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...
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...
Unfolding the Riddling Bifurcation
DEFF Research Database (Denmark)
Maistrenko, Yu.; Popovych, O.; Mosekilde, Erik
1999-01-01
We present analytical conditions for the riddling bifurcation in a system of two symmetrically coupled, identical, smooth one-dimensional maps to be soft or hard and describe a generic scenario for the transformations of the basin of attraction following a soft riddling bifurcation.......We present analytical conditions for the riddling bifurcation in a system of two symmetrically coupled, identical, smooth one-dimensional maps to be soft or hard and describe a generic scenario for the transformations of the basin of attraction following a soft riddling bifurcation....
Semiclassical interference of bifurcations
Schomerus, H
1997-01-01
In semiclassical studies of systems with mixed phase space, the neighbourhood of bifurcations of co-dimension two is felt strongly even though such bifurcations are ungeneric in classical mechanics. We discuss a scenario which reveals this fact and derive the correct semiclassical contribution of the bifurcating orbits to the trace of the unitary time evolution operator. That contribution has a certain collective character rather than being additive in the individual periodic orbits involved. The relevance of our observation is demonstrated by a numerical study of the kicked top; the collective contribution derived is found to considerably improve the semiclassical approximation of the trace.
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 phenomena in control flows
Colonius, Fritz; Fabbri, Roberta; Johnson, Russell; Spadini, Marco
2007-01-01
We study bifurcation phenomena in control flows and the bifurcation of control sets. A Mel'nikov method and the Conley index together with exponential dichotomy theory and integral manifold theory are used.
Energetics and monsoon bifurcations
Seshadri, Ashwin K.
2016-04-01
Monsoons involve increases in dry static energy (DSE), with primary contributions from increased shortwave radiation and condensation of water vapor, compensated by DSE export via horizontal fluxes in monsoonal circulations. We introduce a simple box-model characterizing evolution of the DSE budget to study nonlinear dynamics of steady-state monsoons. Horizontal fluxes of DSE are stabilizing during monsoons, exporting DSE and hence weakening the monsoonal circulation. By contrast latent heat addition (LHA) due to condensation of water vapor destabilizes, by increasing the DSE budget. These two factors, horizontal DSE fluxes and LHA, are most strongly dependent on the contrast in tropospheric mean temperature between land and ocean. For the steady-state DSE in the box-model to be stable, the DSE flux should depend more strongly on the temperature contrast than LHA; stronger circulation then reduces DSE and thereby restores equilibrium. We present conditions for this to occur. The main focus of the paper is describing conditions for bifurcation behavior of simple models. Previous authors presented a minimal model of abrupt monsoon transitions and argued that such behavior can be related to a positive feedback called the `moisture advection feedback'. However, by accounting for the effect of vertical lapse rate of temperature on the DSE flux, we show that bifurcations are not a generic property of such models despite these fluxes being nonlinear in the temperature contrast. We explain the origin of this behavior and describe conditions for a bifurcation to occur. This is illustrated for the case of the July-mean monsoon over India. The default model with mean parameter estimates does not contain a bifurcation, but the model admits bifurcation as parameters are varied.
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...
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.
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. PMID:26428557
Bifurcations and intermittent magnetic activity
International Nuclear Information System (INIS)
The sequence of equilibria of two-dimensional reduced magnetohydrodynamics has been studied as a function of the tearing mode stability parameter Δ'. After a symmetry-breaking bifurcation occurring at Δ' ∼ 0, which originates a state with a small magnetic island, the system undergoes a second bifurcation, of tangent type, at Δ' ∼ 1. Above this value, no stationary solutions with small islands exist. The system rapidly develops an island of macroscopic size. This general property is proposed as a basic ingredient of the intermittent events observed in magnetically confined plasmas. (author)
Bifurcations and intermittent magnetic activity
Energy Technology Data Exchange (ETDEWEB)
Tebaldi, C.; Ottaviani, M.; Porcelli, F. [Commission of the European Communities, Abingdon (United Kingdom). JET Joint Undertaking
1996-04-01
The sequence of equilibria of two-dimensional reduced magnetohydrodynamics has been studied as a function of the tearing mode stability parameter {Delta}`. After a symmetry-breaking bifurcation occurring at {Delta}` {approx} 0, which originates a state with a small magnetic island, the system undergoes a second bifurcation, of tangent type, at {Delta}` {approx} 1. Above this value, no stationary solutions with small islands exist. The system rapidly develops an island of macroscopic size. This general property is proposed as a basic ingredient of the intermittent events observed in magnetically confined plasmas. (author).
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...
Bifurcation of steady tearing states
International Nuclear Information System (INIS)
We apply the bifurcation theory for compact operators to the problem of the nonlinear solutions of the 3-dimensional incompressible visco-resistive MHD equations. For the plane plasma slab model we compute branches of nonlinear tearing modes, which are stationary for the range of parameters investigated up to now
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.
Bifurcation and Secondary Bifurcation of Heavy Periodic Hydroelastic Travelling Waves
Baldi, Pietro; Toland, John F.
2008-01-01
The paper deals with a problem of interaction between hydrodynamics and mechanics of nonlinear elastic bodies. The existence question for two-dimensional symmetric steady waves travelling on the surface of a deep ocean beneath a heavy elastic membrane is analyzed as a problem in bifurcation theory. The behaviour of the two-dimensional cross-section of the membrane is modelled as a thin (unshearable), heavy, hyperelastic Cosserat rod, following Antman's elasticity theory, and the fluid beneath...
Tibial hemimelia and femoral bifurcation.
Ugras, Ali Akin; Sungur, Ibrahim; Akyildiz, Mustafa Fehmi; Ercin, Ersin
2010-02-01
Femoral bifurcation and tibial agenesis are rare anomalies and have been described in both the Gollop-Wolfgang complex and tibial agenesis-ectrodactyly syndrome. This article presents a case of Gollop-Wolfgang complex without hand ectrodactyly. Tibial agenesis-ectrodactyly syndrome and Gollop-Wolfgang complex are variants of tibial field defect, which includes distal femoral duplication, tibial aplasia, oligo-ectrodactylous toe defects, and preaxial polydactyly, occasionally associated with hand ectrodactyly.This article describes the case of a patient with bilateral tibial hemimelia and left femoral bifurcation. The proximal tibial anlage had not been identified in the patient's left leg. After failed fibular transfer procedure, the knee was disarticulated. The other leg was treated with tibiofibular synostosis and centralization of fibula to os calcis. At 7-year follow-up, the patient ambulates with an above-knee prosthesis and uses an orthopedic boot for ankle stability.In patients with a congenital absence of the tibia, accurate diagnosis is of the utmost importance in planning future treatment. In the absence of proximal tibial anlage, especially in patients with femoral bifurcation, the knee should be disarticulated. Tibiofibular synostosis is a good choice in the presence of a proximal tibial anlage and good quadriceps function. PMID:20192156
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.
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
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...
Bifurcation of the spin-wave equations
International Nuclear Information System (INIS)
We study the bifurcations of the spin-wave equations that describe the parametric pumping of collective modes in magnetic media. Mechanisms describing the following dynamical phenomena are proposed: (i) sequential excitation of modes via zero eigenvalue bifurcations; (ii) Hopf bifurcations followed (or not) by Feingenbaum cascades of period doubling; (iii) local and global homoclinic phenomena. Two new organizing center for routes to chaos are identified; in the classification given by Guckenheimer and Holmes [GH], one is a codimension-two local bifurcation, with one pair of imaginary eigenvalues and a zero eigenvalue, to which many dynamical consequences are known; secondly, global homoclinic bifurcations associated to splitting of separatrices, in the limit where the system can be considered a Hamiltonian subjected to weak dissipation and forcing. We outline what further numerical and algebraic work is necessary for the detailed study following this program. (author)
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 ...
Nonlinear stability control and λ-bifurcation
International Nuclear Information System (INIS)
Passive techniques for nonlinear stability control are presented for a model of fluidelastic instability. They employ the phenomena of λ-bifurcation and a generalization of it. λ-bifurcation occurs when a branch of flutter solutions bifurcates supercritically from a basic solution and terminates with an infinite period orbit at a branch of divergence solutions which bifurcates subcritically from the basic solution. The shape of the bifurcation diagram then resembles the greek letter λ. When the system parameters are in the range where flutter occurs by λ-bifurcation, then as the flow velocity increase the flutter amplitude also increases, but the frequencies of the oscillations decrease to zero. This diminishes the damaging effects of structural fatigue by flutter, and permits the flow speed to exceed the critical flutter speed. If generalized λ-bifurcation occurs, then there is a jump transition from the flutter states to a divergence state with a substantially smaller amplitude, when the flow speed is sufficiently larger than the critical flutter speed
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.
Bifurcations of Periodic Orbits and Uniform Approximations
Schomerus, H; Schomerus, Henning; Sieber, Martin
1997-01-01
We derive uniform approximations for contributions to Gutzwiller's periodic-orbit sum for the spectral density which are valid close to bifurcations of periodic orbits in systems with mixed phase space. There, orbits lie close together and give collective contributions, while the individual contributions of Gutzwiller's type would diverge at the bifurcation. New results for the tangent, the period doubling and the period tripling bifurcation are given. They are obtained by going beyond the local approximation and including higher order terms in the normal form of the action. The uniform approximations obtained are tested on the kicked top and are found to be in excellent agreement with exact quantum results.
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.
Coexistence of periods in a bifurcation
International Nuclear Information System (INIS)
Highlights: ► The bifurcation of the Varley–Gradwell–Hassell population model is revisited. ► The structure of the attractor mediating the bifurcation to chaos is studied. ► Geometric arguments are given for the coexistence of periods in the attractor. ► An algebraic method for the localization of these bifurcations is provided. - Abstract: A particular type of order-to-chaos transition mediated by an infinite set of coexisting neutrally stable limit cycles of different periods is studied in the Varley–Gradwell–Hassell population model. We prove by an algebraic method that this kind of transition can only happen for a particular bifurcation parameter value. Previous results on the structure of the attractor at the transition point are here simplified and extended.
Continuation and Bifurcation software in MATLAB
Ravnås, Eirik
2008-01-01
This article contains discussions of the algorithms used for the construction of the continuation software implemented in this thesis. The aim of the continuation was to be able to perform continuation of equilibria and periodic solutions originating from a Hopf bifurcation point. Algorithms for detection of simple branch points, folds, and Hopf bifurcation points have also been implemented. Some considerations are made with regard to optimization, and two schemes for mesh adaptation of perio...
Stability and bifurcation of mutual system with time delay
International Nuclear Information System (INIS)
In this paper, we study the stability and bifurcation in a mutual model with a delay τ, where τ is regarded as a parameter. It is found that there are stability switches, and Hopf bifurcation occur when the delay τ passes through a sequence of critical values. A formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions in the first bifurcation value is given using the normal form method and center manifold theorem
Bifurcation Analysis of the Wound Rotor Induction Motor
Salas-Cabrera, R.; Hernandez-Colin, A.; Roman-Flores, J.; Salas-Cabrera, N.
This work deals with the bifurcation phenomena that occur during the open-loop operation of a single-fed three-phase wound rotor induction motor. This paper demonstrates the occurrence of saddle-node bifurcation, hysteresis, supercritical saddle-node bifurcation, cusp and Hopf bifurcation during the individual operation of this electromechanical system. Some experimental results associated with the bifurcation phenomena are presented.
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.
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.
Internal carotid artery bifurcation aneurysms. Surgical experience
International Nuclear Information System (INIS)
Internal carotid artery (ICA) bifurcation aneurysms are relatively uncommon and frequently rupture at a younger age compared to other intracranial aneurysms. We have treated a total of 999 patients for intracranial aneurysms, of whom 89 (8.9%) had ICA bifurcation aneurysms, and 42 of the 89 patients were 30 years of age or younger. The present study analyzed the clinical records of 70 patients with ICA bifurcation aneurysms treated from mid 1997 to mid 2003. Multiple aneurysms were present in 15 patients. Digital subtraction angiography films were studied in 55 patients to identify vasospasm and aneurysm projection. The aneurysm projected superiorly in most of these patients (37/55, 67.3%). We preferred to minimize frontal lobe retraction, so widely opened the sylvian fissure to approach the ICA bifurcation and aneurysm neck. Elective temporary clipping was employed before the final dissection and permanent clip application. Vasospasm was present in 24 (43.6%) of 55 patients. Forty-eight (68.6%) of the 70 patients had good outcome, 14 (20%) had poor outcome, and eight (11.4%) died. Patients with ICA bifurcation aneurysms tend to bleed at a much younger age compared to those with other intracranial aneurysms. Wide opening of the sylvian fissure and elective temporary clipping of the ICA reduces the risk of intraoperative rupture and perforator injury. Mortality was mainly due to poor clinical grade and intraoperative premature aneurysm rupture. (author)
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.
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.
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 ...
Lassen, Jens Flensted; Holm, Niels Ramsing; Banning, Adrian; Burzotta, Francesco; Lefèvre, Thierry; Chieffo, Alaide; Hildick-Smith, David; Louvard, Yves; Stankovic, Goran
2016-05-17
Coronary bifurcations are involved in 15-20% of all percutaneous coronary interventions (PCI) and remain one of the most challenging lesions in interventional cardiology in terms of procedural success rate as well as long-term cardiac events. The optimal management of bifurcation lesions is, despite a fast growing body of scientific literature, the subject of considerable debate. The European Bifurcation Club (EBC) was initiated in 2004 to support a continuous overview of the field, and aims to facilitate a scientific discussion and an exchange of ideas on the management of bifurcation disease. The EBC hosts an annual, compact meeting, dedicated to bifurcations, which brings together physicians, engineers, biologists, physicists, epidemiologists and statisticians for detailed discussions. Every meeting is finalised with a consensus statement which reflects the unique opportunity of combining the opinions of interventional cardiologists with the opinions of a large variety of other scientists on bifurcation management. The present 11th EBC consensus document represents the summary of the up-to-date EBC consensus and recommendations. It points to the fact that there is a multitude of strategies and approaches to bifurcation stenting within the provisional strategy and in the different two-stent strategies. The main EBC recommendation for PCI of bifurcation lesions remains to use main vessel (MV) stenting with a proximal optimisation technique (POT) and provisional side branch (SB) stenting as a preferred approach. The consensus document covers a moving target. Much more scientific work is needed in non-left main (LM) and LM bifurcation lesions for continuous improvement of the outcome of our patients. PMID:27173860
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.
