to analyze phenomenological bifurcation. We find that the neuronal activity of spiking and bursting chaos remains for finite values of the noise intensity.
HOPF BIFURCATION AND CHAOS OF FINANCIAL SYSTEM ON CONDITION OF SPECIFIC COMBINATION OF PARAMETERS
Institute of Scientific and Technical Information of China (English)
Junhai MA; Yaqiang CUI; Lixia LIU
2008-01-01
This paper studies the global bifurcation and Hopf bifurcation of one kind of complicated financial system with different parameter combinations. Conditions on which bifurcation happens, and the critical system structure when the system transforms from one kind of topological structure to another are studied as well. The criterion for identifying Hopf bifurcation under different parameter combinations is also given. The chaotic character of this system under quasi-periodic force is finally studied. The bifurcation structure graphs are given when two parameters of the combination are fixed while the other parameter varies. The presence and stability of 2 and 3 dimensional torus bifurcation are studied. All of the Lyapunov exponents of the system with different bifurcation parameters and routes leading the system to chaos with different parameter combinations are studied. It is of important theoretical and practical meaning to probe the intrinsic mechanism of such continuous complicated financial system and to find the macro control policies for such kind of system.
Hopf bifurcations in a predator-prey system with multiple delays
Energy Technology Data Exchange (ETDEWEB)
Hu Guangping [School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000 (China); School of Mathematics and Physics, Nanjing University of Information and Technology, Nanjing 210044 (China); Li Wantong [School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000 (China)], E-mail: wtli@lzu.edu.cn; Yan Xiangping [Department of Applied Mathematics, Lanzhou Jiaotong University, Lanzhou 730070 (China)
2009-10-30
This paper is concerned with a two species Lotka-Volterra predator-prey system with three discrete delays. By regarding the gestation period of two species as the bifurcation parameter, the stability of positive equilibrium and Hopf bifurcations of nonconstant periodic solutions are investigated. Furthermore, the direction of Hopf bifurcations and the stability of bifurcated periodic solutions are determined by applying the normal form theory and the center manifold reduction for functional differential equations (FDEs). In addition, the global existence of bifurcated periodic solutions are also established by employing the topological global Hopf bifurcation theorem, which shows that the local Hopf bifurcations imply the global ones after the second critical value of parameter. Finally, to verify our theoretical predictions, some numerical simulations are also included.
Controlling Delay-induced Hopf bifurcation in Internet congestion control system
Ding, Dawei; Luo, Xiaoshu; Liu, Yuliang
2007-01-01
This paper focuses on Hopf bifurcation control in a dual model of Internet congestion control algorithms which is modeled as a delay differential equation (DDE). By choosing communication delay as a bifurcation parameter, it has been demonstrated that the system loses stability and a Hopf bifurcation occurs when communication delay passes through a critical value. Therefore, a time-delayed feedback control method is applied to the system for delaying the onset of undesirable Hopf bifurcation. Theoretical analysis and numerical simulations confirm that the delayed feedback controller is efficient in controlling Hopf bifurcation in Internet congestion control system. Moreover, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determinated by applying the center manifold theorem and the normal form theory.
A bifurcation analysis of boiling water reactor on large domain of parametric spaces
Pandey, Vikas; Singh, Suneet
2016-09-01
The boiling water reactors (BWRs) are inherently nonlinear physical system, as any other physical system. The reactivity feedback, which is caused by both moderator density and temperature, allows several effects reflecting the nonlinear behavior of the system. Stability analyses of BWR is done with a simplified, reduced order model, which couples point reactor kinetics with thermal hydraulics of the reactor core. The linear stability analysis of the BWR for steady states shows that at a critical value of bifurcation parameter (i.e. feedback gain), Hopf bifurcation occurs. These stable and unstable domains of parametric spaces cannot be predicted by linear stability analysis because the stability of system does not include only stability of the steady states. The stability of other dynamics of the system such as limit cycles must be included in study of stability. The nonlinear stability analysis (i.e. bifurcation analysis) becomes an indispensable component of stability analysis in this scenario. Hopf bifurcation, which occur with one free parameter, is studied here and it formulates birth of limit cycles. The excitation of these limit cycles makes the system bistable in the case of subcritical bifurcation whereas stable limit cycles continues in an unstable region for supercritical bifurcation. The distinction between subcritical and supercritical Hopf is done by two parameter analysis (i.e. codimension-2 bifurcation). In this scenario, Generalized Hopf bifurcation (GH) takes place, which separates sub and supercritical Hopf bifurcation. The various types of bifurcation such as limit point bifurcation of limit cycle (LPC), period doubling bifurcation of limit cycles (PD) and Neimark-Sacker bifurcation of limit cycles (NS) have been identified with the Floquet multipliers. The LPC manifests itself as the region of bistability whereas chaotic region exist because of cascading of PD. This region of bistability and chaotic solutions are drawn on the various
Bifurcations and Chaos in a Discrete Predator-prey System with Holling Type-Ⅳ Functional Response
Institute of Scientific and Technical Information of China (English)
Ji-cai Huang
2005-01-01
A discrete predator-prey system with Holling type-Ⅳ functional response obtained by the Euler method is first investigated. The conditions of existence for fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using the center manifold theorem and bifurcation theory. Furthermore, we give the condition for the occurrence of codimension-two bifurcation called the Bogdanov-Takens bifurcation for fixed points and present approximate expressions for saddle-node, Hopf and homoclinic bifurcation sets near the Bogdanov-Takens bifurcation point. We also show, the existence of degenerated fixed point with codimension three at least. The numerical simulations, including bifurcation diagrams, phase portraits, and computation of maximum Lyapunov exponents, not only show the consistence with the theoretical analysis but also exhibit the rich and complex dynamical behaviors such as the attracting invariant circle, period-doubling bifurcation from period-2,3,4 orbits,interior crisis, intermittency mechanic, and sudden disappearance of chaotic dynamic.
Symmetry restoring bifurcation in collective decision-making.
Zabzina, Natalia; Dussutour, Audrey; Mann, Richard P; Sumpter, David J T; Nicolis, Stamatios C
2014-12-01
How social groups and organisms decide between alternative feeding sites or shelters has been extensively studied both experimentally and theoretically. One key result is the existence of a symmetry-breaking bifurcation at a critical system size, where there is a switch from evenly distributed exploitation of all options to a focussed exploitation of just one. Here we present a decision-making model in which symmetry-breaking is followed by a symmetry restoring bifurcation, whereby very large systems return to an even distribution of exploitation amongst options. The model assumes local positive feedback, coupled with a negative feedback regulating the flow toward the feeding sites. We show that the model is consistent with three different strains of the slime mold Physarum polycephalum, choosing between two feeding sites. We argue that this combination of feedbacks could allow collective foraging organisms to react flexibly in a dynamic environment.
Morphological Transitions of Sliding Drops -- Dynamics and Bifurcations
Engelnkemper, Sebastian; Gurevich, Svetlana V; Thiele, Uwe
2016-01-01
We study fully three-dimensional droplets that slide down an incline employing a thin-film equation that accounts for capillarity, wettability and a lateral driving force in small-gradient (or long-wave) approximation. In particular, we focus on qualitative changes in the morphology and behavior of stationary sliding drops. We employ the inclination angle of the substrate as control parameter and use continuation techniques to analyze for several fixed droplet sizes the bifurcation diagram of stationary droplets, their linear stability and relevant eigenmodes. The obtained predictions on existence ranges and instabilities are tested via direct numerical simulations that are also used to investigate a branch of time-periodic behavior (corresponding to pearling-coalescence cycles) which emerges at a global instability, the related hysteresis in behavior and a period-doubling cascade. The non-trivial oscillatory behavior close to a Hopf bifurcation of drops with a finite-length tail is also studied. Finally, it ...
Isochronous bifurcations in second-order delay differential equations
Directory of Open Access Journals (Sweden)
Andrea Bel
2014-07-01
Full Text Available In this article we consider a special type of second-order delay differential equations. More precisely, we take an equation of a conservative mechanical system in one dimension with an added term that is a function of the difference between the value of the position at time $t$ minus the position at the delayed time $t-\\tau$. For this system, we show that, under certain conditions of non-degeneration and of convergence of the periodic solutions obtained by the Homotopy Analysis Method, bifurcation branches appearing in a neighbourhood of Hopf bifurcation due to the delay are isochronous; i.e., all the emerging cycles have the same frequency.
Numerical Study on the Bifurcation of the North Equatorial Current
Institute of Scientific and Technical Information of China (English)
LIU Yulong; WANG Qi; SONG Jun; ZHU Xiande; GONG Xiaoqing; WU Fang
2011-01-01
A 1.5-layer reduced-gravity model forced by wind stress is used to study the bifurcations of the North Equatorial Current (NEC).The authors found that after removing the Ekman drift,the modelled circulations can serve well as a proxy of the SODA circulations on the σθ=25.0kgm-3 potential density surface based on available long-term reanalysis wind stress data.The modelled results show that the location of the western boundary bifurcation of the NEC depends on both zonal averaged and local zero wind stress curl latitude.The effects of the anomalous wind stress curl added in different areas are also investigated and it is found that they can change the strength of the Mindanao Eddy (ME),and then influence the interior pathway.
Topological bifurcations in a model society of reasonable contrarians
Bagnoli, Franco
2013-01-01
People are often divided into conformists and contrarians, the former tending to align to the majority opinion in their neighborhood and the latter tending to disagree with that majority. In practice, however, the contrarian tendency is rarely followed when there is an overwhelming majority with a given opinion, which denotes a social norm. Such reasonable contrarian behavior is often considered a mark of independent thought, and can be a useful strategy in financial markets. We present the opinion dynamics of a society of reasonable contrarian agents. The model is a cellular automaton of Ising type, with antiferromagnetic pair interactions modeling contrarianism and plaquette terms modeling social norms. We introduce the entropy of the collective variable as a way of comparing deterministic (mean-field) and probabilistic (simulations) bifurcation diagrams. In the mean field approximation the model exhibits bifurcations and a chaotic phase, interpreted as coherent oscillations of the whole society. However, i...
Codimension Two Bifurcations and Rythms in Neural Mass Models
Touboul, Jonathan
2009-01-01
Temporal lobe epilepsy is one of the most common chronic neurological disorder characterized by the occurrence of spontaneous recurrent seizures which can be observed at the level of populations through electroencephalogram (EEG) recordings. This paper summarizes some preliminary works aimed to understand from a theoretical viewpoint the occurrence of this type of seizures and the origin of the oscillatory activity in some classical cortical column models. We relate these rhythmic activities to the structure of the set of periodic orbits in the models, and therefore to their bifurcations. We will be mainly interested Jansen and Rit model, and study the codimension one, two and a codimension three bifurcations of equilibria and cycles of this model. We can therefore understand the effect of the different biological parameters of the system of the apparition of epileptiform activity and observe the emergence of alpha, delta and theta sleep waves in a certain range of parameter. We then present a very quick stud...
Bifurcations and Crises in a Shape Memory Oscillator
Directory of Open Access Journals (Sweden)
Luciano G. Machado
2004-01-01
Full Text Available The remarkable properties of shape memory alloys have been motivating the interest in applications in different areas varying from biomedical to aerospace hardware. The dynamical response of systems composed by shape memory actuators presents nonlinear characteristics and a very rich behavior, showing periodic, quasi-periodic and chaotic responses. This contribution analyses some aspects related to bifurcation phenomenon in a shape memory oscillator where the restitution force is described by a polynomial constitutive model. The term bifurcation is used to describe qualitative changes that occur in the orbit structure of a system, as a consequence of parameter changes, being related to chaos. Numerical simulations show that the response of the shape memory oscillator presents period doubling cascades, direct and reverse, and crises.
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.
Fluid dynamics in airway bifurcations: III. Localized flow conditions.
Martonen, T B; Guan, X; Schreck, R M
2001-04-01
Localized flow conditions (e.g., backflows) in transition regions between parent and daughter airways of bifurcations were investigated using a computational fluid dynamics software code (FIDAP) with a Cray T90 supercomputer. The configurations of the bifurcations were based on Schreck s (1972) laboratory models. The flow intensities and spatial regions of reversed motion were simulated for different conditions. The effects of inlet velocity profiles, Reynolds numbers, and dimensions and orientations of airways were addressed. The computational results showed that backflow was increased for parabolic inlet conditions, larger Reynolds numbers, and larger daughter-to-parent diameter ratios. This article is the third in a systematic series addressed in this issue; the first addressed primary velocity patterns and the second discussed secondary currents.
BIFURCATIONS AND CHAOS CONTROL IN TCP-RED SYSTEM
Institute of Scientific and Technical Information of China (English)
Liu Fang
2006-01-01
Objective Analyzing the nonlinear dynamics of the TCP-RED congestion control system is of great importance. This study will help investigate the loss of stability in Internet and design a proper method for controlling bifurcation and chaos in such system. Methods Based on bifurcation diagram, the effect of parameter on system performance is discussed. By using the state feedback and parameter variation strategy, a simple real time control method is proposed to modify the existing RED scheme. Results With our control method, the parametric sensitivity of RED mechanism is attenuated. Moreover, a sufficient condition on the robust stability of the system is also derived to adjust the parameters in TCP-RED system. Conclusion The proposed method has the advantages of simple implementation and unnecessary knowledge of the exact system.
On 'Comment on Supersymmetry, PT-symmetry and spectral bifurcation'
International Nuclear Information System (INIS)
In 'Comment on Supersymmetry, PT-symmetry and spectral bifurcation', Bagchi and Quesne correctly show the presence of a class of states for the complex Scarf-II potential in the unbroken PT-symmetry regime, which were absent in . However, in the spontaneously broken PT-symmetry case, their argument is incorrect since it fails to implement the condition for the potential to be PT-symmetric: CPT[2(A - B) + α] = 0. It needs to be emphasized that in the models considered in , PT is spontaneously broken, implying that the potential is PT-symmetric, whereas the ground state is not. Furthermore, our supersymmetry (SUSY)-based 'spectral bifurcation' holds independent of the sl(2) symmetry consideration for a large class of PT-symmetric potentials.
Symmetry restoring bifurcation in collective decision-making.
Directory of Open Access Journals (Sweden)
Natalia Zabzina
2014-12-01
Full Text Available How social groups and organisms decide between alternative feeding sites or shelters has been extensively studied both experimentally and theoretically. One key result is the existence of a symmetry-breaking bifurcation at a critical system size, where there is a switch from evenly distributed exploitation of all options to a focussed exploitation of just one. Here we present a decision-making model in which symmetry-breaking is followed by a symmetry restoring bifurcation, whereby very large systems return to an even distribution of exploitation amongst options. The model assumes local positive feedback, coupled with a negative feedback regulating the flow toward the feeding sites. We show that the model is consistent with three different strains of the slime mold Physarum polycephalum, choosing between two feeding sites. We argue that this combination of feedbacks could allow collective foraging organisms to react flexibly in a dynamic environment.
Symmetry restoring bifurcation in collective decision-making.
Zabzina, Natalia; Dussutour, Audrey; Mann, Richard P; Sumpter, David J T; Nicolis, Stamatios C
2014-12-01
How social groups and organisms decide between alternative feeding sites or shelters has been extensively studied both experimentally and theoretically. One key result is the existence of a symmetry-breaking bifurcation at a critical system size, where there is a switch from evenly distributed exploitation of all options to a focussed exploitation of just one. Here we present a decision-making model in which symmetry-breaking is followed by a symmetry restoring bifurcation, whereby very large systems return to an even distribution of exploitation amongst options. The model assumes local positive feedback, coupled with a negative feedback regulating the flow toward the feeding sites. We show that the model is consistent with three different strains of the slime mold Physarum polycephalum, choosing between two feeding sites. We argue that this combination of feedbacks could allow collective foraging organisms to react flexibly in a dynamic environment. PMID:25521109
Finite Element Meshes Auto-Generation for the Welted Bifurcation
Institute of Scientific and Technical Information of China (English)
YUANMei; LIYa-ping
2004-01-01
In this paper, firstly, a mathematical model for a specific kind of welted bifurcation is established, the parametric equation for the intersecting curve is resulted in. Secondly, a method for partitioning finite element meshes of the welted bifurcation is put forward, its main idea is that developing the main pipe surface and the branch pipe surface respectively, dividing meshes on each developing plane and obtaining meshes points, then transforming their plane coordinates into space coordinates. Finally, an applied program for finite element meshes auto-generation is simply introduced, which adopt ObjectARX technique and its running result can be shown in AutoCAD. The meshes generated in AutoCAD can be exported conveniently to most of finite element analysis soft wares, and the finite element computing result can satisfy the engineering precision requirement.
Crystalline undulator radiation and sub-harmonic bifurcation of system
Institute of Scientific and Technical Information of China (English)
Luo Xiao-Hua; He Wei; Wu Mu-Ying; Shao Ming-Zhu; Luo Shi-Yu
2013-01-01
Looking for new light sources,especially short wavelength laser light sources has attracted widespread attention.This paper analytically describes the radiation of a crystalline undulator field by the sine-squared potential.In the classical mechanics and the dipole approximation,the motion equation of a particle is reduced to a generalized pendulum equation with a damping term and a forcing term.The bifurcation behavior of periodic orbits is analyzed by using the Melnikov method and the numerical method,and the stability of the system is discussed.The results show that,in principle,the stability of the system relates to its parameters,and only by adjusting these parameters appropriately can the occurrence of bifurcation be avoided or suppressed.
Complex bifurcations in Bénard-Marangoni convection
Vakulenko, Sergey; Sudakov, Ivan
2016-10-01
We study the dynamics of a system defined by the Navier-Stokes equations for a non-compressible fluid with Marangoni boundary conditions in the two-dimensional case. We show that more complicated bifurcations can appear in this system for a certain nonlinear temperature profile as compared to bifurcations in the classical Rayleigh-Bénard and Bénard-Marangoni systems with simple linear vertical temperature profiles. In terms of the Bénard-Marangoni convection, the obtained mathematical results lead to our understanding of complex spatial patterns at a free liquid surface, which can be induced by a complicated profile of temperature or a chemical concentration at that surface. In addition, we discuss some possible applications of the results to turbulence theory and climate science.
On local bifurcations in neural field models with transmission delays.
van Gils, S A; Janssens, S G; Kuznetsov, Yu A; Visser, S
2013-03-01
Neural field models with transmission delays may be cast as abstract delay differential equations (DDE). The theory of dual semigroups (also called sun-star calculus) provides a natural framework for the analysis of a broad class of delay equations, among which DDE. In particular, it may be used advantageously for the investigation of stability and bifurcation of steady states. After introducing the neural field model in its basic functional analytic setting and discussing its spectral properties, we elaborate extensively an example and derive a characteristic equation. Under certain conditions the associated equilibrium may destabilise in a Hopf bifurcation. Furthermore, two Hopf curves may intersect in a double Hopf point in a two-dimensional parameter space. We provide general formulas for the corresponding critical normal form coefficients, evaluate these numerically and interpret the results. PMID:23192328
Bifurcation Analysis of a Nose Landing Gear System
Tartaruga, Irene; Lowenberg, Mark H.; Cooper, Jonathan E; Sartor, Pia N; Lemmens, Yves
2016-01-01
A methodology is proposed to enable the bifurcation analysis of a multi-body nose landing gear (NLG) model by coupling AUTO, a continuation software, to LMS Virtual.Lab Motion, a multi-body software. The approach uses a Singular Value Decomposition (or High Order Singular Value Decomposition) based technique to enable the computation of the stability bounds (e.g. the onset of shimmy) in a very efficient manner. Sensitivity and uncertainty analyses are performed to determine the influence of v...
SHAPE BIFURCATION OF AN ELASTIC WAFER DUE TO SURFACE STRESS
Institute of Scientific and Technical Information of China (English)
闫琨; 何陵辉; 刘人怀
2003-01-01
A geometrically nonlinear analysis was proposed for the deformation of a freestanding elastically isotropic wafer caused by the surface stress change on one surface. Thelink between the curvature and the change in surface stress was obtained analytically fromenergetic consideration. In contrast to the existing linear analysis, a remarkableconsequence is that, when the wafer is very thin or the surface stress difference between thetwo major surfaces is large enough, the shape of the wafer will bifurcate.
Asymptotic results for bifurcating random coefficient autoregressive processes
Blandin, Vassili
2012-01-01
The purpose of this paper is to study the asymptotic behavior of the weighted least square estimators of the unknown parameters of random coefficient bifurcating autoregressive processes. Under suitable assumptions on the immigration and the inheritance, we establish the almost sure convergence of our estimators, as well as a quadratic strong law and central limit theorems. Our study mostly relies on limit theorems for vector-valued martingales.
Noise, Bifurcations, and Modeling of Interacting Particle Systems
Mier-y-Teran-Romero, Luis; Forgoston, Eric; Schwartz, Ira B.
2011-01-01
We consider the stochastic patterns of a system of communicating, or coupled, self-propelled particles in the presence of noise and communication time delay. For sufficiently large environmental noise, there exists a transition between a translating state and a rotating state with stationary center of mass. Time delayed communication creates a bifurcation pattern dependent on the coupling amplitude between particles. Using a mean field model in the large number limit, we show how the complete...