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.
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.
Bifurcations of a class of singular biological economic models
International Nuclear Information System (INIS)
This paper studies systematically a prey-predator singular biological economic model with time delay. It shows that this model exhibits two bifurcation phenomena when the economic profit is zero. One is transcritical bifurcation which changes the stability of the system, and the other is singular induced bifurcation which indicates that zero economic profit brings impulse, i.e., rapid expansion of the population in biological explanation. On the other hand, if the economic profit is positive, at a critical value of bifurcation parameter, the system undergoes a Hopf bifurcation, i.e., the increase of delay destabilizes the system and bifurcates into small amplitude periodic solution. Finally, by using Matlab software, numerical simulations illustrate the effectiveness of the results obtained here. In addition, we study numerically that the system undergoes a saddle-node bifurcation when the bifurcation parameter goes through critical value of positive economic profit.
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.
Stability and Hopf Bifurcation in the Watt Governor System
Sotomayor, Jorge; Mello, Luis Fernando; Braga, Denis de Carvalho
2006-01-01
In this paper we study the Lyapunov stability and Hopf bifurcation in a system coupling a Watt-centrifugal-governor with a steam-engine. Sufficient conditions for the stability of the equilibrium state in terms of the physical parameters and of the bifurcating periodic orbit at most critical parameters on the bifurcation surface are given.
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.
Bifurcation structure of a model of bursting pancreatic cells
DEFF Research Database (Denmark)
Mosekilde, Erik; Lading, B.; Yanchuk, S.; Maistrenko, Y.
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...
Singular limit cycle bifurcations to closed orbits and invariant tori
International Nuclear Information System (INIS)
This paper investigates singular limit cycle bifurcations for a singularly perturbed system. Based on a series of transformations (the modified curvilinear coordinate, blow-up, and near-identity transformation) and bifurcation theory of periodic orbits and invariant tori, the bifurcations of closed orbits and invariant tori near singular limit cycles are discussed
Singular limit cycle bifurcations to closed orbits and invariant tori
Energy Technology Data Exchange (ETDEWEB)
Ye Zhiyong [Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240 (China); Department of Mathematics, Chongqing Institute of Technology, Chongqing 400050 (China); E-mail: yezhiyong@sjtu.edu.cn; Han Maoan [Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240 (China); E-mail: mahan@sjtu.edu.cn
2006-02-01
This paper investigates singular limit cycle bifurcations for a singularly perturbed system. Based on a series of transformations (the modified curvilinear coordinate, blow-up, and near-identity transformation) and bifurcation theory of periodic orbits and invariant tori, the bifurcations of closed orbits and invariant tori near singular limit cycles are discussed.
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).
Digital subtraction angiography of carotid bifurcation
International Nuclear Information System (INIS)
This study demonstrates the reliability of digital subtraction angiography (DSA) by means of intra- and interobserver investigations as well as indicating the possibility of substituting catheterangiography by DSA in the diagnosis of carotid bifurcation. Whenever insufficient information is obtained from the combination of non-invasive investigation and DSA, a catheterangiogram will be necessary. (Auth.)
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.
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.
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.
International Nuclear Information System (INIS)
We show that maps describing border collision bifurcations (continuous but non-differentiable discrete time maps) are subject to a curse of dimensionality: it is impossible to reduce the study of the general case to low dimensions, since in every dimension the bifurcation can produce fundamentally different attractors (contrary to the case of local bifurcations in smooth systems). In particular we show that n-dimensional border collision bifurcations can have invariant sets of dimension k for integer k from 0 to n. We also show that the border collision normal form is related to grazing-sliding bifurcations of switching dynamical systems. This implies that the dynamics of these two apparently distinct bifurcations (one for discrete time dynamics, the other for continuous time dynamics) are closely related and hence that a similar curse of dimensionality holds in grazing-sliding bifurcations. (paper)
Parametric Controller Design of Hopf Bifurcation System
Directory of Open Access Journals (Sweden)
Jinbo Lu
2015-01-01
Full Text Available A general parametric controller design method is proposed for Hopf bifurcation of nonlinear dynamic system. This method does not increase the dimension of the system. Compared with the existing methods, the controller designed by this method has a lower controller order and a simpler structure, and it does not contain equilibrium points. The method keeps equilibrium of the origin system unchanged. Symbolic computation is used to deduce the constraints of controller, and cylindrical algebraic decomposition is used to find the stability parameter regions in parameter space of controller. The method is then employed for Hopf bifurcation control. Taking Lorenz system as an example, the controller design steps of the method and numerical simulations are discussed. Computer simulation results are presented to confirm the analytical predictions.
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...... the effect of the singularity, combined with results on asymptotics of the second Painleve equation. The stable orbits of smallest amplitude that are {persistently} obtained by these methods remain slightly further away from the slow manifold being distant by an order $\\mathcal O(\\epsilon^{1/3}\\ln^{1...
Sex differences in intracranial arterial bifurcations
DEFF Research Database (Denmark)
Lindekleiv, Haakon M; Valen-Sendstad, Kristian; Morgan, Michael K; Mardal, Kent-Andre; Faulder, Kenneth; Magnus, Jeanette H; Waterloo, Knut; Romner, Bertil; Ingebrigtsen, Tor
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...... 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....
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.
Bifurcated Helical Core Equilibrium States in Tokamaks
International Nuclear Information System (INIS)
Full text: Tokamaks with weak to moderate reversed central magnetic shear in which the minimum of the inverse rotational transform qmin is in the neighbourhood of unity can trigger bifurcated MagnetoHydroDynamic (MHD) equilibrium states. In addition to the standard axisymmetric branch that can be obtained with standard Grad-Shafranov solvers, a novel branch with a three-dimensional (3D) helical core has been computed with the ANIMEC code, an anisotropic pressure extension of the VMEC code. The solutions have imposed nested magnetic flux surfaces and are similar to saturated ideal internal kink modes. The difference in energy between both possible branches is very small. Plasma elongation, current and β enhance the susceptibility for bifurcations to occur. An initial value nonlinear ideal MHD evolution of the axisymmetric branch compares favourably with the helical core equilibrium structures calculated. Peaked prescribed pressure profiles reproduce the 'snake' structures observed in many tokamaks which has led to a new explanation of the snake as a bifurcated helical equilibrium state that results from a saturated ideal internal kink in which pellets or impurities induce a hollow current profile. Snake equilibrium structures are computed in free boundary TCV tokamak simulations. Magnetic field ripple and resonant magnetic perturbations in MAST free boundary calculations do not alter the helical core deformation in a significant manner when qmin is near unity. These bifurcated solutions constitute a paradigm shift that motivates the application of tools developed for stellarator research in tokamak physics investigations. The examination of fast ion confinement in this class of equilibria is performed with the VENUS code in which a coordinate independent noncanonical phase-space Lagrangian formulation of guiding centre drift orbit theory has been implemented. (author)
Torus bifurcations in multilevel converter systems
DEFF Research Database (Denmark)
Zhusubaliyev, Zhanybai T.; Mosekilde, Erik; Yanochkina, Olga O.
2011-01-01
embedded one into the other and with their basins of attraction delineated by intervening repelling tori. The paper illustrates the coexistence of three stable tori with different resonance behaviors and shows how reconstruction of these tori takes place across the borders of different dynamical regimes....... The paper also demonstrates how pairs of attracting and repelling tori emerge through border-collision torus-birth and border-collision torus-fold bifurcations. © 2011 World Scientific Publishing Company....
Perturbed period-doubling bifurcation. I. Theory
DEFF Research Database (Denmark)
Svensmark, Henrik; Samuelsen, Mogens Rugholm
1990-01-01
-defined way that is a function of the amplitude and the frequency of the signal. New scaling laws between the amplitude of the signal and the detuning δ are found; these scaling laws apply to a variety of quantities, e.g., to the shift of the bifurcation point. It is also found that the stability and the...... of a microwave-driven Josephson junction confirm the theory. Results should be of interest in parametric-amplification studies....
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...
The significance of enhanced radionuclide deposition at bronchial bifurcations
International Nuclear Information System (INIS)
Experiments were conducted to quantitate deposition patterns of monodisperse aerosols in surrogates of the human upper respiratory tract. Laryngeal casts and most upper airway bifurcations were sites of preferential particle deposition. Highly concentrated deposits were detected at carinal ridges within bifurcation zones. Together with impaired mucociliary clearance at branching sites, this initial deposition pattern results in localized accumulations of radionuclides within bifurcation zones. For inhaled radon progeny radiation doses are calculated for 3 regions of bronchial airways: tubular airway segments, bifurcation zones (including the carina), and carinal ridges. These calculations indicated that enhanced deposition at branching sites leads to significantly higher doses to epithelial cells located at bifurcations than along tubular airway segments. If cell killing is included in the analysis of lung cancer risk, it reduces carcinogenic potential at bifurcation sites, particularly at high doses. (author)
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.
Nonlinear instability and dynamic bifurcation of a planeinterface during solidification
Institute of Scientific and Technical Information of China (English)
吴金平; 侯安新; 黄定华; 鲍征宇; 高志农; 屈松生
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.
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.
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.
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.
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
Safe, explosive, and dangerous bifurcations in dissipative dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Thompson, J.M.T. (Centre for Nonlinear Dynamics and Its Applications, Civil Engineering Building, University College London, Gower Street, London WC1E6BT (United Kingdom)); Stewart, H.B. (Mathematical Sciences Group, Building 490-A, Department of Applied Science, Brookhaven National Laboratory, Upton, New York 11973 (United States)); Ueda, Y. (Department of Electrical Engineering, Kyoto University, Kyoto 606 (Japan))
1994-02-01
A comprehensive listing of the generic codimension-1 attractor bifurcations of dissipative dynamical systems is presented. It includes local and global bifurcations of regular and chaotic attractors. The bifurcations are classified according to the continuity or discontinuity of the attractor path, which governs the physical outcome that would be observed under a slow control sweep. Related issues of determinacy, hysteresis, basin structure, and intermittency are addressed. Recently discovered chaotic bifurcations are discussed in some detail, with particular reference to the regular or chaotic saddle-type destroyer with which an attractor may collide.
Safe, explosive, and dangerous bifurcations in dissipative dynamical systems
International Nuclear Information System (INIS)
A comprehensive listing of the generic codimension-1 attractor bifurcations of dissipative dynamical systems is presented. It includes local and global bifurcations of regular and chaotic attractors. The bifurcations are classified according to the continuity or discontinuity of the attractor path, which governs the physical outcome that would be observed under a slow control sweep. Related issues of determinacy, hysteresis, basin structure, and intermittency are addressed. Recently discovered chaotic bifurcations are discussed in some detail, with particular reference to the regular or chaotic saddle-type destroyer with which an attractor may collide
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.
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 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...... the individual family, the organization of the solutions exhibit an infinite number of regulatory arranged domains, the so-called swallow tails. We discuss the origin of this structure which has recently been observed in a variety of other systems as well....
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 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.
Swept-parameter-induced postponements and noise on the Hopf bifurcation.
Fronzoni, L.; Moss, F; McClintock, Peter V. E.
1987-01-01
The postponement of Hopf bifurcations driven by a swept bifurcation parameter is demonstrated with an electronic Brusselator. Noise on the swept parameter destroys the postponement and the bifurcation as it is usually defined.
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.
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...
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.
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.
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.
Hopf Bifurcation in a New Four-Dimensional Hyperchaotic System
Li, Xin; Yan, Zhen-Ya
2015-08-01
In this paper, the Hopf bifurcation in a new hyperchaotic system is studied. Based on the first Lyapunov coefficient theory and symbolic computation, the conditions of supercritical and subcritical bifurcation in the new hyperchaotic system are obtained. Numerical simulations are used to illustrate some main results. Supported by National Key Bsic Research Program of China under Grant No. 2011CB302400
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.
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
Non-Gaussian bifurcating models and quasi-likelihood estimation
Basawa, I. V.; J. Zhou
2004-01-01
A general class of Markovian non-Gaussian bifurcating models for cell lineage data is presented. Examples include bifurcating autoregression, random coefficient autoregression, bivariate exponential, bivariate gamma, and bivariate Poisson models. Quasi-likelihood estimation for the model parameters and large-sample properties of the estimates are discussed.
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
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.
Symmetric/asymmetric bifurcation behaviours of a bogie system
Xue-jun, Gao; Ying-hui, Li; Yuan, Yue; True, Hans
2013-02-01
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 system. The speed ranges of asymmetric chaotic motions are, however, small.
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, are...
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
The simplest normal form of Hopf bifurcation
Yu, P.; Leung, A. Y. T.
2003-01-01
Recently, further reduction on normal forms of differential equations leading to the simplest normal forms (SNFs) has received considerable attention. However, the computation of the SNF has been mainly restricted to systems which do not contain perturbation parameters (unfolding), since the computation of the SNF with unfolding is much more complicated than that of the SNF without unfolding. From the practical point of view, only the SNF with perturbation (bifurcation) parameters is useful in analysing physical or engineering problems. It is shown that the SNF with unfolding cannot be obtained using only near-identity transformation. Additional transformations such as time and parameter rescaling need to be introduced. An efficient computational method is presented for computing the algebraic equations that can be used to find the SNF. A physical example is given to show the applicability of the new method.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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...