BIFURCATIONS OF INVARIANT CURVES OF A DIFFERENCE EQUATION
Institute of Scientific and Technical Information of China (English)
贺天兰
2001-01-01
Bifurcation of the invariant curves of a difference equation is studied. The system defined by the difference equation is integrable , so the study of the invariant curves of the difference system can become the study of topological classification of the planar phase portraits defined by a planar Hamiltonian system. By strict qualitative analysis, the classification of the invariant curves in parameter space can be obtained.
Fast automatic algorithm for bifurcation detection in vascular CTA scans
Brozio, Matthias; Gorbunova, Vladlena; Godenschwager, Christian; Beck, Thomas; Bernhardt, Dominik
2012-02-01
Endovascular imaging aims at identifying vessels and their branches. Automatic vessel segmentation and bifurcation detection eases both clinical research and routine work. In this article a state of the art bifurcation detection algorithm is developed and applied on vascular computed tomography angiography (CTA) scans to mark the common iliac artery and its branches, the internal and external iliacs. In contrast to other methods our algorithm does not rely on a complete segmentation of a vessel in the 3D volume, but evaluates the cross-sections of the vessel slice by slice. Candidates for vessels are obtained by thresholding, following by 2D connected component labeling and prefiltering by size and position. The remaining candidates are connected in a squared distanced weighted graph. With Dijkstra algorithm the graph is traversed to get candidates for the arteries. We use another set of features considering length and shape of the paths to determine the best candidate and detect the bifurcation. The method was tested on 119 datasets acquired with different CT scanners and varying protocols. Both easy to evaluate datasets with high resolution and no apparent clinical diseases and difficult ones with low resolution, major calcifications, stents or poor contrast between the vessel and surrounding tissue were included. The presented results are promising, in 75.7% of the cases the bifurcation was labeled correctly, and in 82.7% the common artery and one of its branches were assigned correctly. The computation time was on average 0.49 s +/- 0.28 s, close to human interaction time, which makes the algorithm applicable for time-critical applications.
Bifurcation analysis of fan casing under rotating air flow excitation
Institute of Scientific and Technical Information of China (English)
温登哲; 陈予恕
2014-01-01
A fan casing model of cantilever circular thin shell is constructed based on the geometric characteristics of the thin-walled structure of aero-engine fan casing. According to Donnelly’s shell theory and Hamilton’s principle, the dynamic equations are established. The dynamic behaviors are investigated by a multiple-scale method. The effects of casing geometric parameters and motion parameters on the natural frequency of the system are studied. The transition sets and bifurcation diagrams of the system are obtained through a singularity analysis of the bifurcation equation, showing that various modes of the system such as the bifurcation and hysteresis will appear in different parameter regions. In accordance with the multiple relationship of the fan speed and stator vibration frequency, the fan speed interval with the casing vibration sudden jump is calculated. The dynamic reasons of casing cracks are investigated. The possibility of casing cracking hysteresis interval is analyzed. The results show that cracking is more likely to appear in the hysteresis interval. The research of this paper provides a theoretical basis for fan casing design and system parameter optimization.
Forecasting Bifurcations from Large Perturbation Recoveries in Feedback Ecosystems.
D'Souza, Kiran; Epureanu, Bogdan I; Pascual, Mercedes
2015-01-01
Forecasting bifurcations such as critical transitions is an active research area of relevance to the management and preservation of ecological systems. In particular, anticipating the distance to critical transitions remains a challenge, together with predicting the state of the system after these transitions are breached. In this work, a new model-less method is presented that addresses both these issues based on monitoring recoveries from large perturbations. The approach uses data from recoveries of the system from at least two separate parameter values before the critical point, to predict both the bifurcation and the post-bifurcation dynamics. The proposed method is demonstrated, and its performance evaluated under different levels of measurement noise, with two ecological models that have been used extensively in previous studies of tipping points and alternative steady states. The first one considers the dynamics of vegetation under grazing; the second, those of macrophyte and phytoplankton in shallow lakes. Applications of the method to more complex situations are discussed together with the kinds of empirical data needed for its implementation.
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, chaos, and scan instability in dynamic atomic force microscopy
Cantrell, John H.; Cantrell, Sean A.
2016-03-01
The dynamical motion at any point on the cantilever of an atomic force microscope can be expressed quite generally as a superposition of simple harmonic oscillators corresponding to the vibrational modes allowed by the cantilever shape. Central to the dynamical equations is the representation of the cantilever-sample interaction force as a polynomial expansion with coefficients that account for the interaction force "stiffness," the cantilever-to-sample energy transfer, and the displacement amplitude of cantilever oscillation. Renormalization of the cantilever beam model shows that for a given cantilever drive frequency cantilever dynamics can be accurately represented by a single nonlinear mass-spring model with frequency-dependent stiffness and damping coefficients [S. A. Cantrell and J. H. Cantrell, J. Appl. Phys. 110, 094314 (2011)]. Application of the Melnikov method to the renormalized dynamical equation is shown to predict a cascade of period doubling bifurcations with increasing cantilever drive force that terminates in chaos. The threshold value of the drive force necessary to initiate bifurcation is shown to depend strongly on the cantilever setpoint and drive frequency, effective damping coefficient, nonlinearity of the cantilever-sample interaction force, and the displacement amplitude of cantilever oscillation. The model predicts the experimentally observed interruptions of the bifurcation cascade for cantilevers of sufficiently large stiffness. Operational factors leading to the loss of image quality in dynamic atomic force microscopy are addressed, and guidelines for optimizing scan stability are proposed using a quantitative analysis based on system dynamical parameters and choice of feedback loop parameter.
Numerical bifurcation analysis of the bipedal spring-mass model
Merker, Andreas; Kaiser, Dieter; Hermann, Martin
2015-01-01
The spring-mass model and its numerous extensions are currently one of the best candidates for templates of human and animal locomotion. However, with increasing complexity, their applications can become very time-consuming. In this paper, we present an approach that is based on the calculation of bifurcations in the bipedal spring-mass model for walking. Since the bifurcations limit the region of stable walking, locomotion can be studied by computing the corresponding boundaries. Originally, the model was implemented as a hybrid dynamical system. Our new approach consists of the transformation of the series of initial value problems on different intervals into a single boundary value problem. Using this technique, discontinuities can be avoided and sophisticated numerical methods for studying parametrized nonlinear boundary value problems can be applied. Thus, appropriate extended systems are used to compute transcritical and period-doubling bifurcation points as well as turning points. We show that the resulting boundary value problems can be solved by the simple shooting method with sufficient accuracy, making the application of the more extensive multiple shooting superfluous. The proposed approach is fast, robust to numerical perturbations and allows determining complete manifolds of periodic solutions of the original problem.
Inertial and interceptional deposition of fibers in a bifurcating airway.
Zhang, L; Asgharian, B; Anjilvel, S
1996-01-01
A computer model of a three-dimensional bifurcating airway was constructed in which the parent and daughter airways had different lengths but equal diameters. A diameter of 0.6 cm was chosen for the airways based on the third generation of Weibel's symmetric lung model. Different bifurcation angles of 60 degrees, 90 degrees, and 120 degrees were studied. Airflow fields in the airway were obtained by a finite-element method (FIDAP, Fluid Dynamics International, Evanston, IL) for Reynolds numbers of 500 and 1000, assuming uniform parent inlet velocities. The equations of motion for fiber transport in the airways were obtained, and deposition by the combined mechanisms of impaction and interception was incorporated. A computer code was developed that utilized the flow field data and calculated fiber transport in the airways using the equations of motion for fibers. Deposition efficiency was obtained by simulating a large number of fibers of various sizes. Fiber entering the daughter airways tended to orient themselves parallel to the flow. A site of enhanced deposition (or hot spot) was observed at the carina. The dominant parameter for the deposition was the fiber Stokes number. Flow Reynolds number and airway bifurcation angle were also found to affect the deposition.
Fluid dynamics in airway bifurcations: I. Primary flows.
Martonen, T B; Guan, X; Schreck, R M
2001-04-01
The subject of fluid dynamics within human airways is of great importance for the risk assessment of air pollutants (inhalation toxicology) and the targeted delivery of inhaled pharmacologic drugs (aerosol therapy). As cited herein, experimental investigations of flow patterns have been performed on airway models and casts by a number of investigators. We have simulated flow patterns in human lung bifurcations and compared the results with the experimental data of Schreck (1972). The theoretical analyses were performed using a third-party software package, FIDAP, on the Cray T90 supercomputer. This effort is part of a systematic investigation where the effects of inlet conditions, Reynolds numbers, and dimensions and orientations of airways were addressed. This article focuses on primary flows using convective motion and isovelocity contour formats to describe fluid dynamics; subsequent articles in this issue consider secondary currents (Part II) and localized conditions (Part III). The agreement between calculated and measured results, for laminar flows with either parabolic or blunt inlet conditions to the bifurcations, was very good. To our knowledge, this work is the first to present such detailed comparisons of theoretical and experimental flow patterns in airway bifurcations. The agreement suggests that the methodologies can be employed to study factors affecting airflow patterns and particle behavior in human lungs.
Affordance-controlled bifurcations of action patterns in martial arts.
Hristovski, Robert; Davids, Keith; Araújo, Duarte
2006-10-01
Effects of participant-target distance and perceived handstriking efficiency on emergent behavior in the martial art of boxing were investigated, revealing affordance-controlled nonlinear dynamical effects (i.e. bifurcations) within the participant--target system. Results established the existence of critical values of scaled distances for emergence of first time excitations and annihilations of a diverse range of boxing actions i.e. on the appearance and dissolution of jabs, hooks and uppercuts. Reasons for the action diversity were twofold: (a) topological discontinuous changes (bifurcations) in the number of possible handstrikes, i.e. motor solutions to the hitting task; (b) fine modification of probabilities of emergence of striking patterns. Exploitation of a 'strikeability' affordance available in scaled distance-to-target information by boxers led to a diversity of emergent actions through a cascade of bifurcations in the task perceptual-motor work space. Data suggested that perceived efficiency (E) of an action changed as a function of scaled distance (D) and was correlated with the probability of occurrence of action patterns (P), exhibiting the following dependence P = P(E(D)). The implication is that probability of occurrence (P) depends on efficiency (E), which in turn depends on scaled distance (D) to the target. Accordingly, scaled distance-dependent perceived efficiency seems a viable candidate for a contextual (control) parameter to describe the nonlinear dynamics of striking actions in boxing.
Backward bifurcation and control in transmission dynamics of arboviral diseases.
Abboubakar, Hamadjam; Claude Kamgang, Jean; Tieudjo, Daniel
2016-08-01
In this paper, we derive and analyze a compartmental model for the control of arboviral diseases which takes into account an imperfect vaccine combined with individual protection and some vector control strategies already studied in the literature. After the formulation of the model, a qualitative study based on stability analysis and bifurcation theory reveals that the phenomenon of backward bifurcation may occur. The stable disease-free equilibrium of the model coexists with a stable endemic equilibrium when the reproduction number, R0, is less than unity. Using Lyapunov function theory, we prove that the trivial equilibrium is globally asymptotically stable. When the disease-induced death is not considered, or/and, when the standard incidence is replaced by the mass action incidence, the backward bifurcation does not occur. Under a certain condition, we establish the global asymptotic stability of the disease-free equilibrium of the principal model. Through sensitivity analysis, we determine the relative importance of model parameters for disease transmission. Numerical simulations show that the combination of several control mechanisms would significantly reduce the spread of the disease, if we maintain the level of each control high, and this, over a long period. PMID:27321192
Bifurcation of solutions of separable parameterized equations into lines
Directory of Open Access Journals (Sweden)
Yun-Qiu Shen
2010-09-01
Full Text Available Many applications give rise to separable parameterized equations of the form $A(y, muz+b(y, mu=0$, where $y in mathbb{R}^n$, $z in mathbb{R}^N$ and the parameter $mu in mathbb{R}$; here $A(y, mu$ is an $(N+n imes N$ matrix and $b(y, mu in mathbb{R}^{N+n}$. Under the assumption that $A(y,mu$ has full rank we showed in [21] that bifurcation points can be located by solving a reduced equation of the form $f(y, mu=0$. In this paper we extend that method to the case that $A(y,mu$ has rank deficiency one at the bifurcation point. At such a point the solution curve $(y,mu,z$ branches into infinitely many additional solutions, which form a straight line. A numerical method for reducing the problem to a smaller space and locating such a bifurcation point is given. Applications to equilibrium solutions of nonlinear ordinary equations and solutions of discretized partial differential equations are provided.
Ternary choices in repeated games and border collision bifurcations
International Nuclear Information System (INIS)
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.
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. PMID:26414530
The Flatness of Bifurcations in 3D Dendritic Trees: An Optimal Design.
van Pelt, Jaap; Uylings, Harry B M
2011-01-01
The geometry of natural branching systems generally reflects functional optimization. A common property is that their bifurcations are planar and that daughter segments do not turn back in the direction of the parent segment. The present study investigates whether this also applies to bifurcations in 3D dendritic arborizations. This question was earlier addressed in a first study of flatness of 3D dendritic bifurcations by Uylings and Smit (1975), who used the apex angle of the right circular cone as flatness measure. The present study was inspired by recent renewed interest in this measure. Because we encountered ourselves shortcomings of this cone angle measure, the search for an optimal measure for flatness of 3D bifurcation was the second aim of our study. Therefore, a number of measures has been developed in order to quantify flatness and orientation properties of spatial bifurcations. All these measures have been expressed mathematically in terms of the three bifurcation angles between the three pairs of segments in the bifurcation. The flatness measures have been applied and evaluated to bifurcations in rat cortical pyramidal cell basal and apical dendritic trees, and to random spatial bifurcations. Dendritic and random bifurcations show significant different flatness measure distributions, supporting the conclusion that dendritic bifurcations are significantly more flat than random bifurcations. Basal dendritic bifurcations also show the property that their parent segments are generally aligned oppositely to the bisector of the angle between their daughter segments, resulting in "symmetrical" configurations. Such geometries may arise when during neuronal development the segments at a newly formed bifurcation are subjected to elastic tensions, which force the bifurcation into an equilibrium planar shape. Apical bifurcations, however, have parent segments oppositely aligned with one of the daughter segments. These geometries arise in the case of side
Bifurcations and dynamo action in a Taylor Green flow
Dubrulle, B.; Blaineau, P.; Mafra Lopes, O.; Daviaud, F.; Laval, J.-P.; Dolganov, R.
2007-08-01
We report successive bifurcations in direct numerical simulations (DNSs) of a Taylor-Green flow, in both a hydro- and a magneto-hydrodynamic case. Hydrodynamic bifurcations occur in between different metastable states with different dynamo action, and are triggered by the numerical noise. The various states encountered range from stationary to chaotic or turbulent through possible oscillatory states. The corresponding sequence of bifurcations is reminiscent of the sequence obtained in the von Karman (VK) flow, at aspect ratio Γ=2 (Nore et al 2003 J. Fluid Mech. 477 51). We then use kinematic simulations to compute the dynamo thresholds of the different metastable states. A more detailed study of the turbulent state reveals the existence of two windows of dynamo action. Stochastic numerical simulations are then used to mimic the influence of turbulence on the dynamo threshold of the turbulent state. We show that the dynamo threshold is increased (respectively decreased) by the presence of large scale (resp. small scale) turbulent velocity fluctuations. Finally, DNSs of the magneto-hydrodynamic equations are used to explore the linear and nonlinear stage of the dynamo instability. In the linear stage, we show that the magnetic field favours the bifurcation from the basic state directly towards the turbulent or chaotic stable state. The magnetic field can also temporarily stabilize a metastable state, resulting in cycles of dynamo action, with different Lyapunov exponents. The critical magnetic Reynolds number for dynamo action is found to increase strongly with the Reynolds number. Finally, we provide a preliminary study of the saturation regime above the dynamo threshold. At large magnetic Prandtl number, we have observed two main types of saturations, in agreement with an analytical prediction of Leprovost and Dubrulle (2005 Eur. Phys. J. B 44 395): (i) intermittent dynamo, with vanishing most probable value of the magnetic energy; (ii) dynamo with non vanishing
Stability and bifurcation in a voltage controlled negative-output KY Boost converter
International Nuclear Information System (INIS)
The stability and bifurcation in a voltage controlled negative-output KY Boost converter is studied in this Letter. A glimpse at the stability and bifurcation from the power electronics simulator (PSIM) software are given. And then, its mathematical model and corresponding discrete model are derived. The stability and bifurcation of the converter are determined with the help of the loci of eigenvalues of the Jacobian matrix. It is found that the Hopf bifurcation is easy to come in this converter when the value of its energy-transferring capacitor increases. Finally, the analytical results are confirmed by the circuit experiment. - Research highlights: Stability and bifurcation of this converter are studied via the discrete model. → Hopf bifurcation occurs in this converter and low frequency oscillation appears. → There exists a jump on this converter's output voltage and it should be careful. → A compromise must be done when choosing the value of the capacitor Cb.
Generalized Hopf Bifurcation for Non-smooth Planar Dynamical Systems： the Corner Case
Institute of Scientific and Technical Information of China (English)
邹永魁; TassiloKǖpper; 黄明游
2001-01-01
Piece-wise smooth systems are an important class of ordinary differential equations whosedynamics are known to exhibit complex bifurcation scenarios and chaos. Broadly speaking,piece-wise smooth systems can undergo all the bifurcation that smooth ones can. Moreinterestingly, there is a whole class of bifurcation that are unique to piece-wise smoothsystems, such as the bifurcation caused by the geometric shape of the region in which thevector field is analyzed. For example (see Figure 1), the region is divided into two partsI and Ⅱ by a discontinuity boundary which contains a corner at O. When an orbit crossthe corner, border-collision bifurcation may occur (cf. [1]). The present paper deals withthe mechanics of the generalized Hopf bifurcation when the stationary point locates at thecorner.
Pitchfork bifurcation and vibrational resonance in a fractional-order Duffing oscillator
Indian Academy of Sciences (India)
J H Yang; M A F Sanjuán; W Xiang; H Zhu
2013-12-01
The pitchfork bifurcation and vibrational resonance are studied in a fractional-order Duffing oscillator with delayed feedback and excited by two harmonic signals. Using an approximation method, the bifurcation behaviours and resonance patterns are predicted. Supercritical and subcritical pitchfork bifurcations can be induced by the fractional-order damping, the exciting highfrequency signal and the delayed time. 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 vibrational resonance from no resonance to a single resonance. The delayed time influences the location of the vibrational resonance and the bifurcation point of the fractional order. Pitchfork bifurcation is the necessary condition for the double resonance. The theoretical predictions are in good agreement with the numerical simulations.
Directory of Open Access Journals (Sweden)
S. A.A. El-Marouf
2012-01-01
Full Text Available Problem statement: This study aims to discuss the stability and bifurcation of a system of ordinary differential equations expressing a general nonlinear model of HIV/AIDS which has great interests from scientists and researchers on mathematics, biology, medicine and education. The existance of equilibrium points and their local stability are studied for HIV/AIDS model with two forms of the incidence rates. Conclusion/Recommendations: A comparison with recent published results is given. Hopf bifurcation of solutions of an epidemic model with a general nonlinear incidence rate is established. It is also proved that the system undergoes a series of Bogdanov-Takens bifurcation, i.e., saddle-node bifurcation, Hopf bifurcation and homoclinic bifurcation for suitable values of the parameters.
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.
Bifurcation analysis of a predator–prey model with anti-predator behaviour
International Nuclear Information System (INIS)
We investigated a predator–prey model with a nonmonotonic functional response and anti-predator behaviour such that the adult prey can attack vulnerable predators. By analyzing the existence and stability of all possible equilibria and conducting a bifurcation analysis, we obtained the global dynamics of the proposed system. The system could undergo a saddle-node bifurcation, (supercritical and subcritical) Hopf bifurcation, homoclinic bifurcation and a Bogdanov–Takens bifurcation of codimension 2. Further, we obtained a generic family unfolding for the system by choosing the environmental carrying capacity of the prey and the death rate of the predator as bifurcation parameters. Numerical studies showed that anti-predator behaviour not only makes the coexistence of the prey and predator populations less likely, but also damps the predator–prey oscillations. Therefore, anti-predator behaviour helps the prey population to resist predator aggression
Stability and Hopf Bifurcation in a Delayed SEIRS Worm Model in Computer Network
Directory of Open Access Journals (Sweden)
Zizhen Zhang
2013-01-01
Full Text Available A delayed SEIRS epidemic model with vertical transmission in computer network is considered. Sufficient conditions for local stability of the positive equilibrium and existence of local Hopf bifurcation are obtained by analyzing distribution of the roots of the associated characteristic equation. Furthermore, the direction of the local Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by using the normal form theory and center manifold theorem. Finally, a numerical example is presented to verify the theoretical analysis.
Institute of Scientific and Technical Information of China (English)
Yu Hai WU; Mao An HAN
2007-01-01
A cubic system having three homoclinic loops perturbed by Z3 invariant quintic polynomials is considered.By applying the qualitative method of di erential equations and the numeric computing method,the Hopf bifurcation,homoclinic loop bifurcation and heteroclinic loop bifurcation of the above perturbed system are studied.It is found that the above system has at least 12 limit cycles and the distributions of limit cycles are also given.