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...
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. 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.
Bifurcation control of the Hodgkin-Huxley equations
Energy Technology Data Exchange (ETDEWEB)
Wang Jiang [School of Electrical and Automation Engineering, Tianjin University, 300072 Tianjin (China)]. E-mail: jiangwang@tju.edu.cn; Chen Liangquan [School of Electrical and Automation Engineering, Tianjin University, 300072 Tianjin (China); Fei Xianyang [School of Electrical and Automation Engineering, Tianjin University, 300072 Tianjin (China)
2007-07-15
The Hodgkin-Huxley equations (HH) are parameterized by a number of parameters and show a variety of qualitatively different behaviors. This paper finds that when the externally applied current I {sub ext} varies the bifurcation would occur in the HH equations. The HH model's Hopf bifurcation is controlled by permanent or interval Washout filters (WF), which can transform the subcritical bifurcations into supercritical bifurcations, and can make the HH equations stable directly. Simulation results show the validity of those controllers. We choose the membrane voltage V as an input to the washout filter because V can be readily measured, and the controller can be realized easily. The controller designs described here may boost the development of electrical stimulation systems for patients suffering from different neuron-system dysfunctions.
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.
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.
Multiple bifurcations and periodic 'bubbling' in a delay population model
International Nuclear Information System (INIS)
In this paper, the flip bifurcation and periodic doubling bifurcations of a discrete population model without delay influence is firstly studied and the phenomenon of Feigenbaum's cascade of periodic doublings is also observed. Secondly, we explored the Neimark-Sacker bifurcation in the delay population model (two-dimension discrete dynamical systems) and the unique stable closed invariant curve which bifurcates from the nontrivial fixed point. Finally, a computer-assisted study for the delay population model is also delved into. Our computer simulation shows that the introduction of delay effect in a nonlinear difference equation derived from the logistic map leads to much richer dynamic behavior, such as stable node → stable focus → an lower-dimensional closed invariant curve (quasi-periodic solution, limit cycle) or/and stable periodic solutions → chaotic attractor by cascading bubbles (the combination of potential period doubling and reverse period-doubling) and the sudden change between two different attractors, etc
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.
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)
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.
A Weak Bifurcation Theory for Discrete Time Stochastic Dynamical Systems
Diks, Cees; Wagener, Florian
2006-01-01
This article presents a bifurcation theory of smooth stochastic dynamical systems that are governed by everywhere positive transition densities. The local dependence structure of the unique strictly stationary evolution of such a system can be expressed by the ratio of joint and marginal probability densities; this 'dependence ratio' is a geometric invariant of the system. By introducing a weak equivalence notion of these dependence ratios, we arrive at a bifurcation theory for which in the c...
HIGH BIFURCATION OF THE BRACHIAL ARTERY - A COMMON VARIANT
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Sesi
2015-10-01
Full Text Available 28 cadavers were dissected for variations in the bifurcation of brachial artery bilaterally {n=56} at the department of anatomy, Rangaraya Medical College, Kakinada, A.P. from 2010 to 2015 . Found variations during routine dissections for first year MBBS students. The findings have thrown light on the common as well as rare variants in the anatomy of brachial artery bifurcation and the course of radial and ulnar arteries in current study
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....
Dynamics of Bloch oscillating transistor near the bifurcation threshold
Sarkar, Jayanta; Puska, Antti; Hassel, Juha; Hakonen, Pertti J.
2013-01-01
The tendency to bifurcate can often be utilized to improve performance characteristics of amplifiers or even to build detectors. The Bloch oscillating transistor is such a device. Here, we show that bistable behavior can be approached by tuning the base current and that the critical value depends on the Josephson coupling energy EJ of the device. We demonstrate current-gain enhancement for the device operating near the bifurcation point at small EJ. From our results for the current gains at v...
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.
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...
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.
Hopf Bifurcation Analysis for a Computer Virus Model with Two Delays
Zizhen Zhang; Huizhong Yang
2013-01-01
This paper is concerned with a computer virus model with two delays. Its dynamics are studied in terms of local stability and Hopf bifurcation. Sufficient conditions for local stability of the positive equilibrium and existence of the local Hopf bifurcation are obtained by regarding the possible combinations of the two delays as a bifurcation parameter. Furthermore, explicit formulae for determining direction of the Hopf bifurcation and stability of the bifurcating periodic solutions are o...
Bursting oscillations, bifurcation and synchronization in neuronal systems
International Nuclear Information System (INIS)
Highlights: → We investigate bursting oscillations and related bifurcation in the modified Morris-Lecar neuron. → Two types of fast-slow bursters are analyzed in detail. → We show the properties of some crucial bifurcation points. → Synchronization transition and the neural excitability are explored in the coupled bursters. - Abstract: This paper investigates bursting oscillations and related bifurcation in the modified Morris-Lecar neuron. It is shown that for some appropriate parameters, the modified Morris-Lecar neuron can exhibit two types of fast-slow bursters, that is 'circle/fold cycle' bursting and 'subHopf/homoclinic' bursting with class 1 and class 2 neural excitability, which have different neuro-computational properties. By means of the analysis of fast-slow dynamics and phase plane, we explore bifurcation mechanisms associated with the two types of bursters. Furthermore, the properties of some crucial bifurcation points, which can determine the type of the burster, are studied by the stability and bifurcation theory. In addition, we investigate the influence of the coupling strength on synchronization transition and the neural excitability in two electrically coupled bursters with the same bursting type. More interestingly, the multi-time-scale synchronization transition phenomenon is found as the coupling strength varies.
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).
Bifurcation Analysis Using Rigorous Branch and Bound Methods
Smith, Andrew P.; Crespo, Luis G.; Munoz, Cesar A.; Lowenberg, Mark H.
2014-01-01
For the study of nonlinear dynamic systems, it is important to locate the equilibria and bifurcations occurring within a specified computational domain. This paper proposes a new approach for solving these problems and compares it to the numerical continuation method. The new approach is based upon branch and bound and utilizes rigorous enclosure techniques to yield outer bounding sets of both the equilibrium and local bifurcation manifolds. These sets, which comprise the union of hyper-rectangles, can be made to be as tight as desired. Sufficient conditions for the existence of equilibrium and bifurcation points taking the form of algebraic inequality constraints in the state-parameter space are used to calculate their enclosures directly. The enclosures for the bifurcation sets can be computed independently of the equilibrium manifold, and are guaranteed to contain all solutions within the computational domain. A further advantage of this method is the ability to compute a near-maximally sized hyper-rectangle of high dimension centered at a fixed parameter-state point whose elements are guaranteed to exclude all bifurcation points. This hyper-rectangle, which requires a global description of the bifurcation manifold within the computational domain, cannot be obtained otherwise. A test case, based on the dynamics of a UAV subject to uncertain center of gravity location, is used to illustrate the efficacy of the method by comparing it with numerical continuation and to evaluate its computational complexity.
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.
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.
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...
Bifurcation phenomena near homoclinic systems: A two-parameters analysis
International Nuclear Information System (INIS)
The bifurcations of periodic orbits in a class of autonomous three-variable, nonlinear-differential-equation systems possessing a homoclinic orbit associated with a saddle focus with eigenvalues (rho +- iω, lambda), where Vertical Barrho/lambdaVertical Bar<1 (Sil'nikov's condition), are studied in a two-parameters space. The perturbed homoclinic systems undergo a countable set of tangent bifurcation followed by period-doubling bifurcations leading to a periodic orbits which may be attractors if Vertical Barlambda/lVertical Bar<1/2. The accumulation rate of the critical parameter values at the homoclinic system is exp(-2πVertical Barrho/ωVertical Bar). A global mechanism for the onset of homoclinicity in strongly contractive flows is analyzed. Cusp bifurcations with bistability and hysteresis phenomena exist locally near the onset of homoclinicity. A countable set of these cusp bifurcations with scaling properties related to the eigenvalues rho +- iω of the stationary state are shown to occur in infinitely contractive flows. In the two-parameter space, the periodic orbit attractor domain exhibits a spiral structure globally, around the set of homoclinic systems, in which all the different periodic orbits are continuously connected
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
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
Experimental Study of Bifurcations in A Parametrically Forced Pendulum
Kim, S Y; Yi, J; Jang, J W; Kim, Sang-Yoon
1997-01-01
An experimental study of bifurcations associated with stability of stationary points (SP's) in a parametrically forced magnetic pendulum and a comparison of its results with numerical results are presented. The critical values for which the SP's lose or gain their stability are experimentally measured by varying the two parameters $\\Omega$ (the normalized natural frequency) and $A$ (the normalized driving amplitude). It is observed that, when the amplitude $A$ exceeds a critical value, the normal SP with $\\theta=0$ ($\\theta$ is the angle between the permanent magnet and the magnetic field) becomes unstable either by a period-doubling bifurcation or by a symmetry-breaking pitchfork bifurcation, depending on the values of $\\Omega$. However, in contrast with the normal SP the inverted SP with $\\theta=\\pi$ is observed to become stable as $A$ is increased above a critical value by a pitchfork bifurcation, but it also destabilizes for a higher critical value of $A$ by a period-doubling bifurcation. All of these exp...
Grazing bifurcations and chatter in a pressure relief valve model
Hős, Csaba; Champneys, Alan R.
2012-11-01
This paper considers a simple mechanical model of a pressure relief valve. For a wide region of parameter values, the valve undergoes self-oscillations that involve impact with the valve seat. These oscillations are born in a Hopf bifurcation that can be either super- or sub-critical. In either case, the onset of more complex oscillations is caused by the occurrence of grazing bifurcations, where the limit cycle first becomes tangent to the discontinuity surface that represents valve contact. The complex dynamics that ensues from such points as the flow speed is decreased has previously been reported via brute-force bifurcation diagrams. Here, the nature of the transitions is further elucidated via the numerical continuation of impacting orbits. In addition, two-parameter continuation results for Hopf and grazing bifurcations as well as the continuation of period-doubling bifurcations of impacting orbits are presented. For yet lower flow speeds, new results reveal chattering motion, that is where there are many impacts in a finite time interval. The geometry of the chattering region is analysed via the computation of several pre-images of the grazing set. It is shown how these pre-images organise the dynamics, in particular by separating initial conditions that lead to complete chatter (an accumulation of impacts) from those which do not.
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.
Doubly twisted Neimark-Sacker bifurcation and two coexisting two-dimensional tori
Sekikawa, Munehisa; Inaba, Naohiko
2016-01-01
We discuss a complicated bifurcation structure involving several quasiperiodic bifurcations generated in a three-coupled delayed logistic map where a doubly twisted Neimark-Sacker bifurcation causes a transition from two coexisting periodic attractors to two coexisting invariant closed circles (ICCs) corresponding to two two-dimensional tori in a vector field. Such bifurcation structures are observed in Arnol'd tongues. Lyapunov and bifurcation analyses suggest that the two coexisting ICCs and the two coexisting periodic solutions almost overlap in the two-parameter bifurcation diagram.
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.
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.
Implicit ordinary differential equations: bifurcations and sharpening of equivalence
International Nuclear Information System (INIS)
We obtain a formal classification of generic local bifurcations of an implicit ordinary differential equation at its singular points as a single external parameter varies. This classification consists of four normal forms, each containing a functional invariant. We prove that every deformation in the contact equivalence class of an equation germ which remains quadratic in the derivative can be obtained by a deformation of the independent and dependent variables. Our classification is based on a generalization of this result for families of equations. As an application, we obtain a formal classification of generic local bifurcations on the plane for a linear second-order partial differential equation of mixed type at the points where the domains of ellipticity and hyperbolicity undergo Morse 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...
An explicit example of Hopf bifurcation in fluid mechanics
Kloeden, P.; Wells, R.
1983-01-01
It is observed that a complete and explicit example of Hopf bifurcation appears not to be known in fluid mechanics. Such an example is presented for the rotating Benard problem with free boundary conditions on the upper and lower faces, and horizontally periodic solutions. Normal modes are found for the linearization, and the Veronis computation of the wave numbers is modified to take into account the imposed horizontal periodicity. An invariant subspace of the phase space is found in which the hypotheses of the Joseph-Sattinger theorem are verified, thus demonstrating the Hopf bifurcation. The criticality calculations are carried through to demonstrate rigorously, that the bifurcation is subcritical for certain cases, and to demonstrate numerically that it is subcritical for all the cases in the paper.
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.
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.
Bifurcated equilibria in two-dimensional MHD with diamagnetic effects
Energy Technology Data Exchange (ETDEWEB)
Ottaviani, M. [CEA Cadarache, 13 - Saint-Paul-lez-Durance (France). Dept. de Recherches sur la Fusion Controlee; Tebaldi, C. [Lecce University (Italy). Dept. of Mathematics
1998-12-01
In this work we analyzed the sequence of bifurcated equilibria in two-dimensional reduced magnetohydrodynamics. Diamagnetic effects are studied under the assumption of a constant equilibrium pressure gradient, not altered by the formation of the magnetic island. The formation of an island when the symmetric equilibrium becomes unstable is studied as a function of the tearing mode stability parameter {Delta}` and of the diamagnetic frequency, by employing fixed-points numerical techniques and an initial value code. At larger values of {Delta}` a tangent bifurcation takes place, above which no small island solutions exist. This bifurcation persists up to fairly large values of the diamagnetic frequency (of the order of one tenth of the Alfven frequency). The implications of this phenomenology for the intermittent MHD dynamics observed in tokamaks is discussed. (authors) 20 refs.