LOCAL AND GLOBAL HOPF BIFURCATIONS IN A DELAYED HUMAN RESPIRATORY SYSTEM
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
This paper considers a delayed human respiratory model. Firstly, the stability of the equilibrium of the model is investigated and the occurrence of a sequence of Hopf bifurcations of the model is proved. Secondly, the explicit algorithms which determine the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived by applying the normal form method and the center manifold theory. Finally, the existence of the global periodic solutions is showed under some ass...
Stability and Hopf Bifurcation of Delayed Predator-Prey System Incorporating Harvesting
Directory of Open Access Journals (Sweden)
Fengying Wei
2014-01-01
Full Text Available A kind of delayed predator-prey system with harvesting is considered in this paper. The influence of harvesting and delay is investigated. Our results show that Hopf bifurcations occur as the delay τ passes through critical values. By using of normal form theory and center manifold theorem, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are obtained. Finally, numerical simulations are given to support our theoretical predictions.
Complex dynamics in biological systems arising from multiple limit cycle bifurcation.
Yu, P; Lin, W
2016-12-01
In this paper, we study complex dynamical behaviour in biological systems due to multiple limit cycles bifurcation. We use simple epidemic and predator-prey models to show exact routes to new types of bistability, that is, bistability between equilibrium and periodic oscillation, and bistability between two oscillations, which may more realistically describe the real situations. Bifurcation theory and normal form theory are applied to investigate the multiple limit cycles bifurcating from Hopf critical point. PMID:27042877
Classification of coronary artery bifurcation lesions and treatments: Time for a consensus!
DEFF Research Database (Denmark)
Louvard, Yves; Thomas, Martyn; Dzavik, Vladimir;
2007-01-01
, heterogeneity, and inadequate description of techniques implemented. Methods: The aim is to propose a consensus established by the European Bifurcation Club (EBC), on the definition and classification of bifurcation lesions and treatments implemented with the purpose of allowing comparisons between techniques...... proposes a new classification of bifurcation lesions and their treatments to permit accurate comparisons of well described techniques in homogeneous lesion groups. (c) 2008 Wiley-Liss, Inc. Udgivelsesdato: 2007-Nov-5...
Stability and Bifurcation of Two Kinds of Three-Dimensional Fractional Lotka-Volterra Systems
Directory of Open Access Journals (Sweden)
Jinglei Tian
2014-01-01
Full Text Available Two kinds of three-dimensional fractional Lotka-Volterra systems are discussed. For one system, the asymptotic stability of the equilibria is analyzed by providing some sufficient conditions. And bifurcation property is investigated by choosing the fractional order as the bifurcation parameter for the other system. In particular, the critical value of the fractional order is identified at which the Hopf bifurcation may occur. Furthermore, the numerical results are presented to verify the theoretical analysis.
Delayed Hopf bifurcation in time-delayed slow-fast systems
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
This paper presents an investigation on the phenomenon of delayed bifurcation in time-delayed slow-fast differential systems.Here the two delayed’s have different meanings.The delayed bifurcation means that the bifurcation does not happen immediately at the bifurcation point as the bifurcation parameter passes through some bifurcation point,but at some other point which is above the bifurcation point by an obvious distance.In a time-delayed system,the evolution of the system depends not only on the present state but also on past states.In this paper,the time-delayed slow-fast system is firstly simplified to a slow-fast system without time delay by means of the center manifold reduction,and then the so-called entry-exit function is defined to characterize the delayed bifurcation on the basis of Neishtadt’s theory.It shows that delayed Hopf bifurcation exists in time-delayed slow-fast systems,and the theoretical prediction on the exit-point is in good agreement with the numerical calculation,as illustrated in the two illustrative examples.
Non-Smooth Bifurcation and Chaos in a DC-DC Buck Converter
Institute of Scientific and Technical Information of China (English)
QIN Zhi-Ying; LU Qi-Shao
2007-01-01
A direct-current-dorect-current (DC-DC)buck converter with integrated load current feedback is studied with three kinds of Poicaré maps.The external corner-collision bifurcation occurs when the crossing number per period varies,and the internal corner-collision bifurcations occur along with period-doubling and period-tripling bifurcations in this model.The multi-band chaos roots in external corner-collision bifurcation and often grows into l-band chaos.A new kind of chaotic sliding orbits,which is more complex for non-smooth systems,is also found in this model.
Bifurcation analysis of polynomial models for longitudinal motion at high angle of attack
Institute of Scientific and Technical Information of China (English)
Shi Zhongke; Fan Li
2013-01-01
To investigate the longitudinal motion stability of aircraft maneuvers conveniently,a new stability analysis approach is presented in this paper.Based on describing longitudinal aerodynamics at high angle-of-attack (α ＜ 50°) motion by polynomials,a union structure of two-order differential equation is suggested.By means of nonlinear theory and method,analytical and global bifurcation analyses of the polynomial differential systems are provided for the study of the nonlinear phenomena of high angle-of-attack flight.Applying the theories of bifurcations,many kinds of bifurcations,such as equilibrium,Hopf,homoclinic (heteroclinic) orbit and double limit cycle bifurcations are discussed and the existence conditions for these bifurcations as well as formulas for calculating bifurcation curves are derived.The bifurcation curves divide the parameter plane into several regions; moreover,the complete bifurcation diagrams and phase portraits in different regions are obtained.Finally,our conclusions are applied to analyzing the stability and bifurcations of a practical example of a high angle-of-attack flight as well as the effects of elevator deflection on the asymptotic stability regions of equilibrium.The model and analytical methods presented in this paper can be used to study the nonlinear flight dynamic of longitudinal stall at high angle of attack.
Bifurcation analysis and stability design for aircraft longitudinal motion with high angle of attack
Institute of Scientific and Technical Information of China (English)
Xin Qi; Shi Zhongke
2015-01-01
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 pre-dict the special nonlinear flight phenomena, bifurcation theory and continuation method are employed to systematically analyze the nonlinear motions. With the refinement of the flight dynam-ics for F-8 Crusader longitudinal motion, a framework is derived to identify the stationary bifurca-tion 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 ser-ies 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.
Border-Collision Bifurcations and Chaotic Oscillations in a Piecewise-Smooth Dynamical System
DEFF Research Database (Denmark)
Zhusubaliyev, Z.T.; Soukhoterin, E.A.; Mosekilde, Erik
2002-01-01
-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....... We show that a denumerable set of unstable cycles can arise together with stable cycles at border-collision bifurcations. The characteristic peculiarities of border-collision bifurcational transitions in piecewise-smooth systems are described and we provide a comparison with some recent results....
Dynamic bifurcation of a modified Kuramoto-Sivashinsky equation with higher-order nonlinearity
Institute of Scientific and Technical Information of China (English)
Huang Qiong-Wei; Tang Jia-Shi
2011-01-01
Under the periodic boundary condition,dynamic bifurcation and stability in the modified Kuramoto-Sivashinsky equation with a higher-order nonlinearity p(ux)Puxx are investigated by using the centre manifold reduction procedure.The result shows that as the control parameter crosses a critical value,the system undergoes a bifurcation from the trivial solution to produce a cycle consisting of locally asymptotically stable equilibrium points. Furthermore,for cases in which the distances to the bifurcation points are small enough,one-order approximations to the bifurcation solutions are obtained.
Regularizations of two-fold bifurcations in planar piecewise smooth systems using blowup
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall; Hogan, S. J.
2015-01-01
rigorously how singular canards can persist and how the bifurcation of pseudo-equilibria is related to bifurcations of equilibria in the regularized system. We also show that PWS limit cycles are connected to Hopf bifurcations of the regularization. In addition, we show how regularization can create another...... type of limit cycle that does not appear to be present in the original PWS system. For both types of limit cycle, we show that the criticality of the Hopf bifurcation that gives rise to periodic orbits is strongly dependent on the precise form of the regularization. Finally, we analyse the limit cycles...
Non-smooth saddle-node bifurcations III: Strange attractors in continuous time
Fuhrmann, G.
2016-08-01
Non-smooth saddle-node bifurcations give rise to minimal sets of interesting geometry built of so-called strange non-chaotic attractors. We show that certain families of quasiperiodically driven logistic differential equations undergo a non-smooth bifurcation. By a previous result on the occurrence of non-smooth bifurcations in forced discrete time dynamical systems, this yields that within the class of families of quasiperiodically driven differential equations, non-smooth saddle-node bifurcations occur in a set with non-empty C2-interior.
Practical aspects of backward bifurcation in a mathematical model for tuberculosis.
Gerberry, David J
2016-01-01
In this work, we examine practical aspects of backward bifurcation for a data-based model of tuberculosis that incorporates multiple features which have previously been shown to produce backward bifurcation (e.g. exogenous reinfection and imperfect vaccination) and new considerations such as the treatment of latent TB infection (LTBI) and the BCG vaccine's interference with detecting LTBI. Understanding the interplay between these multiple factors and backward bifurcation is particularly timely given that new diagnostic tests for LTBI detection could dramatically increase rates of both LTBI detection and vaccination in the coming decades. By establishing analytic thresholds for the existence of backward bifurcation, we identify those aspects of TB's complicated pathology that make backward bifurcation more or less likely to occur. We also examine the magnitude of the backward bifurcation produced by the model and its sensitivity to various model parameters. We find that backward bifurcation is unlikely to occur. While increased vaccine coverage and/or increased detection and treatment of LTBI can push the threshold for backward bifurcation into the region of biological plausibility, the resulting bifurcations may still be too small to have any noticeable epidemiological impact.
ELEMENTARY BIFURCATIONS FOR A SIMPLE DYNAMICAL SYSTEM UNDER NON-GAUSSIAN L(é)VY NOISES
Institute of Scientific and Technical Information of China (English)
Chen Huiqin; Duan Jinqiao; Zhang Chengjian
2012-01-01
Nonlinear dynamical systems are sometimes under the influence of random fluctuations.It is desirable to examine possible bifurcations for stochastic dynamical systems when a parameter varies.@@A computational analysis is conducted to investigate bifurcations of a simple dynamical system under non-Gaussian α-stable Lévy motions,by examining the changes in stationary probability density functions for the solution orbits of this stochastic system.The stationary probability density functions are obtained by solving a nonlocal Fokker-Planck equation numerically.This allows numerically investigating phenomenological bifurcation,or P-bifurcation,for stochastic differential equations with non-Gaussian Lévy noises.
Ding, Dawei; Luo, Xiaoshu; Liu, Yuliang
2007-01-01
This paper focuses on the delay induced Hopf bifurcation in a dual model of Internet congestion control algorithms which can be modeled as a time-delay system described by a one-order delay differential equation (DDE). By choosing communication delay as the bifurcation parameter, we demonstrate that the system loses its stability and a Hopf bifurcation occurs when communication delay passes through a critical value. Moreover, the bifurcating periodic solution of system is calculated by means of perturbation methods. Discussion of stability of the periodic solutions involves the computation of Floquet exponents by considering the corresponding Poincare -Lindstedt series expansion. Finally, numerical simulations for verify the theoretical analysis are provided.
Bifurcation Analysis of a Lotka-Volterra Mutualistic System with Multiple Delays
Directory of Open Access Journals (Sweden)
Xin-You Meng
2014-01-01
Full Text Available A class of Lotka-Volterra mutualistic system with time delays of benefit and feedback delays is introduced. By analyzing the associated characteristic equation, the local stability of the positive equilibrium and existence of Hopf bifurcation are obtained under all possible combinations of two or three delays selecting from multiple delays. Not only explicit formulas to determine the properties of the Hopf bifurcation are shown by using the normal form method and center manifold theorem, but also the global continuation of Hopf bifurcation is investigated by applying a global Hopf bifurcation result due to Wu (1998. Numerical simulations are given to support the theoretical results.
Shrinking point bifurcations of resonance tongues for piecewise-smooth, continuous maps
International Nuclear Information System (INIS)
Resonance tongues are mode-locking regions of parameter space in which stable periodic solutions occur; they commonly occur, for example, near Neimark–Sacker bifurcations. For piecewise-smooth, continuous maps these tongues typically have a distinctive lens-chain (or sausage) shape in two-parameter bifurcation diagrams. We give a symbolic description of a class of 'rotational' periodic solutions that display lens-chain structures for a general N-dimensional map. We then unfold the codimension-two, shrinking point bifurcation, where the tongues have zero width. A number of codimension-one bifurcation curves emanate from shrinking points and we determine those that form tongue boundaries
Control of Fold Bifurcation Application on Chemostat around Critical Dilution Rate
DEFF Research Database (Denmark)
Pedersen, Kurt; Jørgensen, Sten Bay
1999-01-01
Based on a bifurcation analysis of a process it is possible to point out where there might be operational problems due to change of stability of the process. One such change is investigated, Fold bifurcations. This type of bifurcation is associated with hysteresis/multiple steady states, which...... complicates operation close to these bifurcations. Typically only one of the steady states is interesting from a production point of view. A novel control law is proposed herein which is able to cope with the operational problems of the process....
Big Bang Bifurcation Analysis and Allee Effect in Generic Growth Functions
Leonel Rocha, J.; Taha, Abdel-Kaddous; Fournier-Prunaret, D.
2016-06-01
The main purpose of this work is to study the dynamics and bifurcation properties of generic growth functions, which are defined by the population size functions of the generic growth equation. This family of unimodal maps naturally incorporates a principal focus of ecological and biological research: the Allee effect. The analysis of this kind of extinction phenomenon allows to identify a class of Allee’s functions and characterize the corresponding Allee’s effect region and Allee’s bifurcation curve. The bifurcation analysis is founded on the performance of fold and flip bifurcations. The dynamical behavior is rich with abundant complex bifurcation structures, the big bang bifurcations of the so-called “box-within-a-box” fractal type being the most outstanding. Moreover, these bifurcation cascades converge to different big bang bifurcation curves with distinct kinds of boxes, where for the corresponding parameter values several attractors are associated. To the best of our knowledge, these results represent an original contribution to clarify the big bang bifurcation analysis of continuous 1D maps.
Coronary bifurcation stenting: insights from in vitro and virtual bench testing.
Mortier, Peter; De Beule, Matthieu; Dubini, Gabriele; Hikichi, Yutaka; Murasato, Yoshinobu; Ormiston, John A
2010-12-01
The various techniques and devices that have been proposed for the treatment of coronary bifurcation lesions have differing levels of complexity and each has one or more limitations. Two highly complementary ex vivo methods are available to study the treatment of bifurcation lesions: in vitro and virtual bench testing. Both methods can be used to develop, evaluate and optimise bifurcation stenting techniques and dedicated devices. The basics, the evolution, the advantages and limitations of both methods are discussed in this paper. Subsequently, a literature overview of the main insights gained from ex vivo testing in the field of bifurcation stenting is given.
Numerical Hopf bifurcation of Runge-Kutta methods for a class of delay differential equations
International Nuclear Information System (INIS)
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 Rd. 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(hp) 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.
Directory of Open Access Journals (Sweden)
Zizhen Zhang
2013-01-01
Full Text Available Hopf bifurcation of a delayed predator-prey system with prey infection and the modified Leslie-Gower scheme is investigated. The conditions for the stability and existence of Hopf bifurcation of the system are obtained. The state feedback and parameter perturbation are used for controlling Hopf bifurcation in the system. In addition, direction of Hopf bifurcation and stability of the bifurcated periodic solutions of the controlled system are obtained by using normal form and center manifold theory. Finally, numerical simulation results are presented to show that the hybrid controller is efficient in controlling Hopf bifurcation.
Energy Technology Data Exchange (ETDEWEB)
Natsheh, Ammar N. [Faculty of Engineering, Al-Ahliyya Amman University, Post Code 19328 Amman (Jordan); Nazzal, Jamal M. [Faculty of Engineering, Al-Ahliyya Amman University, Post Code 19328 Amman (Jordan)]. E-mail: jnazzal@ammanu.edu.jo
2007-08-15
This work describes the bifurcational behavior of a modular peak current-mode controlled DC-DC boost converter with multi bifurcation parameters. The parallel-input/parallel-output converter consists of two identical boost circuits and operates in the continuous-current conduction mode (CCM). A nonlinear mapping in closed form is derived and bifurcation diagrams are generated using MATLAB. A comparison is made between the modular converter diagrams with those of the single boost converter. The effect of introducing mutual coupling between the inductors of the constituent modules is also addressed. Results are verified using the circuit analysis package PSPICE.
The 'Sphere': A Dedicated Bifurcation Aneurysm Flow-Diverter Device.
Peach, Thomas; Cornhill, J Frederick; Nguyen, Anh; Riina, Howard; Ventikos, Yiannis
2014-01-01
We present flow-based results from the early stage design cycle, based on computational modeling, of a prototype flow-diverter device, known as the 'Sphere', intended to treat bifurcation aneurysms of the cerebral vasculature. The device is available in a range of diameters and geometries and is constructed from a single loop of NITINOL(®) wire. The 'Sphere' reduces aneurysm inflow by means of a high-density, patterned, elliptical surface that partially occludes the aneurysm neck. The device is secured in the healthy parent vessel by two armatures in the shape of open loops, resulting in negligible disruption of parent or daughter vessel flow. The device is virtually deployed in six anatomically accurate bifurcation aneurysms: three located at the Basilar tip and three located at the terminus bifurcation of the Internal Carotid artery (at the meeting of the middle cerebral and anterior cerebral arteries). Both steady state and transient flow simulations reveal that the device presents with a range of aneurysm inflow reductions, with mean flow reductions falling in the range of 30.6-71.8% across the different geometries. A significant difference is noted between steady state and transient simulations in one geometry, where a zone of flow recirculation is not captured in the steady state simulation. Across all six aneurysms, the device reduces the WSS magnitude within the aneurysm sac, resulting in a hemodynamic environment closer to that of a healthy vessel. We conclude from extensive CFD analysis that the 'Sphere' device offers very significant levels of flow reduction in a number of anatomically accurate aneurysm sizes and locations, with many advantages compared to current clinical cylindrical flow-diverter designs. Analysis of the device's mechanical properties and deployability will follow in future publications.
Transport bifurcation induced by sheared toroidal flow in tokamak plasmasa)
Highcock, E. G.; Barnes, M.; Parra, F. I.; Schekochihin, A. A.; Roach, C. M.; Cowley, S. C.
2011-10-01
First-principles numerical simulations are used to describe a transport bifurcation in a differentially rotating tokamak plasma. Such a bifurcation is more probable in a region of zero magnetic shear than one of finite magnetic shear, because in the former case the component of the sheared toroidal flow that is perpendicular to the magnetic field has the strongest suppressing effect on the turbulence. In the zero-magnetic-shear regime, there are no growing linear eigenmodes at any finite value of flow shear. However, subcritical turbulence can be sustained, owing to the existence of modes, driven by the ion temperature gradient and the parallel velocity gradient, which grow transiently. Nonetheless, in a parameter space containing a wide range of temperature gradients and velocity shears, there is a sizeable window where all turbulence is suppressed. Combined with the relatively low transport of momentum by collisional (neoclassical) mechanisms, this produces the conditions for a bifurcation from low to high temperature and velocity gradients. A parametric model is constructed which accurately describes the combined effect of the temperature gradient and the flow gradient over a wide range of their values. Using this parametric model, it is shown that in the reduced-transport state, heat is transported almost neoclassically, while momentum transport is dominated by subcritical parallel-velocity-gradient-driven turbulence. It is further shown that for any given input of torque, there is an optimum input of heat which maximises the temperature gradient. The parametric model describes both the behaviour of the subcritical turbulence (which cannot be modelled by the quasi-linear methods used in current transport codes) and the complicated effect of the flow shear on the transport stiffness. It may prove useful for transport modelling of tokamaks with sheared flows.
Dynamics and Bifurcations of Travelling Wave Solutions of (, ) Equations
Indian Academy of Sciences (India)
Dahe Feng; Jibin Li
2007-11-01
By using the bifurcation theory and methods of planar dynamical systems to (, ) equations, the dynamical behavior of different physical structures like smooth and non-smooth solitary wave, kink wave, smooth and non-smooth periodic wave, and breaking wave is obtained. The qualitative change in the physical structures of these waves is shown to depend on the systemic parameters. Under different regions of parametric spaces, various sufficient conditions to guarantee the existence of the above waves are given. Moreover, some explicit exact parametric representations of travelling wave solutions are listed.
Bifurcations of rotating waves in rotating spherical shell convection.
Feudel, F; Tuckerman, L S; Gellert, M; Seehafer, N
2015-11-01
The dynamics and bifurcations of convective waves in rotating and buoyancy-driven spherical Rayleigh-Bénard convection are investigated numerically. The solution branches that arise as rotating waves (RWs) are traced by means of path-following methods, by varying the Rayleigh number as a control parameter for different rotation rates. The dependence of the azimuthal drift frequency of the RWs on the Ekman and Rayleigh numbers is determined and discussed. The influence of the rotation rate on the generation and stability of secondary branches is demonstrated. Multistability is typical in the parameter range considered.
Limit cycles and Hopf bifurcations in a Kolmogorov type system
Directory of Open Access Journals (Sweden)
Simona Muratori
1989-04-01
Full Text Available The paper is devoted to the study of a class of Kolmogorov type systems which can be used to represent the dynamic behaviour of prey and predators. The model is an extension of the classical prey-predator model since it allows intra-specific competition for the predator's species. The analysis shows that the system can only have Kolmogorov's two modes of behaviour: a globally stable equilibrium or a globally stable limit cycle. Moreover, the transition from one of these two modes to the other is a non-catastrophic Hopf bifurcation which can be specified analytically.
Statistical properties of the universal limit map of grazing bifurcations
Li, Denghui; Chen, Hebai; Xie, Jianhua
2016-09-01
In this paper, the statistical properties of an interval map, having a square-root singular point which characterizes grazing bifurcations of impact oscillators, are studied. Firstly, we show that in some parameter regions the map admits an induced Markov structure with an exponential decay tail of the return times. Then we prove that the map has a unique mixing absolutely continuous invariant probability measure. Finally, by applying the Markov tower method, we prove that exponential decay of correlations and the central limit theorem hold for Hölder continuous observations.
Trapping scaling for bifurcations in the Vlasov systems.
Barré, J; Métivier, D; Yamaguchi, Y Y
2016-04-01
We study nonoscillating bifurcations of nonhomogeneous steady states of the Vlasov equation, a situation occurring in galactic models, or for Bernstein-Greene-Kruskal modes in plasma physics. Through an unstable manifold expansion, we show that in one spatial dimension the dynamics is very sensitive to the initial perturbation: the instability may saturate at small amplitude-generalizing the "trapping scaling" of plasma physics-or may grow to produce a large-scale modification of the system. Furthermore, resonances are strongly suppressed, leading to different phenomena with respect to the homogeneous case. These analytical findings are illustrated and extended by direct numerical simulations with a cosine interaction potential.
The symmetry groups of bifurcations of integrable Hamiltonian systems
Energy Technology Data Exchange (ETDEWEB)
Orlova, E I [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
2014-11-30
Two-dimensional atoms are investigated; these are used to code bifurcations of the Liouville foliations of nondegenerate integrable Hamiltonian systems. To be precise, the symmetry groups of atoms with complexity at most 3 are under study. Atoms with symmetry group Z{sub p}⊕Z{sub q} are considered. It is proved that Z{sub p}⊕Z{sub q} is the symmetry group of a toric atom. The symmetry groups of all nonorientable atoms with complexity at most 3 are calculated. The concept of a geodesic atom is introduced. Bibliography: 9 titles.
Equilibrium points and bifurcation control of a chaotic system
Institute of Scientific and Technical Information of China (English)
Liang Cui-Xiang; Tang Jia-Shi
2008-01-01
Based on the Routh-Hurwitz criterion,this paper investigates the stability of a new chaotic system.State feedback controllers are designed to control the chaotic system to the unsteady equilibrium points and limit cycle.Theoretical analyses give the range of value of control parameters to stabilize the unsteady equilibrium points of the chaotic system and its critical parameter for generating Hopf bifurcation.Certain nP periodic orbits can be stabilized by parameter adjustment.Numerical simulations indicate that the method can effectively guide the system trajectories to unsteady equilibrium points and periodic orbits.
Synchronization and basin bifurcations in mutually coupled oscillators
Indian Academy of Sciences (India)
U E Vincent; A N Njah; O Akinlade
2007-05-01
Synchronization behaviour of two mutually coupled double-well Duffig oscillators exhibiting cross-well chaos is examined. Synchronization of the subsystems was observed for coupling strength > 0.4. It is found that when the oscillators are operated in the regime for which two attractors coexist in phase space, basin bifurcation sequences occur leading to + 1, ≥ 2 basins as the coupling is varied – a signature of Wada structure and ﬁnal-state sensitivity. However, in the region of complete synchronization, the basins structure is identical with that of the single oscillators and retains its essential features including fractal basin boundaries.
Imperfect pitchfork bifurcation in asymmetric two-compartment granular gas
Institute of Scientific and Technical Information of China (English)
Zhang Yin; Li Yin-Chang; Liu Rui; Cui Fei-Fei; Pierre Evesque; Hou Mei-Ying
2013-01-01
The clustering behavior of a mono-disperse granular gas is experimentally studied in an asymmetric two-compartment setup.Unlike the random clustering in either compartment in the case of symmetric configuration when lowering the shaking strength to below a critical value,the directed clustering is observed,which corresponds to an imperfect pitchfork bifurcation.Numerical solutions of the flux equation using a modified simple flux function show qualitative agreements with the experimental results.The potential application of this asymmetric structure is discussed.
Stochastic calculus application to dynamic bifurcations and threshold crossings
Jansons, K M; Jansons, Kalvis M.
1997-01-01
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. The threshold crossing problem used, for example, to model the firing of a single cortical neuron is considered, concentrating on quantities that may be experimentally measurable but have so far received little attention. Expressions for the statistics of pre-threshold excursions, occupation density and last crossing time of zero are compared with results from numerical generation of paths.
Bifurcation phenomena of photodetached electron flux in parallel external fields
Institute of Scientific and Technical Information of China (English)
Gao Song; Li Hong-Yun; Yang Guang-Can; Lin Sheng-Lu
2007-01-01
A semiclassical method based on the closed-orbit theory is applied to analysing the dynamics of photodetached electron of H- in the parallel electric and magnetic fields. By simply varying the magnetic field we reveal spatial bifurcations of electron orbits at a fixed emission energy, which is referred to as the fold caustic in classical motion. The quantum manifestations of these singularities display a series of intermittent divergences in electronic flux distributions.We introduce semiclassical uniform approximation to repair the electron wavefunctions locally in a mixed phase space and obtain reasonable results. The approximation provides a better treatment of the problem.
Bifurcation in a Discrete-Time Piecewise Constant Dynamical System
Directory of Open Access Journals (Sweden)
Chenmin Hou
2013-01-01
Full Text Available The study of recurrent neural networks with piecewise constant transition or control functions has attracted much attention recently because they can be used to simulate many physical phenomena. A recurrent and discontinuous two-state dynamical system involving a nonnegative bifurcation parameter is studied. By elementary but novel arguments, we are able to give a complete analysis on its asymptotic behavior when the parameter varies from 0 to . It is hoped that our analysis will provide motivation for further results on large-scale recurrent McCulloch-Pitts-type neural networks and piecewise continuous discrete-time dynamical systems.
Perturbed period-doubling bifurcation. II. Experiments on Josephson junctions
DEFF Research Database (Denmark)
Eriksen, Gert Friis; Hansen, Jørn Bindslev
1990-01-01
We present experimental results on the effect of periodic perturbations on a driven, dynamic system that is close to a period-doubling bifurcation. In the preceding article a scaling law for the change of stability of such a system was derived for the case where the perturbation frequency ω......B as a function of the frequency and the amplitude of the perturbation signal ΔμB(ωS,AS) for a model system, the microwave-driven Josephson tunnel junction, and find reasonable agreement between the experimental results and the theory....
One-dimensional map lattices: Synchronization, bifurcations, and chaotic structures
DEFF Research Database (Denmark)
Belykh, Vladimir N.; Mosekilde, Erik
1996-01-01
The paper presents a qualitative analysis of coupled map lattices (CMLs) for the case of arbitrary nonlinearity of the local map and with space-shift as well as diffusion coupling. The effect of synchronization where, independently of the initial conditions, all elements of a CML acquire uniform...... dynamics is investigated and stable chaotic time behaviors, steady structures, and traveling waves are described. Finally, the bifurcations occurring under the transition from spatiotemporal chaos to chaotic synchronization and the peculiarities of CMLs with specific symmetries are discussed....
Bifurcation and Chaos Control for Nonlinear Laser Systems
Institute of Scientific and Technical Information of China (English)
2001-01-01
In recent years, complexity science, including various bifurcations ,chaos and turbulence, has become a great challenge in various interdisciplinary fields. It promises to have a major impact on many aspects of nature science and engineering, even social and economic science. Candidates of complex system include coupled laser systems, accelerator-driven clean nuclear power system, neural networks, cellular automata, living organism, human brain, chemical reactions and economic systems. This new and challenging research and development area has in effect become a scientific inter-discipline itself, involving systems and control engineers, theoretical and experimental
Backward bifurcation and optimal control of Plasmodium Knowlesi malaria
Abdullahi, Mohammed Baba; Hasan, Yahya Abu; Abdullah, Farah Aini
2014-07-01
A deterministic model for the transmission dynamics of Plasmodium Knowlesi malaria with direct transmission is developed. The model is analyzed using dynamical system techniques and it shows that the backward bifurcation occurs for some range of parameters. The model is extended to assess the impact of time dependent preventive (biological and chemical control) against the mosquitoes and vaccination for susceptible humans, while treatment for infected humans. The existence of optimal control is established analytically by the use of optimal control theory. Numerical simulations of the problem, suggest that applying the four control measure can effectively reduce if not eliminate the spread of Plasmodium Knowlesi in a community.
Bifurcation for Dynamical Systems of Planet-Belt Interaction
Jiang, Ing-Guey; Yeh, Li-Chin
2002-01-01
The dynamical systems of planet-belt interaction are studied by the fixed-point analysis and the bifurcation of solutions on the parameter space is discussed. For most cases, our analytical and numerical results show that the locations of fixed points are determined by the parameters and these fixed points are either structurally stable or unstable. In addition to that, there are two special fixed points: the one on the inner edge of the belt is asymptotically stable and the one on the outer ...
Resonances and bifurcations in systems with elliptical equipotentials
Marchesiello, Antonella
2012-01-01
We present a general analysis of the orbit structure of 2D potentials with self-similar elliptical equipotentials by applying the method of Lie transform normalization. We study the most relevant resonances and related bifurcations. We find that the 1:1 resonance is associated only to the appearance of the loops and leads to the destabilization of either one or the other normal modes, depending on the ellipticity of equipotentials. Inclined orbits are never present and may appear only when the equipotentials are heavily deformed. The 1:2 resonance determines the appearance of bananas and anti-banana orbits: the first family is stable and always appears at a lower energy than the second, which is unstable. The bifurcation sequence also produces the variations in the stability character of the major axis orbit and is modified only by very large deformations of the equipotentials. Higher-order resonances appear at intermediate or higher energies and can be described with good accuracy.
Dynamics of Surfactant Liquid Plugs at Bifurcating Lung Airway Models
Tavana, Hossein
2013-11-01
A surfactant liquid plug forms in the trachea during surfactant replacement therapy (SRT) of premature babies. Under air pressure, the plug propagates downstream and continuously divides into smaller daughter plugs at continuously branching lung airways. Propagating plugs deposit a thin film on airway walls to reduce surface tension and facilitate breathing. The effectiveness of SRT greatly depends on the final distribution of instilled surfactant within airways. To understand this process, we investigate dynamics of splitting of surfactant plugs in engineered bifurcating airway models. A liquid plug is instilled in the parent tube to propagate and split at the bifurcation. A split ratio, R, is defined as the ratio of daughter plug lengths in the top and bottom daughter airway tubes and studied as a function of the 3D orientation of airways and different flow conditions. For a given Capillary number (Ca), orienting airways farther away from a horizontal position reduced R due to the flow of a larger volume into the gravitationally favored daughter airway. At each orientation, R increased with 0.0005 surfactant distribution in airways and develop effective SRT strategies.
Stability and Bifurcation in Magnetic Flux Feedback Maglev Control System
Directory of Open Access Journals (Sweden)
Wen-Qing Zhang
2013-01-01
Full Text Available Nonlinear properties of magnetic flux feedback control system have been investigated mainly in this paper. We analyzed the influence of magnetic flux feedback control system on control property by time delay and interfering signal of acceleration. First of all, we have established maglev nonlinear model based on magnetic flux feedback and then discussed hopf bifurcation’s condition caused by the acceleration’s time delay. The critical value of delayed time is obtained. It is proved that the period solution exists in maglev control system and the stable condition has been got. We obtained the characteristic values by employing center manifold reduction theory and normal form method, which represent separately the direction of hopf bifurcation, the stability of the period solution, and the period of the period motion. Subsequently, we discussed the influence maglev system on stability of by acceleration’s interfering signal and obtained the stable domain of interfering signal. Some experiments have been done on CMS04 maglev vehicle of National University of Defense Technology (NUDT in Tangshan city. The results of experiments demonstrate that viewpoints of this paper are correct and scientific. When time lag reaches the critical value, maglev system will produce a supercritical hopf bifurcation which may cause unstable period motion.
Dark-lines in bifurcation plots of nonlinear dynamic systems
Institute of Scientific and Technical Information of China (English)
Gao Zhi-Ying; Shen Yun-Wen; Liu Meng-Jun
2005-01-01
Based on the regressive character of chaotic motion in nonlinear dynamic systems, a numerical regression algorithm is developed, which can be used to research the dark-lines passing through chaotic regions in bifurcation plots. The dark-lines of the parabolic mapping are obtained by using the numerical regression algorithm, and compared with those that are accurately acquired through dark-line equations. Thus the validity of this algorithm is proved. Furthermore,for the Brussel oscillation system and the piecewise linear dynamic system of a gear pair, the dark-lines are researched by using the regression algorithm. By researching the dark-lines in the bifurcation plots of nonlinear dynamic systems,the periodic windows embedded in chaotic regions can be ascertained by tangential points of dark-lines, and the turning points of chaotic attractors can be also obtained by intersected points. The results show that this algorithm is helpful to analyse dynamic behaviour of systems and control chaotic motion.
Prediction of fibre architecture and adaptation in diseased carotid bifurcations.
LENUS (Irish Health Repository)
Creane, Arthur
2011-12-01
Many studies have used patient-specific finite element models to estimate the stress environment in atherosclerotic plaques, attempting to correlate the magnitude of stress to plaque vulnerability. In complex geometries, few studies have incorporated the anisotropic material response of arterial tissue. This paper presents a fibre remodelling algorithm to predict the fibre architecture, and thus anisotropic material response in four patient-specific models of the carotid bifurcation. The change in fibre architecture during disease progression and its affect on the stress environment in the plaque were predicted. The mean fibre directions were assumed to lie at an angle between the two positive principal strain directions. The angle and the degree of dispersion were assumed to depend on the ratio of principal strain values. Results were compared with experimental observations and other numerical studies. In non-branching regions of each model, the typical double helix arterial fibre pattern was predicted while at the bifurcation and in regions of plaque burden, more complex fibre architectures were found. The predicted change in fibre architecture in the arterial tissue during plaque progression was found to alter the stress environment in the plaque. This suggests that the specimen-specific anisotropic response of the tissue should be taken into account to accurately predict stresses in the plaque. Since determination of the fibre architecture in vivo is a difficult task, the system presented here provides a useful method of estimating the fibre architecture in complex arterial geometries.
Stability and Hopf Bifurcation Analysis of a Gene Expression Model with Diffusion and Time Delay
Directory of Open Access Journals (Sweden)
Yahong Peng
2014-01-01
Full Text Available We consider a model for gene expression with one or two time delays and diffusion. The local stability and delay-induced Hopf bifurcation are investigated. We also derive the formulas determining the direction and the stability of Hopf bifurcations by calculating the normal form on the center manifold.
Computing Bifurcation Diagrams of Steady State KuramotoSivashinsky Equation by Difference Method
Institute of Scientific and Technical Information of China (English)
无
1999-01-01
Utilizing difference formulae, we obtained the discrete systems of steady state Kuramoto-Sivashinsky (K-S) equation. Applied Newton's method and continuation technology to the systems, the bifurcated solutions are derived, and the bifurcation diagrams are constructed. All the results are successful and satisfactory.
Global view of Hopf bifurcations of a van der Pol oscillator with delayed state feedback
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
This paper presents both analytical and numerical studies on the global view of Hopf bifurcations of a van der Pol oscillator with delayed state feedback.Based on a detailed analysis of the stability switches of the trivial equilibrium of the system,the stability charts are given in a parameter space consisting of the time delay and the feedback gains.The center manifold reduc-tion and the normal form method are used to study Hopf bifurcations with respect to the time delay.To gain an insight into the persistence of a Hopf bifurcation as the time delay varies farther away from its critical value,the method of multiple scales is used to obtain the global view of Hopf bifurcations with respect to the time delay.Both the analytical results of Hopf bifurca-tions and global view of those bifurcations are validated via a collocation scheme implemented on DDE-Biftool.The most important discovery in this paper is the well-structured global view of Hopf bifurcations for the system of concern,showing the generality of the persistence of Hopf bifurcations.
RESONANT BIFURCATIONS OF THE HOMOCLINIC MANIFOLD FOR FOURTH-DIMENSIONAL SYSTEM
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
The homoclinic bifurcations under resonant conditions are considered in the ho- moclinic manifold consisting of a series of homoclinic orbits for the fourth-dimensional system.The existence,coexistence and uniqueness of 1-homoclinic orbit,1-periodic orbit and 2-fold 1-periodic orbit are obtained under resonant condition,the correspon- ding bifurcation surfaces and existing regions are also given.
Backward bifurcations, turning points and rich dynamics in simple disease models.
Zhang, Wenjing; Wahl, Lindi M; Yu, Pei
2016-10-01
In this paper, dynamical systems theory and bifurcation theory are applied to investigate the rich dynamical behaviours observed in three simple disease models. The 2- and 3-dimensional models we investigate have arisen in previous investigations of epidemiology, in-host disease, and autoimmunity. These closely related models display interesting dynamical behaviors including bistability, recurrence, and regular oscillations, each of which has possible clinical or public health implications. In this contribution we elucidate the key role of backward bifurcations in the parameter regimes leading to the behaviors of interest. We demonstrate that backward bifurcations with varied positions of turning points facilitate the appearance of Hopf bifurcations, and the varied dynamical behaviors are then determined by the properties of the Hopf bifurcation(s), including their location and direction. A Maple program developed earlier is implemented to determine the stability of limit cycles bifurcating from the Hopf bifurcation. Numerical simulations are presented to illustrate phenomena of interest such as bistability, recurrence and oscillation. We also discuss the physical motivations for the models and the clinical implications of the resulting dynamics.
Stability and Bifurcation Analysis of Man-machine System with Time Delay
Institute of Scientific and Technical Information of China (English)
YANG Ji-hua; LIU Mei
2012-01-01
A mathematical model of man-machine system is considered.Based on the reference [4],the direction and stability of the Hopf bifurcation are determined using the normal form method and the center manifold theory.Furthermore,the existence of Hopf-zero bifurcation is discussed.In the end,some numerical simulations are carried out to illustrate the results found.
The anatomy of the bifurcated neural spine and its occurrence within Tetrapoda.
Woodruff, D Cary
2014-09-01
Vertebral neural spine bifurcation has been historically treated as largely restrictive to sauropodomorph dinosaurs; wherein it is inferred to be an adaptation in response to the increasing weight from the horizontally extended cervical column. Because no extant terrestrial vertebrates have massive, horizontally extended necks, extant forms with large cranial masses were examined for the presence of neural spine bifurcation. Here, I report for the first time on the soft tissue surrounding neural spine bifurcation in a terrestrial quadruped through the dissection of three Ankole-Watusi cattle. With horns weighing up to a combined 90 kg, the Ankole-Watusi is unlike any other breed of cattle in terms of cranial weight and presence of neural spine bifurcation. Using the Ankole-Watusi as a model, it appears that neural spine bifurcation plays a critical role in supporting a large mobile weight adjacent to the girdles. In addition to neural spine bifurcation being recognized within nonavian dinosaurs, this vertebral feature is also documented within many members of temnospondyls, captorhinids, seymouriamorphs, diadectomorphs, Aves, marsupials, artiodactyls, perissodactyls, and Primates, amongst others. This phylogenetic distribution indicates that spine bifurcation is more common than previously thought, and that this vertebral adaptation has contributed throughout the evolutionary history of tetrapods. Neural spine bifurcation should now be recognized as an anatomical component adapted by some vertebrates to deal with massive, horizontal, mobile weights adjacent the girdles.
Bifurcations of a predator-prey model with non-monotonic response function
Broer, H.W.; Naudot, Vincent; Roussarie, Robert; Saleh, Khairul
2005-01-01
A 2-dimensional predator-prey model with five parameters is investigated, adapted from the Volterra-Lotka system by a non-monotonic response function. A description of the various domains of structural stability and their bifurcations is given. The bifurcation structure is reduced to four organising
Stability and Hopf bifurcations in a competitive Lotka-Volterra system with two delays
Energy Technology Data Exchange (ETDEWEB)
Song Yongli E-mail: songyl@sjtu.edu.cn; Han Maoan; Peng Yahong
2004-12-01
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.
Bifurcation Analysis of Gene Propagation Model Governed by Reaction-Diffusion Equations
Directory of Open Access Journals (Sweden)
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.
Clinical outcome after crush versus culotte stenting of coronary artery bifurcation lesions
DEFF Research Database (Denmark)
Kervinen, Kari; Niemelä, Matti; Romppanen, Hannu;
2013-01-01
The aim of the study was to compare long-term follow-up results of crush versus culotte stent techniques in coronary bifurcation lesions.......The aim of the study was to compare long-term follow-up results of crush versus culotte stent techniques in coronary bifurcation lesions....
Long-term results after simple versus complex stenting of coronary artery bifurcation lesions
DEFF Research Database (Denmark)
Maeng, Michael; Holm, Niels Ramsing; Erglis, Andrejs;
2013-01-01
Objectives This study sought to report the 5-year follow-up results of the Nordic Bifurcation Study. Background Randomized clinical trials with short-term follow-up have indicated that coronary bifurcation lesions may be optimally treated using the optional side branch stenting strategy. Methods ...