Bifurcated equilibria in two-dimensional MHD with diamagnetic effects
International Nuclear Information System (INIS)
In this work we analyzed the sequence of bifurcated equilibria in two-dimensional reduced magnetohydrodynamics. Diamagnetic effects are studied under the assumption of a constant equilibrium pressure gradient, not altered by the formation of the magnetic island. The formation of an island when the symmetric equilibrium becomes unstable is studied as a function of the tearing mode stability parameter Δ' and of the diamagnetic frequency, by employing fixed-points numerical techniques and an initial value code. At larger values of Δ' a tangent bifurcation takes place, above which no small island solutions exist. This bifurcation persists up to fairly large values of the diamagnetic frequency (of the order of one tenth of the Alfven frequency). The implications of this phenomenology for the intermittent MHD dynamics observed in tokamaks is discussed. (authors)
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
Numerical Modeling of Bifurcation Evolution in a Sand-bed Braided River
De Haas, T.; Schuurman, F.; Kleinhans, M. G.
2012-12-01
River bifurcations are key units in a braided river. Although simple bifurcations are well understood and can be analyzed by 1D models (e.g. Bolla Pittaluga et al., 2003 and Kleinhans et al., 2008), predicting the stability and dynamics of multiple interacting bifurcations in a braided river with migrating bars requires understanding of the interaction between braid bars, channel network and bifurcations, in particular the upstream curvature and downstream backwater effects. Our objective is to understand the evolution of bifurcations at migrating bars in a braided river and the effects on bar evolution. We used the 3D numerical morphodynamic model Delft3D to produce a dynamically braiding sand bed river. This model solves the 3D-flow and computes sediment transport and bed level change accounting for effects of transverse bed slope. It includes a simple bank erosion model to reactivate emerged areas. The morphology of mid-channel bars produced by the model was analyzed and the partitioning of water and sediment over the bifurcating channels are compared with a 1D model concept. Next, the evolution of bars is linked to that of the bifurcations, in order to infer relations between bar morphology and bifurcation evolution. We find that upstream bar dynamics have a major effect on the stability of bifurcations. Migration and elongation of bars can close the upstream entrance of a bifurcation channel, independent of the stability of the bifurcation. Moreover, bifurcation angle and upstream curvature can be affected by upstream bar migration and elongation, which steers flow and sediment partitioning at the bifurcation. At the same time, the partitioning of water and sediment over a bifurcation affects bar shape. Sediment eroded at one of the bar sides just downstream of the bifurcation deposits downstream of the braid bar in the form of tail bars. Hence bar shape as observable on imagery contains useful information about the evolution of the upstream bifurcation and
Symmetric/asymmetric bifurcation behaviours of a bogie system
DEFF Research Database (Denmark)
Xue-jun, Gao; Ying-hui, Li; Yuan, Yue;
2013-01-01
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...
Bifurcations of a lattice gas flow under external forcing
International Nuclear Information System (INIS)
The authors study the behavior of a Frisch-Hasslacher-Pomeau lattice gas automation under the effect of a spatially periodic forcing. It is shown that the lattice gas dynamics reproduces the steady-state features of the bifurcation pattern predicted by a properly truncated model of the Navier-Stokes equations. In addition, they show that the dynamical evolution of the instabilities driving the bifurcation can be modeled by supplementing the truncated Navier-Stokes equation with a random force chosen on the basis of the automation noise
Complex bifurcations in B\\'enard-Marangoni convection
Vakulenko, Sergey; Lucarini, Valerio
2015-01-01
We study the dynamics of a system as determined 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 some nonlinear vertical temperature profile as compared to bifurcations in classical Rayleigh-B\\'enard and B\\'enard-Marangoni systems with simple linear vertical temperature profile. In terms of the B\\'enard-Marangoni convection, 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.
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...
Dynamics of Bloch oscillating transistor near bifurcation threshold
Sarkar, Jayanta; Puska, Antti; Hassel, Juha; Hakonen, Pertti J.
2013-01-01
Tendency to bifurcate can often be utilized to improve performance characteristics of amplifiers or even to build detectors. Bloch oscillating transistor is such a device. Here we show that bistable behaviour can be approached by tuning the base current and that the critical value depends on the Josephson coupling energy $E_J$ of the device. We demonstrate record-large current gains for device operation near the bifurcation point at small $E_J$. From our results for the current gains at vario...
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.
ΔI = 4 bifurcation: Origins and criteria
International Nuclear Information System (INIS)
The new γ-ray detector arrays have demonstrated that rotational sequences in certain superdeformed bands with angular momentum differing by two can split into two branches. This is commonly called ΔI = 4 bifurcation, and has attracted considerable interest in the nuclear structure community. An alternative approach for the ΔI = 4 bifurcation phenomenon has been presented without introducing either a Y44 deformation or an I4 term in the Hamiltonian explicitly. The optimal criteria for observing the phenomenon have been discussed as well
Global Bifurcation of a Novel Computer Virus Propagation Model
2014-01-01
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 bif...
Inflation, bifurcations of nonlinear curvature Lagrangians and dark energy
Mielke, Eckehard W; Schunck, Franz E
2008-01-01
A possible equivalence of scalar dark matter, the inflaton, and modified gravity is analyzed. After a conformal mapping, the dependence of the effective Lagrangian on the curvature is not only singular but also bifurcates into several almost Einsteinian spaces, distinguished only by a different effective gravitational strength and cosmological constant. A swallow tail catastrophe in the bifurcation set indicates the possibility for the coexistence of different Einsteinian domains in our Universe. This `triple unification' may shed new light on the nature and large scale distribution not only of dark matter but also on `dark energy', regarded as an effective cosmological constant, and inflation.
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.
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.
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.
Morse bifurcations of transition states in bimolecular reactions
MacKay, R. S.; Strub, D. C.
2015-12-01
The transition states and dividing surfaces used to find rate constants for bimolecular reactions are shown to undergo Morse bifurcations, in which they change diffeomorphism class, and to exist for a large range of energies, not just immediately above the critical energy for first connection between reactants and products. Specifically, we consider capture between two molecules and the associated transition states for the case of non-zero angular momentum and general attitudes. The capture between an atom and a diatom, and then a general molecule are presented, providing concrete examples of Morse bifurcations of transition states and dividing surfaces.
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)
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 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.
Stability and Hopf Bifurcation Analysis of a Vector-Borne Disease with Time Delay
Yuanyuan Chen; Ya-Qing Bi
2014-01-01
A delay-differential modelling of vector-borne is investigated. Its dynamics are studied in terms of local analysis and Hopf bifurcation theory, and its linear stability and Hopf bifurcation are demonstrated by studying the characteristic equation. The stability and direction of Hopf bifurcation are determined by applying the normal form theory and the center manifold argument.
Local and global bifurcation and its applications in a predator-prey system with several parameters
International Nuclear Information System (INIS)
A predator-prey system, depending on several parameters, is investigated for bifurcation of equilibria, Hopf bifurcation, global bifurcation occurring saddle connection, and global existence and non-existence of limit cycles, and changes of the topological structure of trajectory as parameters are varied. (author). 8 refs, 4 figs
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 and chaos in electromechanical drive systems with small motors
Czech Academy of Sciences Publication Activity Database
Kratochvíl, Ctirad; Houfek, Lubomír; Houfek, Martin; Krejsa, Jiří
Gliwice: Wydawnictwo Katedry Mechaniki Stosowanej, 2008, s. 55-58. ISBN 978-83-60102-50-3. [12th International Seminar of Applied Mechanics. Wisla (PL), 13.06.2008-15.06.2008] Institutional research plan: CEZ:AV0Z20760514 Keywords : drive system * bifurcation * chaos Subject RIV: JR - Other Machinery
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.
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...
Direction and stability of bifurcating solutions for a Signorini problem
Czech Academy of Sciences Publication Activity Database
Eisner, J.; Kučera, Milan; Recke, L.
2015-01-01
Roč. 113, January (2015), s. 357-371. ISSN 0362-546X Institutional support : RVO:67985840 Keywords : Signorini problem * variational inequality * bifurcation direction Subject RIV: BA - General Mathematics Impact factor: 1.327, year: 2014 http://www.sciencedirect.com/science/article/pii/S0362546X14003228
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...
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.
Experimental bifurcation analysis of an impact oscillator – Determining stability
DEFF Research Database (Denmark)
Bureau, Emil; Schilder, Frank; Elmegård, Michael; Santos, Ilmar; Thomsen, Jon Juel; Starke, Jens
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. As...
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.
Experimental Bifurcation Analysis By Control-based Continuation - Determining Stability’
DEFF Research Database (Denmark)
Bureau, Emil; Santos, Ilmar; Thomsen, Jon Juel; Schilder, Frank; Starke, Jens
2012-01-01
vibration characteristics of dynamical systems change under variation of parameters. The method employs a control scheme to modify the response stability. While this facilitates exploration of the unstable branches of a bifurcation diagram, it unfortunately makes it impossible to distinguish previously...... test ideas on how to determine the stability of equilibria states during continuation....
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.
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.
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 of...... of transient phenomena and to determine the basins of attraction for the various coexisting structures....
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.
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.
Numerical bifurcation analysis of conformal formulations of the Einstein constraints
International Nuclear Information System (INIS)
The Einstein constraint equations have been the subject of study for more than 50 years. The introduction of the conformal method in the 1970s as a parametrization of initial data for the Einstein equations led to increased interest in the development of a complete solution theory for the constraints, with the theory for constant mean curvature (CMC) spatial slices and closed manifolds completely developed by 1995. The first general non-CMC existence result was establish by Holst et al. in 2008, with extensions to rough data by Holst et al. in 2009, and to vacuum spacetimes by Maxwell in 2009. The non-CMC theory remains mostly open; moreover, recent work of Maxwell on specific symmetry models sheds light on fundamental nonuniqueness problems with the conformal method as a parametrization in non-CMC settings. In parallel with these mathematical developments, computational physicists have uncovered surprising behavior in numerical solutions to the extended conformal thin sandwich formulation of the Einstein constraints. In particular, numerical evidence suggests the existence of multiple solutions with a quadratic fold, and a recent analysis of a simplified model supports this conclusion. In this article, we examine this apparent bifurcation phenomena in a methodical way, using modern techniques in bifurcation theory and in numerical homotopy methods. We first review the evidence for the presence of bifurcation in the Hamiltonian constraint in the time-symmetric case. We give a brief introduction to the mathematical framework for analyzing bifurcation phenomena, and then develop the main ideas behind the construction of numerical homotopy, or path-following, methods in the analysis of bifurcation phenomena. We then apply the continuation software package AUTO to this problem, and verify the presence of the fold with homotopy-based numerical methods. We discuss these results and their physical significance, which lead to some interesting remaining questions to
International Nuclear Information System (INIS)
Linear stability of solitary waves near transcritical bifurcations is analyzed for the generalized nonlinear Schrödinger equations with arbitrary forms of nonlinearity and external potentials in arbitrary spatial dimensions. Bifurcation of linear-stability eigenvalues associated with this transcritical bifurcation is analytically calculated. Based on this eigenvalue bifurcation, it is shown that both solution branches undergo stability switching at the transcritical bifurcation point. In addition, the two solution branches have opposite linear stability. These analytical results are compared with the numerical results, and good agreement is obtained.
Evaluation of the cervical carotid bifurcation using MR angiography and cine MRI
Energy Technology Data Exchange (ETDEWEB)
Yamane, Kanji; Shima, Takeshi; Okada, Yoshikazu; Nishida, Masahiro; Okita, Shinji; Hatayama, Takashi; Kagawa, Reiko [Chugoku Rousai Hospital, Kure, Hiroshima (Japan); Yokoyama, Noboru
1995-08-01
MR angiography (MRA) can less invasively evaluate the carotid bifurcation without contrast material. Previous reports on MRA of carotid bifurcation revealed problems of overestimation and false-positive interpretation of stenosis. To clarify reasons causing overestimation and false-positive interpretation we investigated flow dynamics in the carotid bifurcation by cine MRI. Twenty-eight patients who were suspected to have stenosis of the internal carotid artery by MRA were studied. Images of the carotid bifurcation were obtained with 3-D phase contrast method by 0.5-T MR scanner. All patients were examined by IV-DSA or direct carotid angiography. Cine MRI of the carotid bifurcation was obtained with gradinet-echo sequence by 1.5-T MR scanner. Comparison of MRA and conventional angiography in evaluating degree of stenosis in the carotid bifurcation demonstrated that there were 57.1% agreement, 32.1% false-positive estimation and 10.7% overestimation. Cine MRI demonstration turbulent flow in the normal carotid bifurcation and also in the sclerotic bifurcation. Turbulence in the carotid bifurcation with severe sclerosis was greater than that in the normal carotid bifurcation. Turbulent flow could be seen extending distally to the stenotic site of the internal carotid artery. Turbulent flow in the carotid bifurcation, causing a decrease or loss in signal intensity of MRA according to the severity of the turbulence, must be a major contributing factor in false-positive estimation and overestimation of stenosis. (author).
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.
Hopf bifurcations in a predator-prey system with multiple delays
International Nuclear Information System (INIS)
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.
Stability and Bifurcation Analysis of a Three-Species Food Chain Model with Delay
Pal, Nikhil; Samanta, Sudip; Biswas, Santanu; Alquran, Marwan; Al-Khaled, Kamel; Chattopadhyay, Joydev
In the present paper, we study the effect of gestation delay on a tri-trophic food chain model with Holling type-II functional response. The essential mathematical features of the proposed model are analyzed with the help of equilibrium analysis, stability analysis, and bifurcation theory. Considering time-delay as the bifurcation parameter, the Hopf-bifurcation analysis is carried out around the coexisting equilibrium. The direction of Hopf-bifurcation and the stability of the bifurcating periodic solutions are determined by applying the normal form theory and center manifold theorem. We observe that if the magnitude of the delay is increased, the system loses stability and shows limit cycle oscillations through Hopf-bifurcation. The system also shows the chaotic dynamics via period-doubling bifurcation for further enhancement of time-delay. Our analytical findings are illustrated through numerical simulations.
Effect of magnetized electron cooling on a Hopf bifurcation
International Nuclear Information System (INIS)
We have observed longitudinal limit cycle oscillations of a proton beam when a critical threshold in the relative velocity between the proton beam and the cooling electrons has been exceeded. The threshold for the bifurcation of a fixed point into a limit cycle, also known as a Hopf bifurcation, was found to be asymmetric with respect to the relative velocity. Further experiments were performed to verify that the asymmetry was related to electron beam alignment with respect to the stored proton beam. The measured amplitudes of the ensuing limit cycle were used to determine the cooling drag force, which exhibits the essential characteristics of the magnetized cooling, where the limit cycle attractor can coexist with a damping-free region and/or a fixed point attractor. copyright 1996 The American Physical Society
Synchronization of diffusively coupled oscillators near the homoclinic bifurcation
International Nuclear Information System (INIS)
It has been known that a diffusive coupling between two limit cycle oscillations typically leads to the inphase synchronization and also that it is the only stable state in the weak coupling limit. Recently, however, it has been shown that the coupling of the same nature can result in the distinctive dephased synchronization when the limit cycles are close to the homoclinic bifurcation, which often occurs especially for the neuronal oscillators. In this paper we propose a simple physical model using the modified van der Pol equation, which unfolds the generic synchronization behaviors of the latter kind and in which one may readily observe changes in the synchronization behaviors between the distinctive regimes as well. The dephasing mechanism is analyzed both qualitatively and quantitatively in the weak coupling limit. A general form of coupling is introduced and the synchronization behaviors over a wide range of the coupling parameters are explored to construct the phase diagram using the bifurcation analysis. (author)
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.
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
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.
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.
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.
Stability and bifurcation analysis of rotor-bearing-seal system
Ying, G. Y.; Liu, S. L.; Ma, R.; Zheng, S. Y.
2016-05-01
Labyrinth seals were extensively used in turbine units, and the seal fluid forces may induce self-excited vibrations of rotor under certain conditions. It has become the main factor to instability of rotor system. In this paper Muszynska seal fluid force model is used to investigate the stability of the rotor system. Nonlinear equations are numerically solved by Newmark integration method. The effect of different seal clearances and differential pressures on system stability is studied. The calculation results show that the dominant vibration component leading to instability changes with different seal clearance. With the differential pressure increased, the unstable speed is reduced. Then the bifurcation behavior of the system with and without seal force is calculated. Results show that the rotor vibration becomes severe and complicated, and the bifurcation behavior of the system has been changed when seal force is considered.
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...
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 ...
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.
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.
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...
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.
Morse bifurcations of transition states in bimolecular reactions
MacKay, Robert S
2015-01-01
The transition states and dividing surfaces used to find rate constants for bimolecular reactions are shown to undergo qualitative changes, known as Morse bifurcations, and to exist for a large range of energies, not just immediately above the critical energy for first connection between reactants and products. Specifically, we consider capture between two molecules and the associated transition states for the case of non-zero angular momentum and general attitudes. The capture between an atom and a diatom, and then a general molecule are presented, providing concrete examples of Morse bifurcations of transition states and dividing surfaces. The reduction of the $n$-body systems representing the reactions is discussed and reviewed with comments on the difficulties associated with choosing appropriate charts and the global geometry of the reduced spaces.
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...
An Approach to Robust Control of the Hopf Bifurcation
Giacomo Innocenti; Roberto Genesio; Alberto Tesi
2011-01-01
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 ...
Smooth Bifurcation for Variational Inequalities and Reaction-Diffusion Systems
Czech Academy of Sciences Publication Activity Database
Kučera, Milan; Recke, L.; Eisner, Jan
New Jersey : World Scientific, 2003 - (Begehr, H.; Gilbert, R.; Wong, M.), s. 1125-1133 ISBN 981-238-967-9. [International ISAAC Congress/3./. Berlin (DE), 20.08.2001-25.08.2001] R&D Projects: GA ČR GA201/00/0376 Institutional research plan: CEZ:AV0Z1019905; CEZ:AV0Z1019905 Keywords : bifurcation for variational * reaction-diffusion system Subject RIV: BA - General Mathematics
Bifurcations and Transitions to Chaos in An Inverted Pendulum
Kim, Sang-Yoon; Hu, Bambi
1998-01-01
We consider a parametrically forced pendulum with a vertically oscillating suspension point. It is well known that, as the amplitude of the vertical oscillation is increased, its inverted state (corresponding to the vertically-up configuration) undergoes a cascade of ``resurrections,'' i.e., it becomes stabilized after its instability, destabilize again, and so forth ad infinitum. We make a detailed numerical investigation of the bifurcations associated with such resurrections of the inverted...
A reversible bifurcation analysis of the inverted pendulum
Broer, H. W.; Hoveijn, I.; Van Noort, M.
1998-01-01
The inverted pendulum with a periodic parametric forcing is considered as a bifurcation problem in the reversible setting. Parameters are given by the size of the forcing and the frequency ratio. Normal form theory provides an integrable approximation of the Poincare map generated by a planar vector field. Genericity of the model is studied by a perturbation analysis, where the spatial symmetry is optional. Here equivariant singularity theory is used.
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...
Bifurcation Analysis for Phage Lambda with Binding Energy Uncertainty
Ning Xu; Xue Lei; Ping Ao; Jun Zhang
2014-01-01
In a phage λ genetic switch model, bistable dynamical behavior can be destroyed due to the bifurcation caused by inappropriately chosen model parameters. Since the values of many parameters with biological significance often cannot be accurately acquired, it is thus of fundamental importance to analyze how and to which extent the system dynamics is influenced by model parameters, especially those parameters pertaining to binding energies. In this paper, we apply a Jacobian method to investiga...
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.
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.
On projectively equivalent metrics near points of bifurcation
Matveev, Vladimir S.
2008-01-01
Let Riemannian metrics $g$ and $\\bar g$ on a connected manifold $M^n$ have the same geodesics (considered as unparameterized curves). Suppose the eigenvalues of one metric with respect to the other are all different at a point. Then, by the famous Levi-Civita's Theorem, the metrics have a certain standard form near the point. Our main result is a generalization of Levi-Civita's Theorem for the points where the eigenvalues of one metric with respect to the other bifurcate.
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.
Global Hopf bifurcation in the ZIP regulatory system.
Claus, Juliane; Ptashnyk, Mariya; Bohmann, Ansgar; Chavarría-Krauser, Andrés
2015-10-01
Regulation of zinc uptake in roots of Arabidopsis thaliana has recently been modeled by a system of ordinary differential equations based on the uptake of zinc, expression of a transporter protein and the interaction between an activator and inhibitor. For certain parameter choices the steady state of this model becomes unstable upon variation in the external zinc concentration. Numerical results show periodic orbits emerging between two critical values of the external zinc concentration. Here we show the existence of a global Hopf bifurcation with a continuous family of stable periodic orbits between two Hopf bifurcation points. The stability of the orbits in a neighborhood of the bifurcation points is analyzed by deriving the normal form, while the stability of the orbits in the global continuation is shown by calculation of the Floquet multipliers. From a biological point of view, stable periodic orbits lead to potentially toxic zinc peaks in plant cells. Buffering is believed to be an efficient way to deal with strong transient variations in zinc supply. We extend the model by a buffer reaction and analyze the stability of the steady state in dependence of the properties of this reaction. We find that a large enough equilibrium constant of the buffering reaction stabilizes the steady state and prevents the development of oscillations. Hence, our results suggest that buffering has a key role in the dynamics of zinc homeostasis in plant cells. PMID:25312412
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 betwe...... period-doubling cascades. Similar phenomena arise in response to increasing blood pressure. The numerical analyses are supported by existing experimental results on anesthetized rats. ©1996 American Institute of Physics.......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...
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
Spiral blood flow in aorta-renal bifurcation models.
Javadzadegan, Ashkan; Simmons, Anne; Barber, Tracie
2016-07-01
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
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.
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.
DEFF Research Database (Denmark)
Behan, Miles W; Holm, Niels Ramsing; Curzen, Nicholas P;
2011-01-01
crush, 118 culotte, and 59 T-stenting techniques. A composite end point at 9 months of all-cause death, myocardial infarction, and target vessel revascularization occurred in 10.1% of the simple versus 17.3% of the complex group (hazard ratio 1.84 [95% confidence interval 1.28 to 2.66], P=0.......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......=217, simple 9.6% versus complex 15.7%; hazard ratio 1.67 [ 95% confidence interval 0.78 to 3.62], P=0.186), large (=2.75 mm) diameter side branches (n=281, simple 10.4% versus complex 20.7%; hazard ratio 2.42 [ 95% confidence interval 1.22 to 4.80], P=0.011), longer length (>5 mm) ostial side branch...
International Nuclear Information System (INIS)
The system code RAMONA, as well as a recently developed BWR reduced order model (ROM), are employed for the stability analysis of a specific operational point of the Leibstadt nuclear power plant. This has been done in order to assess the ROM's applicability and limitations in a quantitative manner. In the context of a detailed local bifurcation analysis carried out using RAMONA in the neighbourhood of the chosen Leibstadt operational point, a bridge is built between the ROM and the system code. This has been achieved through interpreting RAMONA solutions on the basis of the physical mechanisms identified in the course of applying the ROM. This leads, for the first time, to the identification of a subcritical Poincare-Andronov-Hopf (PAH) bifurcation using a system code. As a consequence, the possibility of the so-called correspondence hypothesis is suggested to underline the relationship between a stable (unstable) limit cycle solution and the occurrence of a supercritical (subcritical) PAH bifurcation in the modeling of boiling water reactor stability behaviour
Directory of Open Access Journals (Sweden)
Emin Gurleyik
2014-01-01
Full Text Available Background: Anatomical variations of the recurrent laryngeal nerve (RLN such as extralaryngeal terminal bifurcation is an important risk for its motor function. Aims: The objective is to study surgical anatomy of bilateral bifurcation of the RLNs in order to decrease risk of vocal cord palsy in patients with bifurcated nerves. Materials and Methods: Surgical anatomy including terminal bifurcation was established in 292 RLNs of 146 patients. We included patients with bilateral bifurcation of RLN in this study. Based on two anatomical landmarks (nerve-artery crossing and laryngeal entry, the cervical course of RLN was classified in four segments: Pre-arterial, arterial, post-arterial and pre-laryngeal. According to these segments, bifurcation point locations along the cervical course of RLNs were compared between both sides in bilateral cases. Results: RLNs were exposed throughout their entire courses. Seventy (48% patients had bifurcated RLNs. We identified terminal bifurcation in 90 (31% of 292 RLNs along the cervical course. Bilateral bifurcation was observed in 20 (28.6% patients with bifurcated RLNs. Bifurcation points were located on arterial and post-arterial segments in 37.5% and 32.5% of cases, respectively. Pre-arterial and pre-laryngeal segments contained bifurcations in 15% of cases. Comparison of both sides indicated that bifurcation points were similar in 5 (25% and different in 15 (75% patients with bilateral bifurcation. Permanent nerve injury did not occur in this series. Conclusion: Bilateral bifurcation of both RLNs was observed in approximately 30% of patients with extralaryngeal bifurcation which is a common anatomical variation. Bifurcation occurred in different segments along cervical course of RLN. Bifurcation point locations differed between both sides in the majority of bilateral cases. Increasing surgeons′ awareness of this variation may lead to safely exposing bifurcated nerves and prevent the injury to extralaryngeal
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.
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.
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.
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 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.
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 Hopf Bifurcation for a Delayed SLBRS Computer Virus Model
Zizhen Zhang; Huizhong Yang
2014-01-01
By incorporating the time delay due to the period that computers use antivirus software to clean the virus into the SLBRS model a delayed SLBRS computer virus model is proposed in this paper. The dynamical behaviors which include local stability and Hopf bifurcation are investigated by regarding the delay as bifurcating parameter. Specially, direction and stability of the Hopf bifurcation are derived by applying the normal form method and center manifold theory. Finally, an illustrative examp...
Stability and Hopf Bifurcation of a Computer Virus Model with Infection Delay and Recovery Delay
Directory of Open Access Journals (Sweden)
Haitao Song
2014-01-01
Full Text Available A computer virus model with infection delay and recovery delay is considered. The sufficient conditions for the global stability of the virus infection equilibrium are established. We show that the time delay can destabilize the virus infection equilibrium and give rise to Hopf bifurcations and stable periodic orbits. By the normal form and center manifold theory, the direction of the Hopf bifurcation and stability of the bifurcating periodic orbits are determined. Numerical simulations are provided to support our theoretical conclusions.
Stability and Hopf Bifurcation in a Computer Virus Model with Multistate Antivirus
Huaqing Li; Xiaofeng Liao; Tao Dong
2012-01-01
By considering that people may immunize their computers with countermeasures in susceptible state, exposed state and using anti-virus software may take a period of time, a computer virus model with time delay based on an SEIR model is proposed. We regard time delay as bifurcating parameter to study the dynamical behaviors which include local asymptotical stability and local Hopf bifurcation. By analyzing the associated characteristic equation, Hopf bifurcation occurs when time delay passes th...
Stability and Hopf Bifurcation of a Computer Virus Model with Infection Delay and Recovery Delay
Haitao Song; Qiaochu Wang; Weihua Jiang
2014-01-01
A computer virus model with infection delay and recovery delay is considered. The sufficient conditions for the global stability of the virus infection equilibrium are established. We show that the time delay can destabilize the virus infection equilibrium and give rise to Hopf bifurcations and stable periodic orbits. By the normal form and center manifold theory, the direction of the Hopf bifurcation and stability of the bifurcating periodic orbits are determined. Numerical simulations are p...