Hopf bifurcation in a dynamic IS-LM model with time delay
Energy Technology Data Exchange (ETDEWEB)
Neamtu, Mihaela [Department of Economic Informatics, Mathematics and Statistics, Faculty of Economics, West University of Timisoara, str. Pestalozzi, nr. 16A, 300115 Timisoara (Romania)]. E-mail: mihaela.neamtu@fse.uvt.ro; Opris, Dumitru [Department of Applied Mathematics, Faculty of Mathematics, West University of Timisoara, Bd. V. Parvan, nr. 4, 300223 Timisoara (Romania)]. E-mail: opris@math.uvt.ro; Chilarescu, Constantin [Department of Economic Informatics, Mathematics and Statistics, Faculty of Economics, West University of Timisoara, str. Pestalozzi, nr. 16A, 300115 Timisoara (Romania)]. E-mail: cchilarescu@rectorat.uvt.ro
2007-10-15
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.
$\\Delta I=4$ and $\\Delta I=8$ bifurcations in rotational bands of diatomic molecules
Bonatsos, Dennis; Lalazissis, G A; Drenska, S B; Minkov, N; Raychev, P P; Roussev, R P; Bonatsos, Dennis
1996-01-01
It is shown that the recently observed $\\Delta I=4$ bifurcation seen in superdeformed nuclear bands is also occurring in rotational bands of diatomic molecules. In addition, signs of a $\\Delta I=8$ bifurcation, of the same order of magnitude as the $\\Delta I=4$ one, are observed both in superdeformed nuclear bands and rotational bands of diatomic molecules.
Anti-control of Hopf Bifurcation in a Delayed Predator-prey Gomp ertz Mo del
Institute of Scientific and Technical Information of China (English)
XU Chang-jin; CHEN Da-xue
2013-01-01
A delayed predator-prey Gompertz model is investigated. The stability is ana-lyzed. Anti-control of Hopf bifurcation for the model is presented. Numerical simulations are performed to confirm that the new feedback controller using time delay is efficient in creating Hopf bifurcation. Finally, main conclusions are included.
Institute of Scientific and Technical Information of China (English)
Ji-cai Huang; Dong-mei Xiao
2004-01-01
In this paper the dynamical behaviors of a predator-prey system with Holling Type-IV functional response are investigated in detail by using the analyses of qualitative method,bifurcation theory,and numerical simulation.The qualitative analyses and numerical simulation for the model indicate that it has a unique stable limit cycle.The bifurcation analyses of the system exhibit static and dynamical bifurcations including saddlenode bifurcation,Hopf bifurcation,homoclinic bifurcation and bifurcation of cusp-type with codimension two(ie,the Bogdanov-Takens bifurcation),and we show the existence of codimension three degenerated equilibrium and the existence of homoclinic orbit by using numerical simulation.
Bifurcations of families of 1D-tori in 4D symplectic maps
Onken, Franziska; Lange, Steffen; Ketzmerick, Roland; Bäcker, Arnd
2016-06-01
The regular structures of a generic 4d symplectic map with a mixed phase space are organized by one-parameter families of elliptic 1d-tori. Such families show prominent bends, gaps, and new branches. We explain these features in terms of bifurcations of the families when crossing a resonance. For these bifurcations, no external parameter has to be varied. Instead, the longitudinal frequency, which varies along the family, plays the role of the bifurcation parameter. As an example, we study two coupled standard maps by visualizing the elliptic and hyperbolic 1d-tori in a 3d phase-space slice, local 2d projections, and frequency space. The observed bifurcations are consistent with the analytical predictions previously obtained for quasi-periodically forced oscillators. Moreover, the new families emerging from such a bifurcation form the skeleton of the corresponding resonance channel.
Bifurcations of families of 1D-tori in 4D symplectic maps.
Onken, Franziska; Lange, Steffen; Ketzmerick, Roland; Bäcker, Arnd
2016-06-01
The regular structures of a generic 4d symplectic map with a mixed phase space are organized by one-parameter families of elliptic 1d-tori. Such families show prominent bends, gaps, and new branches. We explain these features in terms of bifurcations of the families when crossing a resonance. For these bifurcations, no external parameter has to be varied. Instead, the longitudinal frequency, which varies along the family, plays the role of the bifurcation parameter. As an example, we study two coupled standard maps by visualizing the elliptic and hyperbolic 1d-tori in a 3d phase-space slice, local 2d projections, and frequency space. The observed bifurcations are consistent with the analytical predictions previously obtained for quasi-periodically forced oscillators. Moreover, the new families emerging from such a bifurcation form the skeleton of the corresponding resonance channel.
Impact of local flow haemodynamics on atherosclerosis in coronary artery bifurcations.
Antoniadis, Antonios P; Giannopoulos, Andreas A; Wentzel, Jolanda J; Joner, Michael; Giannoglou, George D; Virmani, Renu; Chatzizisis, Yiannis S
2015-01-01
Coronary artery bifurcations are susceptible to atherosclerosis as a result of the unique local flow patterns and the subsequent endothelial shear stress (ESS) environment that are conducive to the development of plaques. Along the lateral walls of the main vessel and side branches, a distinct flow pattern is observed with local low and oscillatory ESS, while high ESS develops at the flow divider (carina). Histopathologic studies have shown that the distribution of plaque at bifurcation regions is related to the local ESS patterns. The local ESS profile also influences the outcome of percutaneous coronary interventions in bifurcation lesions. A variety of invasive and non-invasive imaging modalities have enabled 3D reconstruction of coronary bifurcations and thereby detailed local ESS assessment by computational fluid dynamics. Highly effective strategies for treatment and ultimately prevention of atherosclerosis in coronary bifurcations are anticipated with the use of advanced imaging and computational fluid dynamic techniques.
Anti-Control of Hopf Bifurcation in the Chaotic Liu System with Symbolic Computation
Institute of Scientific and Technical Information of China (English)
LV Zhuo-Sheng; DUAN Li-Xia
2009-01-01
The anti-control of bifurcation refers to the task of creating a certain bifurcation with particular desired properties and location by appropriate controls. We consider, via feedback control and symbolic computation, the problem of anti-control of Hopf bifurcation in the chaotic Liu system. We propose an anti-control scheme and show that compared with the uncontrolled system, the anti-controlled Liu system can exhibit Hopf bifurcation in a much larger parameter region. The anti-control strategy used keeps the equilibrium structure of the Liu system and can be applied to generate Hopf bifurcation at the desired location with preferred stability. We illustrate the efficiency of the anti-control approach under different operating conditions.
Topological Aspect and Bifurcation of Disclination Lines in Two-Dimensional Liquid Crystals
Institute of Scientific and Technical Information of China (English)
YANG Guo-Hong; ZHANG Hui; DUAN Yi-Shi
2002-01-01
Using φ-mapping method and topological current theory, the topological structure and bifurcation ofdisclination lines in two-dimensional liquid crystals are studied. By introducing the strength density and the topologicalcurrent of many disclination lines, the total disclination strength is topologically quantized by the Hopf indices andBrouwer degrees at the singularities of the director field when the Jacobian determinant of director field does not vanish.When the Jacobian determinant vanishes, the origin, annihilation and bifurcation processes of disclination lines arestudied in the neighborhoods of the limit points and bifurcation points, respectively. The branch solutions at the limitpoint and the different directions of all branch curves at the bifurcation point are calculated with the conservation lawof the topological quantum numbers. It is pointed out that a disclination line with a higher strength is unstable and itwill evolve to the lower strength state through the bifurcation process.
Topological Aspect and Bifurcation of Disclination Lines in Two—Dimensional Liquid Crystals
Institute of Scientific and Technical Information of China (English)
YANGGuo－Hong; ZHANGHui; 等
2002-01-01
Using φ-mapping method and topological current theory,the topological structure and bifurcation of disclination lines in two-dimensional liquid crystals are studied.By introducing the strength density and the topological current of many disclination lines,the total disclination strength is topologically quantized by the Hopf indices and Brouwer degrees at the singularities of the director field when the Jacobian determinant of director field does not vanish.When the Jacobian determinant vanishes,the origin,annihilation and bifurcation processes of disclination lines are studied in the neighborhoods of the limit points and bifurcation points,respectively.The branch solutions at the limit point and the different directions of all branch curves at the bifurcation point are calculated with the conservation law of the topological quantum numbers.It is pointed out that a disclination line with a higher strength is unstable and it will evolve to the lower strength state through the bifurcation process.
Xiao, Min; Zheng, Wei Xing; Jiang, Guoping; Cao, Jinde
2015-12-01
In this paper, a fractional-order recurrent neural network is proposed and several topics related to the dynamics of such a network are investigated, such as the stability, Hopf bifurcations, and undamped oscillations. The stability domain of the trivial steady state is completely characterized with respect to network parameters and orders of the commensurate-order neural network. Based on the stability analysis, the critical values of the fractional order are identified, where Hopf bifurcations occur and a family of oscillations bifurcate from the trivial steady state. Then, the parametric range of undamped oscillations is also estimated and the frequency and amplitude of oscillations are determined analytically and numerically for such commensurate-order networks. Meanwhile, it is shown that the incommensurate-order neural network can also exhibit a Hopf bifurcation as the network parameter passes through a critical value which can be determined exactly. The frequency and amplitude of bifurcated oscillations are determined.
Zeros of a Class of Transcendental Equation with Application to Bifurcation of DDE
Kou, Kit Ian; Lou, Yijun; Xia, Yong-Hui
Zeros of a class of transcendental equation with small parameter ɛ(0 ≤ ɛ ≤ 1) are considered in this paper. There have been many works in the literature considering the distribution of zeros of the transcendental equation by choosing the delay τ as bifurcation parameter. Different from standard consideration, we choose ɛ as bifurcation parameter (not the delay τ) to discuss the distribution of zeros of such transcendental equation. After mathematical analysis, the obtained results are successfully applied to the bifurcation analysis in a biological model in the real word phenomenon. In the real world model, the effect of climate changes can be seen as the small parameter perturbation, which can induce bifurcations and instability. We present two methods to analyze the stability and bifurcations.
WAMS-based monitoring and control of Hopf bifurcations in multi-machine power systems
Institute of Scientific and Technical Information of China (English)
Shao-bu WANG; Quan-yuan JIANG; Yi-jia CAO
2008-01-01
A method is proposed to monitor and control Hopf bifurcations in multi-machine power systems using the information from wide area measurement systems (WAMSs). The power method (PM) is adopted to compute the pair of conjugate eigenvalues with the algebraically largest real part and the corresponding eigenvectors of the Jacobian matrix of a power system. The distance between the current equilibrium point and the Hopf bifurcation set can be monitored dynamically by computing the pair of conjugate eigenvalues. When the current equilibrium point is close to the Hopf bifurcation set, the approximate normal vector to the Hopf bifurcation set is computed and used as a direction to regulate control parameters to avoid a Hopf bifurcation in the power system described by differential algebraic equations (DAEs). The validity of the proposed method is demonstrated by regulating the reactive power loads in a 14-bus power system.
Simulation of bifurcated stent grafts to treat abdominal aortic aneurysms (AAA)
Egger, Jan; Freisleben, Bernd
2016-01-01
In this paper a method is introduced, to visualize bifurcated stent grafts in CT-Data. The aim is to improve therapy planning for minimal invasive treatment of abdominal aortic aneurysms (AAA). Due to precise measurement of the abdominal aortic aneurysm and exact simulation of the bifurcated stent graft, physicians are supported in choosing a suitable stent prior to an intervention. The presented method can be used to measure the dimensions of the abdominal aortic aneurysm as well as simulate a bifurcated stent graft. Both of these procedures are based on a preceding segmentation and skeletonization of the aortic, right and left iliac. Using these centerlines (aortic, right and left iliac) a bifurcated initial stent is constructed. Through the implementation of an ACM method the initial stent is fit iteratively to the vessel walls - due to the influence of external forces (distance- as well as balloonforce). Following the fitting process, the crucial values for choosing a bifurcated stent graft are measured, ...
Bifurcation mechanisms of regular and chaotic network signaling in brain astrocytes
Matrosov, V. V.; Kazantsev, V. B.
2011-06-01
Bifurcation mechanisms underlying calcium oscillations in the network of astrocytes are investigated. Network model includes the dynamics of intracellular calcium concentration and intercellular diffusion of inositol 1,4,5-trisphosphate through gap junctions. Bifurcation analysis of underlying nonlinear dynamical system is presented. Parameter regions and principle bifurcation boundaries have been delineated and described. We show how variations of the diffusion rate can lead to generation of network calcium oscillations in originally nonoscillating cells. Different scenarios of regular activity and its transitions to chaotic dynamics have been obtained. Then, the bifurcations have been associated with statistical characteristics of calcium signals showing that different bifurcation scenarios yield qualitative changes in experimentally measurable quantities of the astrocyte activity, e.g., statistics of calcium spikes.
Institute of Scientific and Technical Information of China (English)
YUAN Xue-gang; ZHU Zheng-you
2005-01-01
The problem of spherical cavitated bifurcation was examined for a class of incompressible generalized neo-Hookean materials, in which the materials may be viewed as the homogeneous incompressible isotropic neo-Hookean material with radial perturbations.The condition of void nucleation for this problem was obtained. In contrast to the situation for a homogeneous isotropic neo-Hookean sphere, it is shown that not only there exists a secondary turning bifurcation point on the cavitated bifurcation solution which bifurcates locally to the left from trivial solution, and also the critical load is smaller than that for the material with no perturbations, as the parameters belong to some regions. It is proved that the cavitated bifurcation equation is equivalent to a class of normal forms with single-sided constraints near the critical point by using singularity theory. The stability of solutions and the actual stable equilibrium state were discussed respectively by using the minimal potential energy principle.
The saddle-node-transcritical bifurcation in a population model with constant rate harvesting
Saputra, K V I; Quispel, G R W
2010-01-01
We study the interaction of saddle-node and transcritical bifurcations in a Lotka-Volterra model with a constant term representing harvesting or migration. Because some of the equilibria of the model lie on an invariant coordinate axis, both the saddle-node and the transcritical bifurcations are of codimension one. Their interaction can be associated with either a single or a double zero eigenvalue. We show that in the former case, the local bifurcation diagram is given by a nonversal unfolding of the cusp bifurcation whereas in the latter case it is a nonversal unfolding of a degenerate Bogdanov-Takens bifurcation. We present a simple model for each of the two cases to illustrate the possible unfoldings. We analyse the consequences of the generic phase portraits for the Lotka-Volterra system.
Bifurcation analysis of an impact oscillator with a one-sided elastic constraint near grazing
Ing, James; Pavlovskaia, Ekaterina; Wiercigroch, Marian; Banerjee, Soumitro
2010-03-01
In this paper a linear oscillator undergoing impact with a secondary elastic support is studied experimentally and semi-analytically for near-grazing conditions. The experimentally observed bifurcations are explained with help from simulations based on mapping solutions between locally smooth subspaces. Smooth as well as nonsmooth bifurcations are observed, and the resulting atypical bifurcations are explained, often as an interplay between them. In order to understand the observed bifurcation scenarios, a global analysis is required, due to the influence of stable and unstable orbits which are born in distant bifurcations but become important at near-grazing conditions. The good degree of correspondence between experiment and theory fully justifies the modelling approach.
Bifurcations and degenerate periodic points in a three dimensional chaotic fluid flow.
Smith, L D; Rudman, M; Lester, D R; Metcalfe, G
2016-05-01
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.
Baharoglu, Merih I; Lauric, Alexandra; Wu, Chengyuan; Hippelheuser, James; Malek, Adel M
2014-10-17
Cerebral aneurysms form preferentially at arterial bifurcations. The vascular optimality principle (VOP) decrees that minimal energy loss across bifurcations requires optimal caliber control between radii of parent (r₀) and daughter branches (r1 and r2): r₀(n)=r₁(n)+r₂(n), with n approximating three. VOP entails constant wall shear stress (WSS), an endothelial phenotype regulator. We sought to determine if caliber control is maintained in aneurysmal intracranial bifurcations. Three-dimensional rotational angiographic volumes of 159 middle cerebral artery (MCA) bifurcations (62 aneurysmal) were processed using 3D gradient edge-detection filtering, enabling threshold-insensitive radius measurement. Radius ratio (RR)=r₀(3)/(r₁(3)+r₂(3)) and estimated junction exponent (n) were compared between aneurysmal and non-aneurysmal bifurcations using Student t-test and Wilcoxon rank-sum analysis. The results show that non-aneurysmal bifurcations display optimal caliber control with mean RR of 1.05 and median n of 2.84. In contrast, aneurysmal bifurcations had significantly lower RR (0.76, pbifurcations revealed a daughter branch larger than its parent vessel, an absolute violation of optimality, not witnessed in non-aneurysmal bifurcations. The aneurysms originated more often off the smaller daughter (52%) vs. larger daughter branch (16%). Aneurysm size was not statistically correlated to RR or n. Aneurysmal males showed higher deviation from VOP. Non-aneurysmal MCA bifurcations contralateral to aneurysmal ones showed optimal caliber control. Aneurysmal bifurcations, in contrast to non-aneurysmal counterparts, disobey the VOP and may exhibit dysregulation in WSS-mediated caliber control. The mechanism of this focal divergence from optimality may underlie aneurysm pathogenesis and requires further study.
Bifurcations and degenerate periodic points in a three dimensional chaotic fluid flow
Smith, L. D.; Rudman, M.; Lester, D. R.; Metcalfe, G.
2016-05-01
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.
Noise-induced bifurcations in magnetization dynamics of uniaxial nanomagnets
Energy Technology Data Exchange (ETDEWEB)
Serpico, C., E-mail: serpico@unina.it; Perna, S.; Quercia, A. [Dipartimento di Ingegneria Elettrica e delle Tecnologie dell' Informazione, Università di Napoli “Federico II,” I-80125 Napoli (Italy); Bertotti, G. [Istituto Nazionale di Ricerca Metrologica, I-10135 Torino (Italy); D' Aquino, M. [Dipartimento di Ingegneria, Università di Napoli “Parthenope,” I-80143 Napoli (Italy); Mayergoyz, I. D. [ECE Department and UMIACS, University of Maryland, College Park, Maryland 20742 (United States)
2015-05-07
Stochastic magnetization dynamics in uniformly magnetized nanomagnets is considered. The system is assumed to have rotational symmetry as the anisotropy axis, the applied field, and the spin polarization are all aligned along an axis of symmetry. By appropriate integration of the Fokker-Planck equation associated to the problem, the stochastic differential equation governing the evolution of the angle between the magnetization orientation and the symmetry axis is derived. The drift terms present in this equation contain a noise-induced drift term, which, in combination with drift terms of deterministic origin, can be written as the derivative of an effective potential. Superparamagnetic-like transitions are studied in connections with the bifurcations of the effective potential as temperature and excitation conditions are varied.
Damped bead on a rotating circular hoop - a bifurcation zoo
Dutta, Shovan
2012-01-01
The evergreen problem of a bead on a rotating hoop shows a multitude of bifurcations when the bead moves with friction. This motion is studied for different values of the damping coefficient and rotational speeds of the hoop. Phase portraits and trajectories corresponding to all different modes of motion of the bead are presented. They illustrate the rich dynamics associated with this simple system. For some range of values of the damping coefficient and rotational speeds of the hoop, linear stability analysis of the equilibrium points is inadequate to classify their nature. A technique involving transformation of coordinates and order of magnitude arguments is presented to examine such cases. This may provide a general framework to investigate other complex systems.
10th International Workshop on Bifurcation and Degradation in Geomaterials
Zhao, Jidong
2015-01-01
This book contains contributions to the 10th International Workshop on Bifurcation and Degradation in Geomaterials held in Hong Kong, May 28-30, 2014. This event marks the silver Jubilee anniversary of an international conference series dedicated to the research on localization, instability, degradation and failure of geomaterials since 1988 when its first workshop was organized in Germany. This volume of book collects the latest progresses and state-of-the-art research from top researchers around the world, and covers topics including multiscale modeling, experimental characterization and theoretical analysis of various instability and degradation phenomena in geomaterials as well as their relevance to contemporary issues in engineering practice. This book can be used as a useful reference for research students, academics and practicing engineers who are interested in the instability and degradation problems in geomechanics and geotechnical engineering.
Wake-sleep transition as a noisy bifurcation
Yang, Dong-Ping; McKenzie-Sell, Lauren; Karanjai, Angela; Robinson, P. A.
2016-08-01
A recent physiologically based model of the ascending arousal system is used to analyze the dynamics near the transition from wake to sleep, which corresponds to a saddle-node bifurcation at a critical point. A normal form is derived by approximating the dynamics by those of a particle in a parabolic potential well with dissipation. This mechanical analog is used to calculate the power spectrum of fluctuations in response to a white noise drive, and the scalings of fluctuation variance and spectral width are derived versus distance from the critical point. The predicted scalings are quantitatively confirmed by numerical simulations, which show that the variance increases and the spectrum undergoes critical slowing, both in accord with theory. These signals can thus serve as potential precursors to indicate imminent wake-sleep transition, with potential application to safety-critical occupations in transport, air-traffic control, medicine, and heavy industry.