Schomerus, H
1997-01-01
We investigate classical and semiclassical aspects of codimension--two bifurcations of periodic orbits in Hamiltonian systems. A classification of these bifurcations in autonomous systems with two degrees of freedom or time-periodic systems with one degree of freedom is presented. We derive uniform approximations to be used in semiclassical trace formulas and determine also certain global bifurcations in conjunction with Stokes transitions that become important in the ensuing diffraction catastrophe integrals.
BOUKTIR, Yasser; Chalal, Hocine; HADDAD, Moussa; ABED-MERAIM, Farid
2015-01-01
The ductility limits of an St14 steel are investigated using an elastic‒plastic‒damage model and bifurcation theory. An associative J2-flow theory of plasticity is coupled with damage within the framework of continuum damage mechanics. For strain localization prediction, the bifurcation analysis is adopted. Both the constitutive equations and the localization bifurcation criterion are implemented into the finite element code ABAQUS, within the framework of large strains and a fully three-dime...
International Nuclear Information System (INIS)
Highlights: • A ratio-dependent predator–prey system involving two discrete maturation time delays is studied. • Hopf bifurcations are analyzed by choosing delay parameters as bifurcation parameters. • When a delay parameter passes through a critical value, Hopf bifurcations occur. • The direction of bifurcation, the period and the stability of periodic solution are also obtained. - Abstract: In this paper we give a detailed Hopf bifurcation analysis of a ratio-dependent predator–prey system involving two different discrete delays. By analyzing the characteristic equation associated with the model, its linear stability is investigated. Choosing delay terms as bifurcation parameters the existence of Hopf bifurcations is demonstrated. Stability of the bifurcating periodic solutions is determined by using the center manifold theorem and the normal form theory introduced by Hassard et al. Furthermore, some of the bifurcation properties including direction, stability and period are given. Finally, theoretical results are supported by some numerical simulations
Bifurcation 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.
Example of a quadratic system with two cycles appearing in a homoclinic loop bifurcation
Rousseau, Christiane
We give here a planar quadratic differential system depending on two parameters, λ, δ. There is a curve in the λ-δ space corresponding to a homoclinic loop bifurcation (HLB). The bifurcation is degenerate at one point of the curve and we get a narrow tongue in which we have two limit cycles. This is the first example of such a bifurcation in planar quadratic differential systems. We propose also a model for the bifurcation diagram of a system with two limit cycles appearing at a singular point from a degenerate Hopf bifurcation, and dying in a degenerate HLB. This model shows a deep duality between degenerate Hopf bifurcations and degenerate HLBs. We give a bound for the maximal number of cycles that can appear in certain simultaneous Hopf and homoclinic loop bifurcations. We also give an example of quadratic system depending on three parameters which has at one place a degenerate Hopf bifurcation of order 3, and at another place a Hopf bifurcation of order 2 together with a HLB. We characterize the planar quadratic systems which are integrable in the neighbourhood of a homoclinic loop.
Hopf bifurcation analysis of a tabu learning two-neuron model
International Nuclear Information System (INIS)
Tabu learning neural network applies the concept of tabu search to neural networks for solving optimization problems. In this paper, we study the nonlinear dynamical behaviors of a tabu learning two-neuron model with linear proximity function. By choosing the memory decay rate as the bifurcation parameter, we prove that Hopf bifurcation occurs in the model. The stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation are determined by applying the normal form theory. A numerical example is also presented to verify the theoretical analysis
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.
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. PMID:26493359
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 co...... 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.
A numerical study of crack initiation in a bcc iron system based on dynamic bifurcation theory
International Nuclear Information System (INIS)
Crack initiation under dynamic loading conditions is studied under the framework of dynamic bifurcation theory. An atomistic model for BCC iron is considered to explicitly take into account the detailed molecular interactions. To understand the strain-rate dependence of the crack initiation process, we first obtain the bifurcation diagram from a computational procedure using continuation methods. The stability transition associated with a crack initiation, as well as the connection to the bifurcation diagram, is studied by comparing direct numerical results to the dynamic bifurcation theory [R. Haberman, SIAM J. Appl. Math. 37, 69–106 (1979)].
A numerical study of crack initiation in a bcc iron system based on dynamic bifurcation theory
Li, Xiantao
2014-10-01
Crack initiation under dynamic loading conditions is studied under the framework of dynamic bifurcation theory. An atomistic model for BCC iron is considered to explicitly take into account the detailed molecular interactions. To understand the strain-rate dependence of the crack initiation process, we first obtain the bifurcation diagram from a computational procedure using continuation methods. The stability transition associated with a crack initiation, as well as the connection to the bifurcation diagram, is studied by comparing direct numerical results to the dynamic bifurcation theory [R. Haberman, SIAM J. Appl. Math. 37, 69-106 (1979)].
A numerical study of crack initiation in a bcc iron system based on dynamic bifurcation theory
Energy Technology Data Exchange (ETDEWEB)
Li, Xiantao, E-mail: xli@math.psu.edu [Pennsylvania State University, University Park, Pennsylvania 16802 (United States)
2014-10-28
Crack initiation under dynamic loading conditions is studied under the framework of dynamic bifurcation theory. An atomistic model for BCC iron is considered to explicitly take into account the detailed molecular interactions. To understand the strain-rate dependence of the crack initiation process, we first obtain the bifurcation diagram from a computational procedure using continuation methods. The stability transition associated with a crack initiation, as well as the connection to the bifurcation diagram, is studied by comparing direct numerical results to the dynamic bifurcation theory [R. Haberman, SIAM J. Appl. Math. 37, 69–106 (1979)].
Stability and bifurcation analysis in a magnetic bearing system with time delays
International Nuclear Information System (INIS)
A kind of magnetic bearing system with time delay is considered. Firstly, linear stability of the model is investigated by analyzing the distribution of the roots of the associated characteristic equation. According to the analysis results, the bifurcation diagram is drawn in the appropriate parameter plane. It is found that the Ho pf bifurcation occurs when the delay passes through a sequence of critical values. Then the explicit algorithm for determining the direction of the Ho pf bifurcations and the stability of the bifurcating periodic solutions are derived, using the theory of normal form and center manifold. Finally, some numerical simulations are carried out to illustrate the results found
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.
Stochastic bifurcation for a tumor-immune system with symmetric Lévy noise
Xu, Yong; Feng, Jing; Li, JuanJuan; Zhang, Huiqing
2013-10-01
In this paper, we investigate stochastic bifurcation for a tumor-immune system in the presence of a symmetric non-Gaussian Lévy noise. Stationary probability density functions will be numerically obtained to define stochastic bifurcation via the criteria of its qualitative change, and bifurcation diagram at parameter plane is presented to illustrate the bifurcation analysis versus noise intensity and stability index. The effects of both noise intensity and stability index on the average tumor population are also analyzed by simulation calculation. We find that stochastic dynamics induced by Gaussian and non-Gaussian Lévy noises are quite different.
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.
Directory of Open Access Journals (Sweden)
Yanhui Zhai
2014-01-01
Full Text Available The paper investigated an avian influenza virus propagation model with nonlinear incidence rate and delay based on SIR epidemic model. We regard delay as bifurcating parameter to study the dynamical behaviors. At first, local asymptotical stability and existence of Hopf bifurcation are studied; Hopf bifurcation occurs when time delay passes through a sequence of critical values. An explicit algorithm for determining the direction of the Hopf bifurcations and stability of the bifurcation periodic solutions is derived by applying the normal form theory and center manifold theorem. What is more, the global existence of periodic solutions is established by using a global Hopf bifurcation result.
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.
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.
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.
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.
Bifurcation and "self-organization" of a system
Aldabergenov, M.; Balakaeva, G.
2016-04-01
Triangulation of a multicomponent system was shown on example of the CaO-SiO2-H2O system. "The Gibbs function normalized to the total number of electrons" was applied in order to reflect all the possible transformations of components of the system at non-equilibrium as well as at equilibrium conditions. The bifurcation points of the system are located at the each intersection of the line connected compositions of the interacting components and the stable secant line. It was shown the possibility of the "self-organization" processes which is based on the exchange as well as that reactions.
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.
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.
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
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.
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....
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.
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 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 ...
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.
First-passage times, mobile traps, and Hopf bifurcations.
Tzou, Justin C; Xie, Shuangquan; Kolokolnikov, Theodore
2014-12-01
For a random walk on a confined one-dimensional domain, we consider mean first-passage times (MFPT) in the presence of a mobile trap. The question we address is whether a mobile trap can improve capture times over a stationary trap. We consider two scenarios: a randomly moving trap and an oscillating trap. In both cases, we find that a stationary trap actually performs better (in terms of reducing expected capture time) than a very slowly moving trap; however, a trap moving sufficiently fast performs better than a stationary trap. We explicitly compute the thresholds that separate the two regimes. In addition, we find a surprising relation between the oscillating trap problem and a moving-sink problem that describes reduced dynamics of a single spike in a certain regime of the Gray-Scott model. Namely, the above-mentioned threshold corresponds precisely to a Hopf bifurcation that induces oscillatory motion in the location of the spike. We use this correspondence to prove the uniqueness of the Hopf bifurcation. PMID:25615075
On the Crack Bifurcation and Fanning of Crack Growth Data
Forman, Royce G.; Zanganeh, Mohammad
2015-01-01
Crack growth data obtained from ASTM load shedding method for different R values show some fanning especially for aluminum alloys. It is believed by the authors and it has been shown before that the observed fanning is due to the crack bifurcation occurs in the near threshold region which is a function of intrinsic properties of the alloy. Therefore, validity of the ASTM load shedding test procedure and results is confirmed. However, this position has been argued by some experimentalists who believe the fanning is an artifact of the test procedure and thus the obtained results are invalid. It has been shown that using a special test procedure such as using compressively pre-cracked specimens will eliminate the fanning effect. Since not using the fanned data fit can result in a significantly lower calculated cyclic life, design of a component, particularly for rotorcraft and propeller systems will considerably be impacted and therefore this study is of paramount importance. In this effort both test procedures i.e. ASTM load shedding and the proposed compressive pre-cracking have been used to study the fatigue crack growth behavior of compact tension specimens made of aluminum alloy 2524-T3. Fatigue crack growth paths have been closely observed using SEM machines to investigate the effects of compression pre-cracking on the crack bifurcation behavior. The results of this study will shed a light on resolving the existing argument by better understanding of near threshold fatigue crack growth behavior.
Bifurcation analysis of a Lyapunov-based controlled boost converter
Spinetti-Rivera, Mario; Olm, Josep M.; Biel, Domingo; Fossas, Enric
2013-11-01
Lyapunov-based controlled boost converters have a unique equilibrium point, which is globally asymptotically stable, for known resistive loads. This article investigates the dynamic behaviors that appear in the system when the nominal load differs from the actual one and no action is taken by the controller to compensate for the mismatch. Exploiting the fact that the closed-loop system is, in fact, planar and quadratic, one may provide not only local but also global stability results: specifically, it is proved that the number of equilibria of the converter may grow up to three and that, in any case, the system trajectories are always bounded, i.e. it is a bounded quadratic system. The possible phase portraits of the closed-loop system are also characterized in terms of the selected bifurcation parameters, namely, the actual load value and the gain of the control law. Accordingly, the analysis allows the numerical illustration of many bifurcation phenomena that appear in bounded quadratic systems through a physical example borrowed from power electronics.
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.
Bifurcated canonical profiles for a current channel in a plasma
International Nuclear Information System (INIS)
By assuming an anomalous heat conduction of the form 1/T and a power law for the total dissipation, it is possible to show the existence of bifurcated universal profiles for current density and temperature. This is done without a priori imposing an abstract relaxation procedure through a variational approach having less transparent constrains attached to it. The exact solutions are in simple demonstration showing that Kadomtsev's arguments for ruling out the heat conduction dependence on the inverse temperature (κ ∝ T-1), do not hold, although his reasoning for a non-local dependence in the κ still holds. The H and L bifurcated branches also exist for pure ohmic heated tokamaks and they coincide with the canonical profiles for 1/T heat conduction. The branching occurs for q(edge)/q(axis) = 2 in the circular symmetric case with a power law for the total dissipation. The current profiles are labelled universal in the sense of being the same no matter what exponent one has in the power law approximation, and they resemble the observed profiles in most tokamaks. The general consideration in the first part may suggest that the results from the special model are qualitatively correct in a more general physical setting. (orig.)
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.
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 ...
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.
Toward Online Control of Local Bifurcation in Power Systems via Network Topology Optimization
Wang, Lei; Chiang, Hsiao-Dong
This paper presents online methods for controlling local bifurcations of power grids with the goal of increasing bifurcation values (i.e. increasing load margins) via network topology optimization, a low-cost control. In other words, this paper presents online methods for increasing power transfer capability subject to static stability limit via switching transmission line out/in (i.e. disconnecting a transmission line or connecting a transmission line). To illustrate the impact of network topology on local bifurcations, two common local bifurcations, i.e. saddle-node bifurcation and structure-induced bifurcation on small power grids with different network topologies are shown. A three-stage online control methodology of local bifurcations via network topology optimization is presented to delay local bifurcations of power grids. Online methods must meet the challenging requirements of online applications such as the speed requirement (in the order of minutes), accuracy requirement and robustness requirement. The effectiveness of the three-stage methodology for online applications is demonstrated on the IEEE 118-bus and a 1648-bus practical power systems.
Bifurcation approach to the predator-prey population models (Version of the computer book)
International Nuclear Information System (INIS)
Hierarchically organized family of predator-prey systems is studied. The classification is founded on two interacting principles: the biological and mathematical ones. The different combinations of biological factors included correspond to different bifurcations (up to codimension 3). As theoretical so computing methods are used for analysis, especially concerning non-local bifurcations. (author). 6 refs, figs
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.
Hopf bifurcation in an open monetary economic system: Taylor versus inflation targeting rules
International Nuclear Information System (INIS)
The main aim of the present work is to detect the Hopf bifurcation in policy relevant economic dynamical system. The study employs two deferent forms of monetary policy rules namely: Taylor rule and inflation targeting rule. The results show that there exists Hopf bifurcation between policy relevant variables in both types of rules in our open economic system
Song, Yongli; Zhang, Tonghua; Tadé, Moses O
2008-12-01
We investigate the dynamics of a damped harmonic oscillator with delayed feedback near zero eigenvalue singularity. We perform a linearized stability analysis and multiple bifurcations of the zero solution of the system near zero eigenvalue singularity. Taking the time delay as the bifurcation parameter, the presence of steady-state bifurcation, Bogdanov-Takens bifurcation, triple zero, and Hopf-zero singularities is demonstrated. In the case when the system has a simple zero eigenvalue, center manifold reduction and normal form theory are used to investigate the stability and the types of steady-state bifurcation. The stability of the zero solution of the system near the simple zero eigenvalue singularity is completely solved. PMID:19123623
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.
International Nuclear Information System (INIS)
The stability and the Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback are studied. By considering the energy in the air-gap field of the AC motor, the dynamical equation of the electromechanical coupling transmission system is deduced and a time delay feedback is introduced to control the dynamic behaviors of the system. The characteristic roots and the stable regions of time delay are determined by the direct method, and the relationship between the feedback gain and the length summation of stable regions is analyzed. Choosing the time delay as a bifurcation parameter, we find that the Hopf bifurcation occurs when the time delay passes through a critical value. A formula for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is given by using the normal form method and the center manifold theorem. Numerical simulations are also performed, which confirm the analytical results. (paper)
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, ...
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.
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.
International Nuclear Information System (INIS)
Objective: To investigate flow patterns at carotid bifurcation in vivo by combining computational fluid dynamics (CFD)and MR angiography imaging. Methods: Seven subjects underwent contrast-enhanced MR angiography of carotid artery in Siemens 3.0 T MR. Flow patterns of the carotid artery bifurcation were calculated and visualized by combining MR vascular imaging post-processing and CFD. Results: The flow patterns of the carotid bifurcations in 7 subjects were varied with different phases of a cardiac cycle. The turbulent flow and back flow occurred at bifurcation and proximal of internal carotid artery (ICA) and external carotid artery (ECA), their occurrence and conformation were varied with different phase of a cardiac cycle. The turbulent flow and back flow faded out quickly when the blood flow to the distal of ICA and ECA. Conclusion: CFD combined with MR angiography can be utilized to visualize the cyclical change of flow patterns of carotid bifurcation with different phases of a cardiac cycle. (authors)
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.
International Nuclear Information System (INIS)
This paper is concerned with a delayed cooperation diffusion system with Dirichlet boundary conditions. By applying the implicit function theorem, the normal form theory and the center manifold reduction, the asymptotic stability of positive equilibrium and Hopf bifurcation are investigated. It is shown that an increase in delay will destabilize the positive equilibrium and lead to the occurrence of a supercritical Hopf bifurcation when the delay crosses through a sequence of critical values. Based on the normal form theory and the center manifold reduction for partial functional differential equations (PFDEs), we find that the bifurcating periodic solution occurring from the first Hopf bifurcation point is stable on the center manifold and those occurring from the other bifurcation points are unstable. Finally, some numerical simulations are given to illustrate our results
Energy Technology Data Exchange (ETDEWEB)
Li Wantong [School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000 (China)], E-mail: wtli@lzu.edu.cn; Yan Xiangping; Zhang Cunhua [School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000 (China); Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070 (China)
2008-10-15
This paper is concerned with a delayed cooperation diffusion system with Dirichlet boundary conditions. By applying the implicit function theorem, the normal form theory and the center manifold reduction, the asymptotic stability of positive equilibrium and Hopf bifurcation are investigated. It is shown that an increase in delay will destabilize the positive equilibrium and lead to the occurrence of a supercritical Hopf bifurcation when the delay crosses through a sequence of critical values. Based on the normal form theory and the center manifold reduction for partial functional differential equations (PFDEs), we find that the bifurcating periodic solution occurring from the first Hopf bifurcation point is stable on the center manifold and those occurring from the other bifurcation points are unstable. Finally, some numerical simulations are given to illustrate our results.
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.
Bifurcation analysis of a semiconductor laser subject to phase conjugate feedback
International Nuclear Information System (INIS)
In this thesis we present a detailed bifurcation analysis of a semiconductor laser subject to phase-conjugate feedback (PCF). Mathematically, lasers with feedback are modelled by delay differential equations (DDEs) with an infinite-dimensional phase space. This is why, in the past, systems described by DDEs were only studied by numerical simulation. We employ new numerical bifurcation tools for DDEs that go much beyond mere simulation. More precisely, we continue steady states and periodic orbits, irrespective of their stability with the package DDE-BIFTOOL, and present here the first algorithm for computing unstable manifolds of saddle-periodic orbits with one unstable Floquet multiplier in systems of DDEs. Together, these tools make it possible, for the first time, to numerically study global bifurcations in DDEs. Specifically, we first show how periodic solutions of the PCF laser are all connected to one another via a locked steady state solution. A one-parameter study of these steady states reveals heteroclinic bifurcations, which turn out to be responsible for bistability and excitability at the locking boundaries. We then perform a full two-parameter investigation of the locking range, where we continue bifurcations of steady states and heteroclinic bifurcations. This leads to the identification of a number of codimension- two bifurcation points. Here, we also make a first attempt at providing a two-parameter study of bifurcations of periodic orbits in a system of DDEs. Finally, our new method for the computation of unstable manifolds of saddle periodic orbits is used to show how a torus breaks up with a sudden transition to chaos in a crisis bifurcation. In more general terms, we believe that the results presented in this thesis showcase the usefulness of continuation and manifold computations and will contribute to the theory of global bifurcations in DDEs. (author)
Hopf bifurcation for simple food chain model with delay
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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 in asymmetric plasma divided by a magnetic filter
International Nuclear Information System (INIS)
A magnetic filter (MF) reflecting electrons from both sides can separate a low-temperature and low-density subplasma from a high-temperature and high-density main plasma. The one-dimensional numerical simulation by the particle-in-cell code revealed that, depending on the asymmetry, the plasma divided by the MF behaves dynamically or statically [K. Ohi et al., Physics of Plasmas 8, 23 (2001)]. The transition between the two bifurcated states is discontinuous. In the dynamic state, the autonomous potential oscillation in the subplasma is synchronized with the passage of the shock wave structure generated by the modulated ion beam from the main plasma. The stationary phase of the dynamic state appears after the amplitude of the potential oscillation in the subplasma grows exponentially from the thermal noise. In the static state, the system is stable to the growth of the potential oscillation in the subplasma. (author)
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.
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.
Bifurcations, Chaos, Controlling and Synchronization of Certain Nonlinear Oscillators
Lakshmanan, M
1997-01-01
In this set of lectures, we review briefly some of the recent developments in the study of the chaotic dynamics of nonlinear oscillators, particularly of damped and driven type. By taking a representative set of examples such as the Duffing, Bonhoeffer-van der Pol and MLC circuit oscillators, we briefly explain the various bifurcations and chaos phenomena associated with these systems. We use numerical and analytical as well as analogue simulation methods to study these systems. Then we point out how controlling of chaotic motions can be effected by algorithmic procedures requiring minimal perturbations. Finally we briefly discuss how synchronization of identically evolving chaotic systems can be achieved and how they can be used in secure communications.
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.
Bifurcations of travelling waves in population taxis models
International Nuclear Information System (INIS)
A penetrating analysis of the wave dynamic modes of a conceptual population system described by the 'reaction - taxis - diffusion' and 'reaction - autotaxis - cross-diffusion' polynomial models is carried out for the case of increasing degrees of the reaction and taxis (autotaxis) functions. It is shown that a 'suitable' nonlinear taxis can affect the wave front sets and generate nonmonotone waves, such as trains and pulses which represent the exact solutions of the model system. Parametric critical points whose neighborhood displays the full spectrum of possible model wave regimes are identified and a wave mode systematization in the form of bifurcation diagrams is given. This enables standard criteria of approach to 'dangerous boundaries' to be developed. As possible applications, 'pulsing density patches' in forest insect populations as well as plankton communities and some other examples are discussed. (from the current literature)
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.
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.
Bifurcation and multiplicity results for a nonhomogeneous semilinear elliptic problem
Directory of Open Access Journals (Sweden)
Kuan-Ju Chen
2008-11-01
Full Text Available In this article we consider the problem $$displaylines{ -Delta u(x+u(x=lambda (a(xu^{p}+h(xquadhbox{in }mathbb{R}^N, cr uin H^{1}(mathbb{R}^N,quad u>0quadhbox{in }mathbb{R}^N, }$$ where $lambda$ is a positive parameter. We assume there exist $mu >2$ and $C>0$ such that $a(x-1geq -Ce^{-mu |x|}$ for all $xin mathbb{R}^N$. We prove that there exists a positive $lambda^*$ such that there are at least two positive solutions for $lambdain (0,lambda^*$ and a unique positive solution for $lambda =lambda^*$. Also we show that $(lambda ^{*},u(lambda^*$ is a bifurcation point in $C^{2,alpha}(mathbb{R}^Ncap H^{2}(mathbb{R}^N$.
Graphene induced bifurcation of energy levels at low input power
Li, Rujiang; Lin, Shisheng; Liu, Xu; Chen, Hongsheng
2015-01-01
We study analytically the energy states in the waveguide system of graphene coated dielectric nanowire based on the explicit form of nonlinear surface conductivity of graphene. The energy levels of different plasmonic modes can be tuned by the input power at the order of a few tenths of mW. The self-focusing behavior and self-defocusing behavior are exhibited in the lower and upper bifurcation branches, respectively, which are separated by a saturation of input power. Moreover, due to the nonlinearity of graphene, the dispersion relations for different input powers evolve to an energy band which is in sharp contrast with the discrete energy level in the limit of zero power input.
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.
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.
Rotational digital subtraction angiography of carotid artery bifurcation stenoses
International Nuclear Information System (INIS)
Purpose: A prospektive study was designed to evaluate, whether multiplanar imaging with rotational digital subtraction angiography (R-DSA) could improve assessment of carotid artery bifurcation stenosis. Patients and methods: 45 patients with suspected stenosis of the ICA were examined with DSA in standard projections (0 -(45 )-90 ) and additional R-DSA of each ICA from 0-90 in 10 steps. We compared imaging quality and degree of stenosis as well as exposure of the patients to radiation and contrast media. Results: 79/82 R-DSA (96%) were suitable for evaluation of stenosis, 58/82 (70%) matched the quality standard of single projection DSA. Specificity and sensitivity of the R-DSA to diagnose high grade ACI stenosis were 100% and 94%, respectively. 7/79 R-DSA revealed a higher and 3/79 a lower degree of stenosis than the corresponding DSA. Regarding the degree of stenosis there was no significant difference between the two modalities (p>0,05), but R-DSA detected 4 stenoses greater than 60% that were estimated to be lower than 60% by DSA. Radiation dose for R-DSA was equivalent to one DSA run (170 cGycm2). The average amount of contrast media (25 ml) was slightly higher than for 2-3 single-projection DSA (19,8 ml). Conclusions: R-DSA provides high quality imaging of the carotid bifurcation with multiplanar projections facilitating exact grading of vessel stenosis. The number of cases (n=2) is to small to judge the value of R-DSA as to (tandem-) stenosis of the distal ICA. Still, diagnostic value and low radiation exposure justify the use of R-DSA as additional series to standard protocols. (orig.)
Influence of Bifurcation Geometry on Fluvial Fish Migration Patterns
McElroy, B. J.; Braaten, P.; Jacobson, R. B.
2011-12-01
Large fish can migrate long distances upstream in rivers prior to spawning. Subject to energetic expenditure requirements, some fish, such as the endangered pallid sturgeon (Scaphirhynchus albus), optimize migration by traversing pathways that connect the inner banks of bends in series. This strategy has straightforward application in single-thread channels, but it is unclear if it holds in multi-thread systems. Given the nature of migration pathway optimization, we hypothesize that fish would select between alternative channels at bifurcations based on the connectivity of banks; a fish will continue along a contiguous path on an inner bank until it encounters a thalweg cross-over. This single rule is enough to completely define a unique migration pathway through an arbitrary reach. Our hypothesis is tested with data collected from telemetered pallid sturgeon intensively tracked in the Missouri and Yellowstone Rivers. Fish were implanted with transmitters before spring spawning migrations, tracked, and mapped onto channel geometries with aerial photographs. In the Yellowstone River where bifurcations occur naturally with a wide range of geometries and with a wide range of size ratios, the hypothesized pathways were selected 3:1 over alternatives. In contrast, pallid sturgeon in the Lower Missouri River selected against the hypothesized pathways 2:1 in favor of staying in the main channel instead of traversing the engineered side-channel chutes. Although the overall numbers of replicates are low, we suggest that the difference is real and reflects an aspect of diminished quality of engineered side-channel chutes in the Missouri River.
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.
Hopf-pitchfork bifurcation and periodic phenomena in nonlinear financial system with delay
International Nuclear Information System (INIS)
Highlights: ► We derive the unfolding of a financial system with Hopf-pitchfork bifurcation. ► We show the coexistence of a pair of stable small amplitudes periodic solutions. ► At the same time, also there is a pair of stable large amplitudes periodic solutions. ► Chaos can appear by period-doubling bifurcation far away from Hopf-pitchfork value. ► The study will be useful for interpreting economics phenomena in theory. - Abstract: In this paper, we identify the critical point for a Hopf-pitchfork bifurcation in a nonlinear financial system with delay, and derive the normal form up to third order with their unfolding in original system parameters near the bifurcation point by normal form method and center manifold theory. Furthermore, we analyze its local dynamical behaviors, and show the coexistence of a pair of stable periodic solutions. We also show that there coexist a pair of stable small-amplitude periodic solutions and a pair of stable large-amplitude periodic solutions for different initial values. Finally, we give the bifurcation diagram with numerical illustration, showing that the pair of stable small-amplitude periodic solutions can also exist in a large region of unfolding parameters, and the financial system with delay can exhibit chaos via period-doubling bifurcations as the unfolding parameter values are far away from the critical point of the Hopf-pitchfork bifurcation.