Intermittency in an optomechanical cavity near a subcritical Hopf bifurcation
Suchoi, Oren; Ella, Lior; Shtempluk, Oleg; Buks, Eyal
2014-09-01
We experimentally study an optomechanical cavity consisting of an oscillating mechanical resonator embedded in a superconducting microwave transmission line cavity. Tunable optomechanical coupling between the mechanical resonator and the microwave cavity is introduced by positioning a niobium-coated single-mode optical fiber above the mechanical resonator. The capacitance between the mechanical resonator and the coated fiber gives rise to optomechanical coupling, which can be controlled by varying the fiber-resonator distance. We study radiation-pressure-induced self-excited oscillation as a function of microwave driving parameters (frequency and power). Intermittency between limit-cycle and steady-state behaviors is observed with blue-detuned driving frequency. The experimental results are accounted for by a model that takes into account the Duffing-like nonlinearity of the microwave cavity. A stability analysis reveals a subcritical Hopf bifurcation near the region where intermittency is observed.
Hopf bifurcation for simple food chain model with delay
Directory of Open Access Journals (Sweden)
Mario Cavani
2009-06-01
Full Text Available In this article we consider a chemostat-like model for a simple food chain where there is a well stirred nutrient substance that serves as food for a prey population of microorganisms, which in turn, is the food for a predator population of microorganisms. The nutrient-uptake of each microorganism is of Holling type I (or Lotka-Volterra form. We show the existence of a global attractor for solutions of this system. Also we show that the positive globally asymptotically stable equilibrium point of the system undergoes a Hopf bifurcation when the dynamics of the microorganisms at the bottom of the chain depends on the history of the prey population by means of a distributed delay that takes an average of the microorganism in the middle of the chain.
Bifurcation to a stable limiter MARFE in Tore Supra
Energy Technology Data Exchange (ETDEWEB)
Dachicourt, R., E-mail: remi.dachicourt@cea.fr [CEA, IRFM, F-13108 Saint-Paul Lez Durance (France); Monier-Garbet, P.; Gil, C.; Guirlet, R.; Tamain, P.; Meyer, O.; Devynck, P.; Pégourié, B.; Clairet, F.; Bucalossi, J.; Corre, Y.; Ségui, J.L [CEA, IRFM, F-13108 Saint-Paul Lez Durance (France)
2013-07-15
This paper reports on the observation on the tokamak Tore Supra of a very high density, highly radiating edge regime featuring a high recycling divertor. This regime is stable over several energy confinement times, without any additional external control. It is achieved through strong deuterium gas puffing, in an ICRH heated plasma scenario. When the electron density reaches ∼1.1 times the Greenwald density, a bifurcation occurs, leading to strong edge asymmetries: electron density, enhanced edge radiated power localized close to the limiter surface, and a consistent reduction of the conducted power to the limiter. A Greenwald fraction up to ∼1.4 is then achieved, without any loss of confinement, and with low plasma core contamination.
Bifurcation sequences in the symmetric 1:1 Hamiltonian resonance
Marchesiello, Antonella
2015-01-01
We present a general review of the bifurcation sequences of periodic orbits in general position of a family of resonant Hamiltonian normal forms with nearly equal unperturbed frequencies, invariant under $Z_2 \\times Z_2$ symmetry. The rich structure of these classical systems is investigated with geometric methods and the relation with the singularity theory approach is also highlighted. The geometric approach is the most straightforward way to obtain a general picture of the phase-space dynamics of the family as is defined by a complete subset in the space of control parameters complying with the symmetry constraint. It is shown how to find an energy-momentum map describing the phase space structure of each member of the family, a catastrophe map that captures its global features and formal expressions for action-angle variables. Several examples, mainly taken from astrodynamics, are used as applications.
Bifurcation analysis of magnetic reconnection in Hall-MHD-systems
Homann, Holger; Grauer, Rainer
2005-08-01
The influence of the Hall-term on the width of the magnetic islands of the tearing-mode is examined. We applied the center manifold (CMF) theory to a magnetohydrodynamic (MHD)-system. The MHD-system was chosen to be incompressible and includes in addition to viscosity the Hall-term in Ohm’s law. For certain values of physical parameters the corresponding center manifold is two-dimensional and therefore the original partial differential equations could be reduced to a two-dimensional system of ordinary ones. This amplitude equations exhibit a pitchfork-bifurcation which corresponds to the occurrence of the tearing-mode. Eigenvalue-problems and linear equations due to the center manifold reduction were solved numerically with the Arpack++-library. An important result of this analysis is the growth of the tearing mode island width by increasing the Hall-parameter, a feature which has been observed in recent numerical simulations of collisionless reconnection.
Wall Shear Stress Distribution in Patient Specific Coronary Artery Bifurcation
Directory of Open Access Journals (Sweden)
Vahab Dehlaghi
2010-01-01
Full Text Available Problem statement: Atherogenesis is affected by hemodynamic parameters, such as wall shear stress and wall shear stress spatial gradient. These parameters are largely dependent on the geometry of arterial tree. Arterial bifurcations contain significant flow disturbances. Approach: The effects of branch angle and vessel diameter ratio at the bifurcations on the wall shear stress distribution in the coronary arterial tree based on CT images were studied. CT images were digitally processed to extract geometrical contours representing the coronary vessel walls. The lumen of the coronary arteries of the patients was segmented using the open source software package (VMTK. The resulting lumens of coronary arteries were fed into a commercial mesh generator (GAMBIT, Fluent Inc. to generate a volume that was filled with tetrahedral elements. The FIDAP software (Fluent Corp. was used to carry out the simulation by solving Navier-Stokes equations. The FIELDVIEW software (Version 10.0, Intelligent Light, Lyndhurst, NJ was used for the visualization of flow patterns and the quantification of wall shear stress. Post processing was done with VMTK and MATLAB. A parabolic velocity profile was prescribed at the inlets and outlets, except for 1. Stress free outlet was assigned to the remaining outlet. Results: The results show that for angle lower than 90°, low shear stress regions are observed at the non-flow divider and the apex. For angle larger than 90°, low shear stress regions only at the non-flow divider. By increasing of diameter of side branch ratio, low shear stress regions in the side branch appear at the non-flow divider. Conclusion: It is concluded that not only angle and diameter are important, but also the overall 3D shape of the artery. More research is required to further quantify the effects angle and diameter on shear stress patterns in coronaries.
Shell structure and orbit bifurcations in finite fermion systems
Energy Technology Data Exchange (ETDEWEB)
Magner, A. G., E-mail: magner@kinr.kiev.ua; Yatsyshyn, I. S. [National Academy of Sciences of Ukraine, Institute for Nuclear Research (Ukraine); Arita, K. [Nagoya Institute of Technology, Department of Physics (Japan); Brack, M. [University of Regensburg, Institute for Theoretical Physics (Germany)
2011-10-15
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).
Global Hopf Bifurcation on Two-Delays Leslie-Gower Predator-Prey System with a Prey Refuge
Directory of Open Access Journals (Sweden)
Qingsong Liu
2014-01-01
Full Text Available A modified Leslie-Gower predator-prey system with two delays is investigated. By choosing τ1 and τ2 as bifurcation parameters, we show that the Hopf bifurcations occur when time delay crosses some critical values. Moreover, we derive the equation describing the flow on the center manifold; then we give the formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the theoretical results and chaotic behaviors are observed. Finally, using a global Hopf bifurcation theorem for functional differential equations, we show the global existence of the periodic solutions.
Bifurcations of a two-dimensional discrete time plant-herbivore system
Khan, Abdul Qadeer; Ma, Jiying; Xiao, Dongmei
2016-10-01
In this paper, bifurcations of a two dimensional discrete time plant-herbivore system formulated by Allen et al. (1993) have been studied. It is proved that the system undergoes a transcritical bifurcation in a small neighborhood of a boundary equilibrium and a Neimark-Sacker bifurcation in a small neighborhood of the unique positive equilibrium. An invariant closed curve bifurcates from the unique positive equilibrium by Neimark-Sacker bifurcation, which corresponds to the periodic or quasi-periodic oscillations between plant and herbivore populations. For a special form of the system, which appears in Kulenović and Ladas (2002), it is shown that the system can undergo a supercritical Neimark-Sacker bifurcation in a small neighborhood of the unique positive equilibrium and a stable invariant closed curve appears. This bifurcation analysis provides a theoretical support on the earlier numerical observations in Allen et al. (1993) and gives a supportive evidence of the conjecture in Kulenović and Ladas (2002). Some numerical simulations are also presented to illustrate our theocratical results.
BIFURCATION AND UNIVERSAL UNFOLDING FOR A ROTATING SHAFT WITH UNSYMMETRICAL STIFFNESS
Institute of Scientific and Technical Information of China (English)
陈芳启; 吴志强; 陈予恕
2002-01-01
The 1/2 subharmonic resonance bifurcation and universal unfolding are studied for a rotating shaft with unsymmetrical stiffness. The bifurcation behavior of the response amplitude with respect to the detuning parameter was studied for this class of problems by Xiao et al. Obviously, it is highly important to research the bifurcation behavior of the response amplitude with respect to the unsymmetry of stiffness for this problem. Here, by means of the singularity theory, the bifurcation and universal unfolding of amplitude with respect to the unsymmetrical stiffness parameter are discussed. The results indicate that it is a high codimensional bifurcation problem with codimension 5, and the universal unfolding is given. From the mechanical background, we study four forms of two parameter unfoldings contained in the universal unfolding. The transition sets in the parameter plane and the bifurcation diagrams are plotted. The results obtained in this paper show rich bifurcation phenomena and provide some guidance for the analysis and design of dynamic buckling experiments of this class of system, especially, for the choice of system parameters.
Bifurcation boundary conditions for current programmed PWM DC-DC converters at light loading
Fang, Chung-Chieh
2012-10-01
Three types of bifurcations (instabilities) in the PWM DC-DC converter at light loading under current mode control in continuous-conduction mode (CCM) or discontinuous-conduction mode (DCM) are analysed: saddle-node bifurcation (SNB) in CCM or DCM, border-collision bifurcation during the CCM-DCM transition, and period-doubling bifurcation in CCM. Different bifurcations occur in some particular loading ranges. Bifurcation boundary conditions separating stable regions from unstable regions in the parametric space are derived. A new methodology to analyse the SNB in the buck converter based on the peak inductor current is proposed. The same methodology is applied to analyse the other types of bifurcations and converters. In the buck converter, multiple stable/unstable CCM/DCM steady-state solutions may coexist. Possibility of multiple solutions deserves careful study, because an ignored solution may merge with a desired stable solution and make both disappear. Understanding of SNB can explain some sudden disappearances or jumps of steady-state solutions observed in switching converters.
On the effect of AVR gain on bifurcations of subsynchronous resonance in power systems
Energy Technology Data Exchange (ETDEWEB)
Widyan, Mohammad S. [Electrical Engineering Department, The Hashemite University, 13115 Zarqa (Jordan)
2010-07-15
This paper presents the effect of the automatic voltage regulator (AVR) gain on the bifurcations of subsynchronous resonance (SSR) in power systems. The first system of the IEEE second benchmark model of SSR is chosen for numerical investigations. The dynamics of both axes damper windings of the generator and that of the power system stabilizer (PSS) are included. The bifurcation parameter is the compensation factor. Hopf bifurcation, where a pair of complex conjugate eigenvalues of the linearized model around the operating point transversally crosses from left- to right-half of the complex plane, is detected in all AVR gains. It is shown that the Hopf bifurcation is of subcritical type. The results also show that the location of the Hopf bifurcation point i.e. the stable operating point regions are affected by the value of the AVR gain. The variation of the location of the Hopf bifurcation point as function of the AVR gain for two operating conditions is obtained. Time domain simulation results based on the nonlinear dynamical mathematical model carried out at different compensation factors and AVR gains agree with that of the bifurcation analysis. (author)
Analysis of the flow at a T-bifurcation for a ternary unit
Campero, P.; Beck, J.; Jung, A.
2014-03-01
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.
Institute of Scientific and Technical Information of China (English)
ZHANG Zi-Zhen; YANG Hui-Zhong
2013-01-01
In this paper,we consider a predator-prey system with modified Leslie-Gower and Holling type III schemes.By regarding the time delay as the bifurcation parameter,the local asymptotic stability of the positive equilibrium is investigated.And we find that Hopf bifurcations can occur as the time delay crosses some critical values.In particular,special attention is paid to the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions.In addition,the global existence of periodic solutions bifurcating from the Hopf bifurcation are considered by applying a global Hopf bifurcation result.Finally,numerical simulations are carried out to illustrate the main theoretical results.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper,an introduction to the bifurcation theory and its applicability to the study of sub-synchronous resonance (SSR) phenomenon in power system are presented. The continuation and bifurcation analysis software AUTO97 is adopted to investigate SSR for a single-machine-infinite-bus power system with series capacitor compensation. The investigation results show that SSR is the result of unstable limit cycle after bifurcation. When the system exhibits SSR, some complex periodical orbit bifurcations, such as torus bifurcation and periodical fold bifurcation, may happen with the variation of limit cycle. Furthermore, the initial operation condition may greatly influence the ultimate state of the system. The time-domain simulation is carried out to verify the effectiveness of the results obtained from the bifurcation analysis.
Institute of Scientific and Technical Information of China (English)
DUAN XianZhong; WEN JinYu; CHENG ShiJie
2009-01-01
In this paper, an introduction to the bifurcation theory and its applicability to the study of sub-syn-chronous resonance (SSR) phenomenon in power system are presented. The continuation and bifur-cation analysis software AUTO97 is adopted to investigate SSR for a single-machine-infinite-bus power system with series capacitor compensation. The investigation results show that SSR is the result of unstable limit cycle after bifurcation. When the system exhibits SSR, some complex periodical orbit bifurcations, such as torus bifurcation and periodical fold bifurcation, may happen with the variation of limit cycle. Furthermore, the initial operation condition may greatly influence the ultimate state of the system. The time-domain simulation is carried out to verify the effectiveness of the results obtained from the bifurcation analysis.
Bifurcation structure of the C-type period-doubling transition
DEFF Research Database (Denmark)
Laugesen, Jakob Lund; Mosekilde, Erik; Zhusubaliyev, Zhanybai T.
2012-01-01
(Arneodo et al. (1983) [15]). Using the Rössler system as an example, we present a detailed analysis of the bifurcation structure associated with the forcing of a three-dimensional period-doubling system. We explain how this structure is related to the recently discovered phenomenon of multi-layered tori...... and discuss different bifurcation scenarios that transform a resonance torus into a period-doubled ergodic torus. Similar bifurcation phenomena have recently been observed in a biologically relevant model of kidney blood flow regulation in response to fluctuations in arterial pressure....
Hopf Bifurcations of a Stochastic Fractional-Order Van der Pol System
Directory of Open Access Journals (Sweden)
Xiaojun Liu
2014-01-01
Full Text Available The Hopf bifurcation of a fractional-order Van der Pol (VDP for short system with a random parameter is investigated. Firstly, the Chebyshev polynomial approximation is applied to study the stochastic fractional-order system. Based on the method, the stochastic system is reduced to the equivalent deterministic one, and then the responses of the stochastic system can be obtained by numerical methods. Then, according to the existence conditions of Hopf bifurcation, the critical parameter value of the bifurcation is obtained by theoretical analysis. Then, numerical simulations are carried out to verify the theoretical results.
Synergetic-bifurcated prediction model of slope occurrence and its application
Institute of Scientific and Technical Information of China (English)
HUANG; Zhiquan; WANG; Sijing
2003-01-01
Landslide prediction is one of the most important aspects of prevention and control for geological hazards and the environmental protection. In order to study the nonlinear methods for landslide prediction, the synergetic-bifurcated model of predicting the timing of slope failure is established by combining Synergetics with Bifurcation Theory based on single-state variable friction law in this paper. The synergetic effects and bifurcated process of the factors in the slope evolution can be characterized in the model. Taking the Xintan Landslide as an example, the prediction of landslide is carried out based on the model suggested.
Bifurcation and Solitary Waves of the Combined KdV and KdV Equation
Institute of Scientific and Technical Information of China (English)
HUA Cun-Cai; LIU Yan-Zhu
2002-01-01
Bifurcation, bistability and solitary waves of the combined KdV and mKdV equation are investigatedsystematically. At first, bifurcation and bistability are analyzed by selecting an integral constant as the bifurcationparameter. Then, different conditions expressed in terms of the bifurcation parameter are obtained for the existence ofbreather-like, algebraic, pulse-like solitary waves, and shock waves. All types of the solitary wave and shock wave solutionsare given by direct integration. Finally, an approximate analytic method by employing the interpolation polynomials iscomplete and the theoretical methods are the simplest hitherto.
Bifurcation and solitary waves of the nonlinear wave equation with quartic polynomial potential
Institute of Scientific and Technical Information of China (English)
化存才; 刘延柱
2002-01-01
For the nonlinear wave equation with quartic polynomial potential, bifurcation and solitary waves are investigated. Based on the bifurcation and the energy integral of the two-dimensional dynamical system satisfied by the travelling waves, it is very interesting to find different sufficient and necessary conditions in terms of the bifurcation parameter for the existence and coexistence of bright, dark solitary waves and shock waves. The method of direct integration is developed to give all types of solitary wave solutions. Our method is simpler than other newly developed ones. Some results are similar to those obtained recently for the combined KdV-mKdV equation.
Bifurcation and pattern formation in a coupled higher autocatalator reaction diffusion system
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Spatiotemporal structures arising in two identical cells, which are governed by higher autocatalator kinetics and coupled via diffusive interchange of autocatalyst,are discussed.The stability of the unique homogeneous steady state is obtained by the linearized theory.A necessary condition for bifurcations in spatially non-uniform solutions in uncoupled and coupled systems is given.Further information about Turing pattern solutions near bifurcation points is obtained by weakly nonlinear theory.Finally, the stability of equilibrium points of the amplitude equation is discussed by weakly nonlinear theory, with the bifurcation branches of the weakly coupled system.
BIFURCATION OF FLOW AND MASS TRANSPORT IN A CURVED BLOOD VESSEL
Institute of Scientific and Technical Information of China (English)
TAN Wenchang(谭文长); WEI Lan(魏兰); ZHAO Yaohua(赵耀华); TAKASHI Masuoka
2003-01-01
A numerical analysis of flow and concentration fields of macromolecules in a slightly curved blood vessel was carried out. Based on these results, the effect of the bifurcation of a flow on the mass transport in a curved blood vessel was discussed. The macromolecules turned out to be easier to deposit in the inner part of the curved blood vessel near the critical Dean number. Once the Dean number is higher than the critical number, the bifurcation of the flow appears. This bifurcation can prevent macromolecules from concentrating in the inner part of the curved blood vessel. This result is helpful for understanding the possible correlations between the blood dynamics and atherosclerosis.
Complete bifurcation analysis of DC-DC converters under current mode control
Pikulin, D.
2014-03-01
The purpose of this research is to investigate to what extend application of novel method of complete bifurcation groups to the analysis of global dynamics of piecewise-smooth hybrid systems enables one to highlight new nonlinear effects before periodic and chaotic regimes. Results include the construction of complete one and two-parameter bifurcation diagrams, detection of various types of bifurcation groups and investigation of their interactions, localization of rare attractors, and the investigation of different principles of birth of chaotic attractors. Effectiveness of the approach is illustrated in respect to one of the most widely used switching systems-boost converter under current mode control operating in continuous current mode.
CENTER CONDITIONS AND BIFURCATION OF LIMIT CYCLES FOR A CLASS OF FIFTH DEGREE SYSTEMS
Institute of Scientific and Technical Information of China (English)
HuangWentao; LiuYirong
2004-01-01
The center conditions and bifurcation of limit cycles for a class of fifth degree systems are investigated. Two recursive formulas to compute singular quantities at infinity and at the origin are given. The first nine singular point quantities at infinity and first seven singular point quantities at the origin for the system are given in order to get center conditions and study bifurcation of limit cycles. Two fifth degree systems are constructed. One allows the appearance of eight limit cycles in the neighborhood of infinity,which is the first example that a polynomial differential system bifurcates eight limit cycles at infinity. The other perturbs six limit cycles at the origin.
Simulation of Blood Flow at Vessel Bifurcation by Lattice Boltzmann Method
Institute of Scientific and Technical Information of China (English)
KANG Xiu-Ying; LIU Da-He; ZHOU Jing; JIN Yong-Juan
2005-01-01
@@ The application of the lattice Boltzmann method to the large vessel bifurcation blood flow is investigated in awide range of Reynolds numbers. The velocity, shear stress and pressure distributions at the bifurcation arepresented in detail. The flow separation zones revealed with increase of Reynolds number are located in theareas of the daughter branches distal to the outer corners of the bifurcation where some deposition of particularblood components might occur to form arteriosclerosis. The results also demonstrate that the lattice Boltzmannmethod is adaptive to simulating the flow in larger vessels under a high Reynolds number.
Simulation of Blood Flow at Vessel Bifurcation by Lattice Boltzmann Method
Kang, Xiu-Ying; Liu, Da-He; Zhou, Jing; Jin, Yong-Juan
2005-11-01
The application of the lattice Boltzmann method to the large vessel bifurcation blood flow is investigated in a wide range of Reynolds numbers. The velocity, shear stress and pressure distributions at the bifurcation are presented in detail. The flow separation zones revealed with increase of Reynolds number are located in the areas of the daughter branches distal to the outer corners of the bifurcation where some deposition of particular blood components might occur to form arteriosclerosis. The results also demonstrate that the lattice Boltzmann method is adaptive to simulating the flow in larger vessels under a high Reynolds number.
Synchronization and Bifurcation Analysis in Coupled Networks of Discrete-Time Systems
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Synchronization and bifurcation analysis in coupled networks of discrete-time systems are investigated in the present paper. We mainly focus on some special coupling matrix, i.e., the sum of each row equals a nonzero constant u and the network connection is directed. A result that the network can reach a new synchronous state, which is not the asymptotic limit set determined by the node state equation, is derived. It is interesting that the network exhibits bifurcation if we regard the constant u as a bifurcation parameter at the synchronous state. Numerical simulations are given to show the efficiency of our derived conclusions.
Bifurcation in a thin liquid film flowing over a locally heated surface
Katkar, Harshwardhan H
2014-01-01
We investigate the non-linear dynamics of a two-dimensional film flowing down a finite heater, for a non-volatile and a volatile liquid. An oscillatory instability is predicted beyond a critical value of Marangoni number using linear stability theory. Continuation along the Marangoni number using non-linear evolution equation is used to trace bifurcation diagram associated with the oscillatory instability. Hysteresis, a characteristic attribute of a sub-critical Hopf bifurcation, is observed in a critical parametric region. The bifurcation is universally observed for both, a non-volatile film and a volatile film.
Bifurcations, chaos, and sensitivity to parameter variations in the Sato cardiac cell model
Otte, Stefan; Berg, Sebastian; Luther, Stefan; Parlitz, Ulrich
2016-08-01
The dynamics of a detailed ionic cardiac cell model proposed by Sato et al. (2009) is investigated in terms of periodic and chaotic action potentials, bifurcation scenarios, and coexistence of attractors. Starting from the model's standard parameter values bifurcation diagrams are computed to evaluate the model's robustness with respect to (small) parameter changes. While for some parameters the dynamics turns out to be practically independent from their values, even minor changes of other parameters have a very strong impact and cause qualitative changes due to bifurcations or transitions to coexisting attractors. Implications of this lack of robustness are discussed.
Bifurcation Analysis and Chaos Control in a Modified Finance System with Delayed Feedback
Yang, Jihua; Zhang, Erli; Liu, Mei
2016-06-01
We investigate the effect of delayed feedback on the finance system, which describes the time variation of the interest rate, for establishing the fiscal policy. By local stability analysis, we theoretically prove the existences of Hopf bifurcation and Hopf-zero bifurcation. By using the normal form method and center manifold theory, we determine the stability and direction of a bifurcating periodic solution. Finally, we give some numerical solutions, which indicate that when the delay passes through certain critical values, chaotic oscillation is converted into a stable equilibrium or periodic orbit.
Bifurcation analysis of periodic orbits of a non-smooth Jeffcott rotor model
Páez Chávez, Joseph; Wiercigroch, Marian
2013-09-01
We investigate complex dynamics occurring in a non-smooth model of a Jeffcott rotor with a bearing clearance. A bifurcation analysis of the rotor system is carried out by means of the software TC-HAT [25], a toolbox of AUTO 97 [6] allowing path-following and detection of bifurcations of periodic trajectories of non-smooth dynamical systems. The study reveals a rich variety of dynamics, which includes grazing-induced fold and period-doubling bifurcations, as well as hysteresis loops produced by a cusp singularity. Furthermore, an analytical expression predicting grazing incidences is derived.
Nonlinear dynamics and bifurcation for a Jeffcott rotor with seal aerodynamic excitations
International Nuclear Information System (INIS)
The nonlinear vibration and bifurcation characteristics of a Jeffcott rotor aerodynamically excited by gas seals are presented in this paper. The Muszynska's model is adopted to express the seal forces as the nonlinear function of rotor displacement, velocity and acceleration. The Runge-Kutta method is used to obtain the displacement and bifurcation diagrams with parameters of the pressure drop and the length of the seal. Various period-multiple bifurcations are found showing complexity of the rotor's motion under the aerodynamic excitation of the seal
Stability and bifurcation analysis for a delayed Lotka-Volterra predator-prey system
Yan, Xiang-Ping; Chu, Yan-Dong
2006-11-01
The present paper deals with a delayed Lotka-Volterra predator-prey system. By linearizing the equations and by analyzing the locations on the complex plane of the roots of the characteristic equation, we find the necessary conditions that the parameters should verify in order to have the oscillations in the system. In addition, the normal form of the Hopf bifurcation arising in the system is determined to investigate the direction and the stability of periodic solutions bifurcating from these Hopf bifurcations. To verify the obtained conditions, a special numerical example is also included.
Stability and bifurcation analysis on a three-species food chain system with two delays
Cui, Guo-Hu; Yan, Xiang-Ping
2011-09-01
The present paper deals with a three-species Lotka-Volterra food chain system with two discrete delays. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the asymptotic stability of the positive equilibrium and existence of local Hopf bifurcations are investigated. Furthermore, by using the normal form theory and the center manifold reduction, explicit formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions. Finally, to verify our theoretical predictions, some numerical simulations are also included at the end of this paper.
STABILITY AND BIFURCATION BEHAVIORS ANALYSIS IN A NONLINEAR HARMFUL ALGAL DYNAMICAL MODEL
Institute of Scientific and Technical Information of China (English)
WANG Hong-li; FENG Jian-feng; SHEN Fei; SUN Jing
2005-01-01
A food chain made up of two typical algae and a zooplankton was considered. Based on ecological eutrophication, interaction of the algal and the prey of the zooplankton, a nutrient nonlinear dynamic system was constructed. Using the methods of the modern nonlinear dynamics, the bifurcation behaviors and stability of the model equations by changing the control parameter r were discussed. The value of r for bifurcation point was calculated, and the stability of the limit cycle was also discussed. The result shows that through quasi-periodicity bifurcation the system is lost in chaos.
Clip reconstruction of a large right MCA bifurcation aneurysm. Case report
Directory of Open Access Journals (Sweden)
Giovani A.
2014-06-01
Full Text Available We report a case of complex large middle cerebral artery (MCA bifurcation aneurysm that ruptured during dissection from the very adherent MCA branches but was successfully clipped and the MCA bifurcation reconstructed using 4 Yasargill clips. Through a right pterional craniotomy the sylvian fissure was largely opened as to allow enough workspace for clipping the aneurysm and placing a temporary clip on M1. The pacient recovered very well after surgery and was discharged after 1 week with no neurological deficit. Complex MCA bifurcation aneurysms can be safely reconstructed using regular clips, without the need of using fenestrated clips or complex by-pass procedures.
Stability and Bifurcation in a Delayed Reaction-Diffusion Equation with Dirichlet Boundary Condition
Guo, Shangjiang; Ma, Li
2016-04-01
In this paper, we study the dynamics of a diffusive equation with time delay subject to Dirichlet boundary condition in a bounded domain. The existence of spatially nonhomogeneous steady-state solution is investigated by applying Lyapunov-Schmidt reduction. The existence of Hopf bifurcation at the spatially nonhomogeneous steady-state solution is derived by analyzing the distribution of the eigenvalues. The direction of Hopf bifurcation and stability of the bifurcating periodic solution are also investigated by means of normal form theory and center manifold reduction. Moreover, we illustrate our general results by applications to the Nicholson's blowflies models with one- dimensional spatial domain.
STABILITY AND LOCAL BIFURCATION IN A SIMPLY-SUPPORTED BEAM CARRYING A MOVING MASS
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The stability and local bifurcation of a simply-supported flexible beam (Bernoulli-Euler type) carrying a moving mass and subjected to harmonic axial excitation are investigated.In the theoretical analysis, the partial differential equation of motion with the fifth-order nonlinear term is solved using the method of multiple scales (a perturbation technique). The stability and local bifurcation of the beam are analyzed for 1/2 sub harmonic resonance. The results show that some of the parameters, especially the velocity of moving mass and external excitation, affect the local bifurcation significantly. Therefore, these parameters play important roles in the system stability.
Delay-induced stochastic bifurcations in a bistable system under white noise
International Nuclear Information System (INIS)
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
Stochastic bifurcations in a bistable Duffing-Van der Pol oscillator with colored noise.
Xu, Yong; Gu, Rencai; Zhang, Huiqing; Xu, Wei; Duan, Jinqiao
2011-05-01
This paper aims to investigate Gaussian colored-noise-induced stochastic bifurcations and the dynamical influence of correlation time and noise intensity in a bistable Duffing-Van der Pol oscillator. By using the stochastic averaging method, theoretically, one can obtain the stationary probability density function of amplitude for the Duffing-Van der Pol oscillator and can reveal interesting dynamics under the influence of Gaussian colored noise. Stochastic bifurcations are discussed through a qualitative change of the stationary probability distribution, which indicates that system parameters, noise intensity, and noise correlation time, respectively, can be treated as bifurcation parameters. They also imply that the effects of multiplicative noise are rather different from that of additive noise. The results of direct numerical simulation verify the effectiveness of the theoretical analysis. Moreover, the largest Lyapunov exponent calculations indicate that P and D bifurcations have no direct connection.
Local and global bifurcations at infinity in models of glycolytic oscillations
DEFF Research Database (Denmark)
Sturis, Jeppe; Brøns, Morten
1997-01-01
We investigate two models of glycolytic oscillations. Each model consists of two coupled nonlinear ordinary differential equations. Both models are found to have a saddle point at infinity and to exhibit a saddle-node bifurcation at infinity, giving rise to a second saddle and a stable node...... at infinity. Depending on model parameters, a stable limit cycle may blow up to infinite period and amplitude and disappear in the bifurcation, and after the bifurcation, the stable node at infinity then attracts all trajectories. Alternatively, the stable node at infinity may coexist with either a stable...... sink (not at infinity) or a stable limit cycle. This limit cycle may then disappear in a heteroclinic bifurcation at infinity in which the unstable manifold from one saddle at infinity joins the stable manifold of the other saddle at infinity. These results explain prior reports for one of the models...
Delay-induced stochastic bifurcations in a bistable system under white noise.
Sun, Zhongkui; Fu, Jin; Xiao, Yuzhu; Xu, Wei
2015-08-01
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.
Bifurcation and complex dynamics of a discrete-time predator-prey system involving group defense
Directory of Open Access Journals (Sweden)
S. M. Sohel Rana
2015-09-01
Full Text Available In this paper, we investigate the dynamics of a discrete-time predator-prey system involving group defense. The existence and local stability of positive fixed point of the discrete dynamical system is analyzed algebraically. It is shown that the system undergoes a flip bifurcation and a Neimark-Sacker bifurcation in the interior of R+2 by using bifurcation theory. Numerical simulation results not only show the consistence with the theoretical analysis but also display the new and interesting dynamical behaviors, including phase portraits, period-7, 20-orbits, attracting invariant circle, cascade of period-doubling bifurcation from period-20 leading to chaos, quasi-periodic orbits, and sudden disappearance of the chaotic dynamics and attracting chaotic set. The Lyapunov exponents are numerically computed to characterize the complexity of the dynamical behaviors.
Bifurcation Tools for Flight Dynamics Analysis and Control System Design Project
National Aeronautics and Space Administration — The purpose of the project is the development of a computational package for bifurcation analysis and advanced flight control of aircraft. The development of...
Delay-induced stochastic bifurcations in a bistable system under white noise
Energy Technology Data Exchange (ETDEWEB)
Sun, Zhongkui, E-mail: sunzk@nwpu.edu.cn; Fu, Jin; Xu, Wei [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China); Xiao, Yuzhu [Department of Mathematics and Information Science, Chang' an University, Xi' an 710086 (China)
2015-08-15
In this paper, the effects of noise and time delay on stochastic bifurcations are investigated theoretically and numerically in a time-delayed Duffing-Van der Pol oscillator subjected to white noise. Due to the time delay, the random response is not Markovian. Thereby, approximate methods have been adopted to obtain the Fokker-Planck-Kolmogorov equation and the stationary probability density function for amplitude of the response. Based on the knowledge that stochastic bifurcation is characterized by the qualitative properties of the steady-state probability distribution, it is found that time delay and feedback intensity as well as noise intensity will induce the appearance of stochastic P-bifurcation. Besides, results demonstrated that the effects of the strength of the delayed displacement feedback on stochastic bifurcation are accompanied by the sensitive dependence on time delay. Furthermore, the results from numerical simulations best confirm the effectiveness of the theoretical analyses.
Bifurcation Tools for Flight Dynamics Analysis and Control System Design Project
National Aeronautics and Space Administration — Modern bifurcation analysis methods have been proposed for investigating flight dynamics and control system design in highly nonlinear regimes and also for the...
DNS of bifurcations in an air-filled rotating baroclinic annulus
Randriamampianina, A; Read, P L; Maubert, P; Randriamampianina, Anthony; Fruh, Wolf-Gerrit; Read, Peter L.; Maubert, Pierre
2006-01-01
Three-dimensional Direct Numerical Simulation (DNS) on the nonlinear dynamics and a route to chaos in a rotating fluid subjected to lateral heating is presented here and discussed in the context of laboratory experiments in the baroclinic annulus. Following two previous preliminary studies by Maubert and Randriamampianina, the fluid used is air rather than a liquid as used in all other previous work. This study investigated a bifurcation sequence from the axisymmetric flow to a number of complex flows. The transition sequence, on increase of the rotation rate, from the axisymmetric solution via a steady, fully-developed baroclinic wave to chaotic flow followed a variant of the classical quasi-periodic bifurcation route, starting with a subcritical Hopf and associated saddle-node bifurcation. This was followed by a sequence of two supercritical Hopf-type bifurcations, first to an amplitude vacillation, then to a three-frequency quasi-periodic modulated amplitude vacillation (MAV), and finally to a chaotic MAV\\...
Bifurcation Analysis in an n-Dimensional Diffusive Competitive Lotka-Volterra System with Time Delay
Chang, Xiaoyuan; Wei, Junjie
2015-06-01
In this paper, we investigate the stability and Hopf bifurcation of an n-dimensional competitive Lotka-Volterra diffusion system with time delay and homogeneous Dirichlet boundary condition. We first show that there exists a positive nonconstant steady state solution satisfying the given asymptotic expressions and establish the stability of the positive nonconstant steady state solution. Regarding the time delay as a bifurcation parameter, we explore the system that undergoes a Hopf bifurcation near the positive nonconstant steady state solution and derive a calculation method for determining the direction of the Hopf bifurcation. Finally, we cite the stability of a three-dimensional competitive Lotka-Volterra diffusion system with time delay to illustrate our conclusions.
Symmetry, cusp bifurcation and chaos of an impact oscillator between two rigid sides
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Both the symmetric period n-2 motion and asymmetric one of a one-degree-of-freedom impact oscillator are considered. The theory of bifurcations of the fixed point is applied to such model, and it is proved that the symmetric periodic motion has only simulation shows that one symmetric periodic orbit could bifurcate into two antisymmetric ones via pitchfork bifurcation. While the control parameter changes continuously,the two antisymmetric periodic orbits will give birth to two synchronous antisymmetric period-doubling sequences, and bring about two antisymmetric chaotic attractors subsequently. If the symmetric system is transformed into asymmetric one, bifurcations of the asymmetric period n-2 motion can be described by a two-parameter unfolding of cusp,and the pitchfork changes into one unbifurcated branch and one fold branch.
Codimension-two homoclinic bifurcations underlying spike adding in the Hindmarsh-Rose burster
Linaro, Daniele; Desroches, Mathieu; Storace, Marco
2011-01-01
The well-studied Hindmarsh-Rose model of neural action potential is revisited from the point of view of global bifurcation analysis. This slow-fast system of three paremeterised differential equations is arguably the simplest reduction of Hodgkin-Huxley models capable of exhibiting all qualitatively important distinct kinds of spiking and bursting behaviour. First, keeping the singular perturbation parameter fixed, a comprehensive two-parameter bifurcation diagram is computed by brute force. Of particular concern is the parameter regime where lobe-shaped regions of irregular bursting undergo a transition to stripe-shaped regions of periodic bursting. The boundary of each stripe represents a fold bifurcation that causes a smooth spike-adding transition where the number of spikes in each burst is increased by one. Next, numerical continuation studies reveal that the global structure is organised by various curves of homoclinic bifurcations. In particular the lobe to stripe transition is organised by a sequence ...
Stability and Bifurcation Analysis of a Modified Epidemic Model for Computer Viruses
Directory of Open Access Journals (Sweden)
Chuandong Li
2014-01-01
Full Text Available We extend the three-dimensional SIR model to four-dimensional case and then analyze its dynamical behavior including stability and bifurcation. It is shown that the new model makes a significant improvement to the epidemic model for computer viruses, which is more reasonable than the most existing SIR models. Furthermore, we investigate the stability of the possible equilibrium point and the existence of the Hopf bifurcation with respect to the delay. By analyzing the associated characteristic equation, it is found that Hopf bifurcation occurs when the delay passes through a sequence of critical values. An analytical condition for determining the direction, stability, and other properties of bifurcating periodic solutions is obtained by using the normal form theory and center manifold argument. The obtained results may provide a theoretical foundation to understand the spread of computer viruses and then to minimize virus risks.
Delay-induced stochastic bifurcations in a bistable system under white noise.
Sun, Zhongkui; Fu, Jin; Xiao, Yuzhu; Xu, Wei
2015-08-01
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. PMID:26328553
BIFURCATIONS OF A CANTILEVERED PIPE CONVEYING STEADY FLUID WITH A TERMINAL NOZZLE
Institute of Scientific and Technical Information of China (English)
Xu Jian; Huang Yuying
2000-01-01
This paper studies interactions of pipe and fluid and deals with bifurcations of a cantilevered pipe conveying a steady fluid, clamped at one end and having a nozzle subjected to nonlinear constraints at the free end. Either the nozzle parameter or the flow velocity is taken as a variable parameter. The discrete equations of the system are obtained by the Ritz-Galerkin method. The static stability is studied by the Routh criteria. The method of averaging is employed to investigate the stability of the periodic motions. A Runge-Kutta scheme is used to examine the analytical results and the chaotic motions. Three critical values are given. The first one makes the system lose the static stability by pitchfork bifurcation. The second one makes the system lose the dynamical stability by Hopf bifurcation. The third one makes the periodic motions of the system lose the stability by doubling-period bifurcation.
Kuehn, Christian
2011-01-01
Bifurcations can cause dynamical systems with slowly varying parameters to transition to far-away attractors. The terms "critical transition" or "tipping point" have been used to describe this situation. Critical transitions have been observed in an astonishingly diverse set of applications from ecosystems and climate change to medicine and finance. The goal of this paper is to bring together a variety of techniques from dynamical systems theory to analyze critical transitions. In particular, we shall focus on identifying indicators for catastrophic shifts in the dynamics. Starting from classical bifurcation theory and incorporating multiple time scale dynamics we are able to give a detailed analysis of local bifurcations that induce critical transitions. We characterize several early warning signs for a transition such as slowing down and bifurcation delay. Then we take into account stochastic effects and proceed to model critical transitions by fast-slow stochastic differential equations. The interplay betw...
Bifurcation analysis and the travelling wave solutions of the Klein–Gordon–Zakharov equations
Indian Academy of Sciences (India)
Zaiyun Zhang; Fnag-Li Xia; Xin-Ping Li
2013-01-01
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 using the bifurcation method (Feng et al, Appl. Math. Comput. 189, 271 (2007); Li et al, Appl. Math. Comput. 175, 61 (2006)).
Bifurcation analysis on a delayed SIS epidemic model with stage structure
Directory of Open Access Journals (Sweden)
Kejun Zhuang
2007-05-01
Full Text Available In this paper, a delayed SIS (Susceptible Infectious Susceptible model with stage structure is investigated. We study the Hopf bifurcations and stability of the model. Applying the normal form theory and the center manifold argument, we derive the explicit formulas determining the properties of the bifurcating periodic solutions. The conditions to guarantee the global existence of periodic solutions are established. Also some numerical simulations for supporting the theoretical are given.
On the Computation of Degenerate Hopf Bifurcations for n-Dimensional Multiparameter Vector Fields
Directory of Open Access Journals (Sweden)
Michail P. Markakis
2016-01-01
Full Text Available The restriction of an n-dimensional nonlinear parametric system on the center manifold is treated via a new proper symbolic form and analytical expressions of the involved quantities are obtained as functions of the parameters by lengthy algebraic manipulations combined with computer assisted calculations. Normal forms regarding degenerate Hopf bifurcations up to codimension 3, as well as the corresponding Lyapunov coefficients and bifurcation portraits, can be easily computed for any system under consideration.
Impact of third-order dispersion on nonlinear bifurcations in optical resonators
Energy Technology Data Exchange (ETDEWEB)
Leo, François [Service OPERA-photonique, Université libre de Bruxelles (ULB), 50 Avenue F.D. Roosevelt, CP 194/5, B-1050 Bruxelles (Belgium); Photonics Research Group, Department of Information Technology, Ghent University–IMEC, Ghent B-9000 (Belgium); Coen, Stéphane [Department of Physics, c, Private Bag, 92019, Auckland (New Zealand); Kockaert, Pascal; Emplit, Philippe; Haelterman, Marc [Service OPERA-photonique, Université libre de Bruxelles (ULB), 50 Avenue F.D. Roosevelt, CP 194/5, B-1050 Bruxelles (Belgium); Mussot, Arnaud [PhLAM, Université de Lille 1, Bât. P5-bis, UMR CNRS/USTL 8523, F-59655 Villeneuve d' Ascq (France); Taki, Majid, E-mail: abdelmajid.taki@univ-lille1.fr [PhLAM, Université de Lille 1, Bât. P5-bis, UMR CNRS/USTL 8523, F-59655 Villeneuve d' Ascq (France)
2015-09-18
It is analytically shown that symmetry breaking, in dissipative systems, affects the nature of the bifurcation at onset of instability resulting in transitions from super to subcritical bifurcations. In the case of a nonlinear fiber cavity, we have derived an amplitude equation to describe the nonlinear dynamics above threshold. An analytical expression of the critical transition curve is obtained and the predictions are in excellent agreement with the numerical solutions of the full dynamical model.
BIFURCATION ANALYSIS AND PHASE PORTRAITS OF AN ASYMMETRIC TRIAXIAL GYROSTAT WITH TWO ROTORS
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
This paper deals with the bifurcations and phase portraits of an asymmetric triaxial gyrostat with two rotors, which is a 3-dimensional generalized Hamiltonian system with a quadratic Hamiltonian depending on three independent parameters. The number and stability of equilibria are analyzed, and corresponding bifurcation conditions of parameters are obtained. Moreover, by Maple software, all possible phase portraits are plotted out. Except for some planar orbits under particular parametric conditions, genera...
Numerical investigation of blood flow in a deformable coronary bifurcation and non-planar branch
Razavi, Seyed Esmail; Omidi, Amir Ali; Saghafi Zanjani, Massoud
2014-01-01
Introduction: Among cardiovascular diseases, arterials stenosis is recognized more commonly than the others. Hemodynamic characteristics of blood play a key role in the incidence of stenosis. This paper numerically investigates the pulsatile blood flow in a coronary bifurcation with a non-planar branch. To create a more realistic analysis, the wall is assumed to be compliant. Furthermore, the flow is considered to be three-dimensional, incompressible, and laminar. Methods: The effects of non-Newtonian blood, compliant walls and different angles of bifurcation on hemodynamic characteristics of flow were evaluated. Shear thinning of blood was simulated with the Carreau-Yasuda model. The current research was mainly focused on the flow characteristics in bifurcations since atherosclerosis occurs mostly in bifurcations. Moreover, as the areas with low shear stresses are prone to stenosis, these areas were identified. Results: Our findings indicated that the compliant model of the wall, bifurcation’s angle, and other physical properties of flow have an impact on hemodynamics of blood flow. Lower wall shear stress was observed in the compliant wall than that in the rigid wall. The outer wall of bifurcation in all models had lower wall shear stress. In bifurcations with larger angles, wall shear stress was higher in outer walls, and lower in inner walls. Conclusion: The non-Newtonian blood vessels and different angles of bifurcation on hemodynamic characteristics of flow evaluation confirmed a lower wall shear stress in the compliant wall than that in the rigid wall, while the wall shear stress was higher in outer walls but lower in inner walls in the bifurcation regions with larger angles. PMID:25671176
Limit cycles bifurcated from a center in a three dimensional system
Directory of Open Access Journals (Sweden)
Bo Sang
2016-04-01
Full Text Available Based on the pseudo-division algorithm, we introduce a method for computing focal values of a class of 3-dimensional autonomous systems. Using the $\\epsilon^1$-order focal values computation, we determine the number of limit cycles bifurcating from each component of the center variety (obtained by Mahdi et al. It is shown that at most four limit cycles can be bifurcated from the center with identical quadratic perturbations and that the bound is sharp.
Institute of Scientific and Technical Information of China (English)
WV Xiao-Bo; MO Juan; YANG Ming-Hao; ZHENG Qiao-Hua; GU Hua-Guang; HEN Wei
2008-01-01
@@ Two different bifurcation scenarios, one is novel and the other is relatively simpler, in the transition procedures of neural firing patterns are studied in biological experiments on a neural pacemaker by adjusting two parameters. The experimental observations are simulated with a relevant theoretical model neuron. The deterministic non-periodic firing pattern lying within the novel bifurcation scenario is suggested to be a new case of chaos, which has not been observed in previous neurodynamical experiments.
Hayato Goto
2015-01-01
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schr\\"odinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillat...
Impact of third order dispersion on nonlinear bifurcations in optical resonators
Leo, François; Kockaert, Pascal; Emplit, Philippe; Haelterman, Marc; Mussot, Arnaud; Taki, Majid
2014-01-01
It is analytically shown that symmetry breaking, in dissipative systems, affects the nature of the bifurcation at onset of instability resulting in transitions from super to subcritical bifurcations. In the case of a nonlinear fiber cavity, we have derived an amplitude equation to describe the nonlinear dynamics above threshold. An analytical expression of the critical transition curve is obtained and the predictions are in excellent agreement with the numerical solutions of the full dynamical model.
The Newton filtration and d-determination of bifurcation problems related to C0 contact equivalence
Institute of Scientific and Technical Information of China (English)
SU Dan; ZHANG Dunmu
2006-01-01
In this paper, from the Newton filtration's point of view, we construct the singular Riemannian metric and use the method in singular theory to study the bifurcation problems, and give the sufficient condition of d-determination of bifurcation problems with respect to C0 contact equivalence. The special cases of the main result in this paper are the results of Sun Weizhi and Zou Jiancheng.
Theoretical and Experimental Study of Hopf Bifurcation and Limit Cycles of Railway Vehicle Hunting
Institute of Scientific and Technical Information of China (English)
Zeng Jing; Zhang Weihua; Shen Zhiyun
1996-01-01
The nonlinear hunting stability of railway vehicles is studied theoretically and experimentally in this paper. The Hopf bifurcation point is determined through calculating the eigenvalues of the system linearization equations incorporating with the golden cut method. The bifurcated limit cycles are computed by use of the shooting method to solve the boundary value problem of the system differential equations. Experimental validation to the numerical results is carricd out by utilizing the full scale roller test rig.
Zhu Changsheng; Heinz Ulbrich
2000-01-01
In this paper, the bifurcation behavior of a flexible rotor supported on nonlinear squeeze film dampers without centralized springs is analyzed numerically by means of rotor trajectories, Poincar maps, bifurcation diagrams and power spectra, based on the short bearing and cavitated film assumptions. It is shown that there also exist two different operations (i.e., socalled bistable operations) in some speed regions in the rotor system supported on the nonlinear squeeze film dampers without ce...
Geometric theory predicts bifurcations in minimal wiring cost trees in biology are flat
Yihwa Kim; Robert Sinclair; Nol Chindapol; Jaap A Kaandorp; Erik De Schutter
2012-01-01
The complex three-dimensional shapes of tree-like structures in biology are constrained by optimization principles, but the actual costs being minimized can be difficult to discern. We show that despite quite variable morphologies and functions, bifurcations in the scleractinian coral Madracis and in many different mammalian neuron types tend to be planar. We prove that in fact bifurcations embedded in a spatial tree that minimizes wiring cost should lie on planes. This biologically motivated...
Stability and Hopf bifurcation in a delayed competitive web sites model
Energy Technology Data Exchange (ETDEWEB)
Xiao Min [Department of Mathematics, Southeast University, Nanjing 210096 (China): Department of Mathematics, Nanjing Xiaozhuang College, Nanjing 210017 (China); Cao Jinde [Department of Mathematics, Southeast University, Nanjing 210096 (China)]. E-mail: jdcao@seu.edu.cn
2006-04-24
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.
Evidence for bifurcation and universal chaotic behavior in nonlinear semiconducting devices
Energy Technology Data Exchange (ETDEWEB)
Testa, J.; Perez, J.; Jeffries, C.
1982-01-01
Bifurcations, chaos, and extensive periodic windows in the chaotic regime are observed for a driven LRC circuit, the capacitive element being a nonlinear varactor diode. Measurements include power spectral analysis; real time amplitude data; phase portraits; and a bifurcation diagram, obtained by sampling methods. The effects of added external noise are studied. These data yield experimental determinations of several of the universal numbers predicted to characterize nonlinear systems having this route to chaos.
Interspike interval statistics of the neurons that exhibit the supercritical Hopf bifurcation
保坂, 亮介; 池口, 徹
2006-01-01
We evaluated statistical characteristics of spike trains of neurons that exhibit a supercritical Hopf bifurcation by higher order statistical coefficients, a coefficient of variation and a coefficient of skewness, and showed that the estimated statistical coefficients are different from those of neurons that exhibit a subcritical Hopf bifurcation. Then, we compared the statistical coefficients of spike trains observed from cortical neurons, and showed that the neurons that exhibit the supercr...
Stability and Hopf bifurcation in a delayed competitive web sites model
Xiao, Min; Cao, Jinde
2006-04-01
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.
WHAT ARE THE SEPARATRIX VALUES NAMED BY LEONTOVICH ON HOMOCLINIC BIFURCATION
Institute of Scientific and Technical Information of China (English)
LUO Hai-ying; LI Ji-bin
2005-01-01
For a given system, by using the Tkachev method which concerned with the proof of the stability of a multiple limit cycle, the exact computation formula of the third separatrix values named by Leontovich for the multiple limit cycle bifurcation was given,which was one of the main criterions for the number of limit cycles bifurcated from a homoclinic orbit and the stability of the homoclinic loop, and a computation formula for higher separatrix values was conjectured.
Energy Technology Data Exchange (ETDEWEB)
Sun, Kai [School of Materials Science and Engineering, Beijing Institute of Technology, Beijing 100081 (China); National Key Laboratory of Science and Technology on Materials under Shock and Impact, Beijing Institute of Technology, Beijing 100081 (China); Yu, Xiaodong [School of Materials Science and Engineering, Beijing Institute of Technology, Beijing 100081 (China); National Key Laboratory of Science and Technology on Materials under Shock and Impact, Beijing Institute of Technology, Beijing 100081 (China); Laboratory of Advanced Materials Behavior Characteristics, Beijing Institute of Technology and Institute of Space Medico-Engineering, Beijing 100081 (China); Tan, Chengwen, E-mail: tanchengwen@126.com [School of Materials Science and Engineering, Beijing Institute of Technology, Beijing 100081 (China); National Key Laboratory of Science and Technology on Materials under Shock and Impact, Beijing Institute of Technology, Beijing 100081 (China); Laboratory of Advanced Materials Behavior Characteristics, Beijing Institute of Technology and Institute of Space Medico-Engineering, Beijing 100081 (China); Ma, Honglei [Laboratory of Advanced Materials Behavior Characteristics, Beijing Institute of Technology and Institute of Space Medico-Engineering, Beijing 100081 (China); Wang, Fuchi; Cai, Hongnian [School of Materials Science and Engineering, Beijing Institute of Technology, Beijing 100081 (China); National Key Laboratory of Science and Technology on Materials under Shock and Impact, Beijing Institute of Technology, Beijing 100081 (China)
2014-02-10
Adiabatic shear band (ASB) bifurcations in Ti–6Al–4V alloys with equiaxed, bimodal, and lamellar microstructures under ballistic impact were studied using transmission electron microscopy (TEM). Focused ion beam (FIB) technology was used to accurately prepare TEM samples in the ASB regions, which contained the regions in front of the ASB bifurcation, behind the ASB bifurcation, and the bifurcation regions. ASB consisted of dynamically recrystallized equiaxed grains and incompletely and dynamically recrystallized striped subgrains. ASB bifurcation occurred when the deformation incongruity between striped subgrains and surrounding equiaxed grains intensified sufficiently. Microstructure has an important effect on the number and morphology of ASB bifurcations. More ASB bifurcations formed in Ti–6Al–4V alloys with bimodal and lamellar microstructures than in the alloy with equiaxed microstructure because of the different amounts and distributions of striped subgrains. In the equiaxed microstructure, fewer subgrains were preserved in ASBs. Thus, forming deformation incongruities sufficiently intense to induce ASB bifurcation was difficult. In the bimodal microstructure, numerous striped subgrains and deformation incongruity locations were observed. More randomly distributed deformation incongruity locations would ultimately lead to more random ASB bifurcations. In the lamellar microstructure, the striped subgrains arranged along different directions in different colonies caused more intense deformation incongruity than when the subgrains were in the same colony. ASB bifurcation more commonly occurred at colony boundaries.
Hopf and Generalized Hopf Bifurcations in a Recurrent Autoimmune Disease Model
Zhang, Wenjing; Yu, Pei
This paper is concerned with bifurcation and stability in an autoimmune model, which was established to study an important phenomenon — blips arising from such models. This model has two equilibrium solutions, disease-free equilibrium and disease equilibrium. The positivity of the solutions of the model and the global stability of the disease-free equilibrium have been proved. In this paper, we particularly focus on Hopf bifurcation which occurs from the disease equilibrium. We present a detailed study on the use of center manifold theory and normal form theory, and derive the normal form associated with Hopf bifurcation, from which the approximate amplitude of the bifurcating limit cycles and their stability conditions are obtained. Particular attention is also paid to the bifurcation of multiple limit cycles arising from generalized Hopf bifurcation, which may yield bistable phenomenon involving equilibrium and oscillating motion. This result may explain some complex dynamical behavior in real biological systems. Numerical simulations are compared with the analytical predictions to show a very good agreement.
Anatomy and function relation in the coronary tree: from bifurcations to myocardial flow and mass.
Kassab, Ghassan S; Finet, Gerard
2015-01-01
The study of the structure-function relation of coronary bifurcations is necessary not only to understand the design of the vasculature but also to use this understanding to restore structure and hence function. The objective of this review is to provide quantitative relations between bifurcation anatomy or geometry, flow distribution in the bifurcation and degree of perfused myocardial mass in order to establish practical rules to guide optimal treatment of bifurcations including side branches (SB). We use the scaling law between flow and diameter, conservation of mass and the scaling law between myocardial mass and diameter to provide geometric relations between the segment diameters of a bifurcation, flow fraction distribution in the SB, and the percentage of myocardial mass perfused by the SB. We demonstrate that the assessment of the functional significance of an SB for intervention should not only be based on the diameter of the SB but also on the diameter of the mother vessel as well as the diameter of the proximal main artery, as these dictate the flow fraction distribution and perfused myocardial mass, respectively. The geometric and flow rules for a bifurcation are extended to a trifurcation to ensure optimal therapy scaling rules for any branching pattern.
Simulation of bifurcated stent grafts to treat abdominal aortic aneurysms (AAA)
Egger, J.; Großkopf, S.; Freisleben, B.
2007-03-01
In this paper a method is introduced, to visualize bifurcated stent grafts in CT-Data. The aim is to improve therapy planning for minimal invasive treatment of abdominal aortic aneurysms (AAA). Due to precise measurement of the abdominal aortic aneurysm and exact simulation of the bifurcated stent graft, physicians are supported in choosing a suitable stent prior to an intervention. The presented method can be used to measure the dimensions of the abdominal aortic aneurysm as well as simulate a bifurcated stent graft. Both of these procedures are based on a preceding segmentation and skeletonization of the aortic, right and left iliac. Using these centerlines (aortic, right and left iliac) a bifurcated initial stent is constructed. Through the implementation of an ACM method the initial stent is fit iteratively to the vessel walls - due to the influence of external forces (distance- as well as balloonforce). Following the fitting process, the crucial values for choosing a bifurcated stent graft are measured, e.g. aortic diameter, right and left common iliac diameter, minimum diameter of distal neck. The selected stent is then simulated to the CT-Data - starting with the initial stent. It hereby becomes apparent if the dimensions of the bifurcated stent graft are exact, i.e. the fitting to the arteries was done properly and no ostium was covered.
Bifurcating fronts for the Taylor-Couette problem in infinite cylinders
Hărăguş-Courcelle, M.; Schneider, G.
We show the existence of bifurcating fronts for the weakly unstable Taylor-Couette problem in an infinite cylinder. These fronts connect a stationary bifurcating pattern, here the Taylor vortices, with the trivial ground state, here the Couette flow. In order to show the existence result we improve a method which was already used in establishing the existence of bifurcating fronts for the Swift-Hohenberg equation by Collet and Eckmann, 1986, and by Eckmann and Wayne, 1991. The existence proof is based on spatial dynamics and center manifold theory. One of the difficulties in applying center manifold theory comes from an infinite number of eigenvalues on the imaginary axis for vanishing bifurcation parameter. But nevertheless, a finite dimensional reduction is possible, since the eigenvalues leave the imaginary axis with different velocities, if the bifurcation parameter is increased. In contrast to previous work we have to use normalform methods and a non-standard cut-off function to obtain a center manifold which is large enough to contain the bifurcating fronts.
Energy Technology Data Exchange (ETDEWEB)
Hajihosseini, Amirhossein, E-mail: hajihosseini@khayam.ut.ac.ir [School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5746 (Iran, Islamic Republic of); Center of Excellence in Biomathematics, School of Mathematics, Statistics and Computer Science, University of Tehran, Tehran 14176-14411 (Iran, Islamic Republic of); Maleki, Farzaneh, E-mail: farzanmaleki83@khayam.ut.ac.ir [School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran 14176-14411 (Iran, Islamic Republic of); School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5746 (Iran, Islamic Republic of); Center of Excellence in Biomathematics, School of Mathematics, Statistics and Computer Science, University of Tehran, Tehran 14176-14411 (Iran, Islamic Republic of); Rokni Lamooki, Gholam Reza, E-mail: rokni@khayam.ut.ac.ir [School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran 14176-14411 (Iran, Islamic Republic of); School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5746 (Iran, Islamic Republic of); Center of Excellence in Biomathematics, School of Mathematics, Statistics and Computer Science, University of Tehran, Tehran 14176-14411 (Iran, Islamic Republic of)
2011-11-15
Highlights: > We construct a recurrent neural network by generalizing a specific n-neuron network. > Several codimension 1 and 2 bifurcations take place in the newly constructed network. > The newly constructed network has higher capabilities to learn periodic signals. > The normal form theorem is applied to investigate dynamics of the network. > A series of bifurcation diagrams is given to support theoretical results. - Abstract: A class of recurrent neural networks is constructed by generalizing a specific class of n-neuron networks. It is shown that the newly constructed network experiences generic pitchfork and Hopf codimension one bifurcations. It is also proved that the emergence of generic Bogdanov-Takens, pitchfork-Hopf and Hopf-Hopf codimension two, and the degenerate Bogdanov-Takens bifurcation points in the parameter space is possible due to the intersections of codimension one bifurcation curves. The occurrence of bifurcations of higher codimensions significantly increases the capability of the newly constructed recurrent neural network to learn broader families of periodic signals.
Emergence of the bifurcation structure of a Langmuir–Blodgett transfer model
Köpf, Michael H
2014-10-07
© 2014 IOP Publishing Ltd & London Mathematical Society. We explore the bifurcation structure of a modified Cahn-Hilliard equation that describes a system that may undergo a first-order phase transition and is kept permanently out of equilibrium by a lateral driving. This forms a simple model, e.g., for the deposition of stripe patterns of different phases of surfactant molecules through Langmuir-Blodgett transfer. Employing continuation techniques the bifurcation structure is numerically investigated using the non-dimensional transfer velocity as the main control parameter. It is found that the snaking structure of steady front states is intertwined with a large number of branches of time-periodic solutions that emerge from Hopf or period-doubling bifurcations and end in global bifurcations (sniper and homoclinic). Overall the bifurcation diagram has a harp-like appearance. This is complemented by a two-parameter study in non-dimensional transfer velocity and domain size (as a measure of the distance to the phase transition threshold) that elucidates through which local and global codimension 2 bifurcations the entire harp-like structure emerges.
Patient-specific computer modelling of coronary bifurcation stenting: the John Doe programme.
Mortier, Peter; Wentzel, Jolanda J; De Santis, Gianluca; Chiastra, Claudio; Migliavacca, Francesco; De Beule, Matthieu; Louvard, Yves; Dubini, Gabriele
2015-01-01
John Doe, an 81-year-old patient with a significant distal left main (LM) stenosis, was treated using a provisional stenting approach. As part of an European Bifurcation Club (EBC) project, the complete stenting procedure was repeated using computational modelling. First, a tailored three-dimensional (3D) reconstruction of the bifurcation anatomy was created by fusion of multislice computed tomography (CT) imaging and intravascular ultrasound. Second, finite element analysis was employed to deploy and post-dilate the stent virtually within the generated patient-specific anatomical bifurcation model. Finally, blood flow was modelled using computational fluid dynamics. This proof-of-concept study demonstrated the feasibility of such patient-specific simulations for bifurcation stenting and has provided unique insights into the bifurcation anatomy, the technical aspects of LM bifurcation stenting, and the positive impact of adequate post-dilatation on blood flow patterns. Potential clinical applications such as virtual trials and preoperative planning seem feasible but require a thorough clinical validation of the predictive power of these computer simulations.
Axisymmetric bifurcations of thick spherical shells under inflation and compression
deBotton, G.
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.