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)
Bifurcation diagram globally underpinning neuronal firing behaviors modified by SK conductance
International Nuclear Information System (INIS)
Neurons in the brain utilize various firing trains to encode the input signals they have received. Firing behavior of one single neuron is thoroughly explained by using a bifurcation diagram from polarized resting to firing, and then to depolarized resting. This explanation provides an important theoretical principle for understanding neuronal biophysical behaviors. This paper reports the novel experimental and modeling results of the modification of such a bifurcation diagram by adjusting small conductance potassium (SK) channel. In experiments, changes in excitability and depolarization block in nucleus accumbens shell and medium-spiny projection neurons are explored by increasing the intensity of injected current and blocking the SK channels by apamin. A shift of bifurcation points is observed. Then, a Hodgkin—Huxley type model including the main electrophysiological processes of such neurons is developed to reproduce the experimental results. The reduction of SK channel conductance also shifts the bifurcations, which is in consistence with experiment. A global bifurcation paradigm of this shift is obtained by adjusting two parameters, intensity of injected current and SK channel conductance. This work reveals the dynamics underpinning modulation of neuronal firing behaviors by biologically important ionic conductance. The results indicate that small ionic conductance other than that responsible for spike generation can modify bifurcation points and shift the bifurcation diagram and, thus, change neuronal excitability and adaptation. (interdisciplinary physics and related areas of science and technology)
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.
Bifurcations, stability, and dynamics of multiple matter-wave vortex states
International Nuclear Information System (INIS)
In the present work, we offer a unifying perspective between the dark soliton stripe and the vortex multipole (dipole, tripole, aligned quadrupole, quintopole, etc.) states that emerge in the context of quasi-two-dimensional Bose-Einstein condensates. In particular, we illustrate that the multivortex states with the vortices aligned along the (former) dark soliton stripe sequentially bifurcate from the latter state in a supercritical pitchfork manner. Each additional bifurcation adds an extra mode to the dark soliton instability and an extra vortex to the configuration; moreover, the bifurcating states inherit the stability properties of the soliton prior to the bifurcation. The critical points of this bifurcation are computed analytically via a few-mode truncation of the system, which clearly showcases the symmetry-breaking nature of the corresponding bifurcation. We complement this small(-er) amplitude, few mode bifurcation picture, with a larger amplitude, particle-based description of the ensuing vortices. The latter enables us to characterize the equilibrium position of the vortices, as well as their intrinsic dynamics and anomalous modes, thus providing a qualitative description of the nonequilibrium multivortex dynamics.
Bifurcations, stability, and dynamics of multiple matter-wave vortex states
Middelkamp, S.; Kevrekidis, P. G.; Frantzeskakis, D. J.; Carretero-González, R.; Schmelcher, P.
2010-07-01
In the present work, we offer a unifying perspective between the dark soliton stripe and the vortex multipole (dipole, tripole, aligned quadrupole, quintopole, etc.) states that emerge in the context of quasi-two-dimensional Bose-Einstein condensates. In particular, we illustrate that the multivortex states with the vortices aligned along the (former) dark soliton stripe sequentially bifurcate from the latter state in a supercritical pitchfork manner. Each additional bifurcation adds an extra mode to the dark soliton instability and an extra vortex to the configuration; moreover, the bifurcating states inherit the stability properties of the soliton prior to the bifurcation. The critical points of this bifurcation are computed analytically via a few-mode truncation of the system, which clearly showcases the symmetry-breaking nature of the corresponding bifurcation. We complement this small(-er) amplitude, few mode bifurcation picture, with a larger amplitude, particle-based description of the ensuing vortices. The latter enables us to characterize the equilibrium position of the vortices, as well as their intrinsic dynamics and anomalous modes, thus providing a qualitative description of the nonequilibrium multivortex dynamics.
Bifurcation Structures in a Family of 1D Discontinuous Linear-Hyperbolic Invertible Maps
Makrooni, Roya; Gardini, Laura; Sushko, Iryna
2015-12-01
We consider a family of one-dimensional discontinuous invertible maps from an application in engineering. It is defined by a linear function and by a hyperbolic function with real exponent. The presence of vertical and horizontal asymptotes of the hyperbolic branch leads to particular codimension-two border collision bifurcation (BCB) such that if the parameter point approaches the bifurcation value from one side then the related cycle undergoes a regular BCB, while if the same bifurcation value is approached from the other side then a nonregular BCB occurs, involving periodic points at infinity, related to the asymptotes of the map. We investigate the bifurcation structure in the parameter space. Depending on the exponent of the hyperbolic branch, different period incrementing structures can be observed, where the boundaries of a periodicity region are related either to subcritical, or supercritical, or degenerate flip bifurcations of the related cycle, as well as to a regular or nonregular BCB. In particular, if the exponent is positive and smaller than one, then the period incrementing structure with bistability regions is observed and the corresponding flip bifurcations are subcritical, while if the exponent is larger than one, then the related flip bifurcations are supercritical and, thus, also the regions associated with cycles of double period are involved into the incrementing structure.
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.
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.
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.
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.
Dynamics near manifolds of equilibria of codimension one and bifurcation without parameters
Directory of Open Access Journals (Sweden)
Stefan Liebscher
2011-05-01
Full Text Available We investigate the breakdown of normal hyperbolicity of a manifold of equilibria of a flow. In contrast to classical bifurcation theory we assume the absence of any flow-invariant foliation at the singularity transverse to the manifold of equilibria. We call this setting bifurcation without parameters. We provide a description of general systems with a manifold of equilibria of codimension one as a first step towards a classification of bifurcations without parameters. This is done by relating the problem to singularity theory of maps.
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.
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 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.
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.
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.
Bifurcation analysis of the logistic map via two periodic impulsive forces
International Nuclear Information System (INIS)
The complex dynamics of the logistic map via two periodic impulsive forces is investigated in this paper. The influences of the system parameter and the impulsive forces on the dynamics of the system are studied respectively. With the parameter varying, the system produces the phenomenon such as periodic solutions, chaotic solutions, and chaotic crisis. Furthermore, the system can evolve to chaos by a cascading of period-doubling bifurcations. The Poincaré map of the logistic map via two periodic impulsive forces is constructed and its bifurcation is analyzed. Finally, the Floquet theory is extended to explore the bifurcation mechanism for the periodic solutions of this non-smooth map. (general)
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.
The stability and Hopf bifurcation for a predator-prey system with time delay
International Nuclear Information System (INIS)
In this paper, we consider a predator-prey system with time delay where the predator dynamics is logistic with the carrying capacity proportional to prey population. We study the impact of the time delay on the stability of the model and by choosing the delay time τ as a bifurcation parameter, we show that Hopf bifurcation can occur as the delay time τ passes some critical values. Using normal form theory and central manifold argument, we also establish the direction and the stability of Hopf bifurcation. Finally, we perform numerical simulations to support our 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.
Analysis of the magnetohydrodynamic equations and study of the nonlinear solution bifurcations
International Nuclear Information System (INIS)
The nonlinear problems related to the plasma magnetohydrodynamic instabilities are studied. A bifurcation theory is applied and a general magnetohydrodynamic equation is proposed. Scalar functions, a steady magnetic field and a new equation for the velocity field are taken into account. A method allowing the obtention of suitable reduced equations for the instabilities study is described. Toroidal and cylindrical configuration plasmas are studied. In the cylindrical configuration case, analytical calculations are performed and two steady bifurcated solutions are found. In the toroidal configuration case, a suitable reduced equation system is obtained; a qualitative approach of a steady solution bifurcation on a toroidal Kink type geometry is carried out
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.
Bifurcations for a coupled Schrödinger system with multiple components
Bartsch, Thomas; Tian, Rushun; Wang, Zhi-Qiang
2015-10-01
In this paper, we study local bifurcations of an indefinite elliptic system with multiple components: -Δ{uj} + auj = μjuj^3 + β sum_{k ≠ j}uk^2uj, uj > 0 in Ω, uj = 0 on partial Ω,quad j = 1, . . . ,n. Here {Ω subset{R}^N} is a smooth and bounded domain, {n ≥ 3, a branch {{T}_ω}. Then we find a sequence of local bifurcations with respect to {{T}_ω}, and we find global bifurcation branches of partially synchronized solutions.
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.
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.
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.
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...
The influences of curvature and torsions on flows in a helical bifurcated stent-graft
Shim, Jeong Hyun; Eun Lee, Kyung; Yoo, Jung Yul
2008-11-01
A bifurcated stent-graft signifies an improvement in surgical technique for treatment of a lesion in the branched blood vessel. However, there still remains a high failure rate regarding bifurcated stent-graft due to the occurrence of thrombosis or re-stenosis. The objectives of this study are to understand the effect of torsion in helical bifurcated geometries, to explain how the mixing of flows there may be advantageous to the prevention of the occurrence of thrombosis, and to keep the patency of stent-graft in the aspect of hemodynamics. For clinical applications, flows in a helical bifurcated stent-graft are simulated three-dimensionally using an incompressible Navier-Stokes solver. In this study, the hemodynamics is investigated in terms of mechanical factors, i.e., velocity profiles, vortex patterns and wall shear stress distributions.
Hopf bifurcation in a environmental defensive expenditures model with time delay
International Nuclear Information System (INIS)
In this paper a three-dimensional environmental defensive expenditures model with delay is considered. The model is based on the interactions among visitors V, quality of ecosystem goods E, and capital K, intended as accommodation and entertainment facilities, in Protected Areas (PAs). The tourism user fees (TUFs) are used partly as a defensive expenditure and partly to increase the capital stock. The stability and existence of Hopf bifurcation are investigated. It is that stability switches and Hopf bifurcation occurs when the delay t passes through a sequence of critical values, τ0. It has been that the introduction of a delay is a destabilizing process, in the sense that increasing the delay could cause the bio-economics to fluctuate. Formulas about the stability of bifurcating periodic solution and the direction of Hopf bifurcation are exhibited by applying the normal form theory and the center manifold theorem. Numerical simulations are given to illustrate the results.
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.
Bifurcation and chaos analysis of a nonlinear electromechanical coupling relative rotation system
International Nuclear Information System (INIS)
Hopf bifurcation and chaos of a nonlinear electromechanical coupling relative rotation system are studied in this paper. Considering the energy in air-gap field of AC motor, the dynamical equation of nonlinear electromechanical coupling relative rotation system is deduced by using the dissipation Lagrange equation. Choosing the electromagnetic stiffness as a bifurcation parameter, the necessary and sufficient conditions of Hopf bifurcation are given, and the bifurcation characteristics are studied. The mechanism and conditions of system parameters for chaotic motions are investigated rigorously based on the Silnikov method, and the homoclinic orbit is found by using the undetermined coefficient method. Therefore, Smale horseshoe chaos occurs when electromagnetic stiffness changes. Numerical simulations are also given, which confirm the analytical results. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Judd, S L; Judd, Stephen L.; Silber, Mary
1998-01-01
This paper investigates the competition between both simple (e.g. stripes, hexagons) and ``superlattice'' (super squares, super hexagons) Turing patterns in two-component reaction-diffusion systems. ``Superlattice'' patterns are formed from eight or twelve Fourier modes, and feature structure at two different length scales. Using perturbation theory, we derive simple analytical expressions for the bifurcation equation coefficients on both rhombic and hexagonal lattices. These expressions show that, no matter how complicated the reaction kinectics, the nonlinear reaction terms reduce to just four effective terms within the bifurcation equation coefficients. Moreover, at the hexagonal degeneracy -- when the quadratic term in the hexagonal bifurcation equation disappears -- the number of effective system parameters drops to two, allowing a complete characterization of the possible bifurcation results at this degeneracy. The general results are then applied to specific model equations, to investigate the stabilit...
Stochastic period-doubling bifurcation in biharmonic driven Duffing system with random parameter
International Nuclear Information System (INIS)
Stochastic period-doubling bifurcation is explored in a forced Duffing system with a bounded random parameter as an additional weak harmonic perturbation added to the system. Firstly, the biharmonic driven Duffing system with a random parameter is reduced to its equivalent deterministic one, and then the responses of the stochastic system can be obtained by available effective numerical methods. Finally, numerical simulations show that the phase of the additional weak harmonic perturbation has great influence on the stochastic period-doubling bifurcation in the biharmonic driven Duffing system. It is emphasized that, different from the deterministic biharmonic driven Duffing system, the intensity of random parameter in the Duffing system can also be taken as a bifurcation parameter, which can lead to the stochastic period-doubling bifurcations
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 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...
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.
Hopf bifurcation and chaos from torus breakdown in voltage-mode controlled DC drive systems
International Nuclear Information System (INIS)
Period-doubling bifurcation and its route to chaos have been thoroughly investigated in voltage-mode and current-mode controlled DC motor drives under simple proportional control. In this paper, the phenomena of Hopf bifurcation and chaos from torus breakdown in a voltage-mode controlled DC drive system is reported. It has been shown that Hopf bifurcation may occur when the DC drive system adopts a more practical proportional-integral control. The phenomena of period-adding and phase-locking are also observed after the Hopf bifurcation. Furthermore, it is shown that the stable torus can breakdown and chaos emerges afterwards. The work presented in this paper provides more complete information about the dynamical behaviors of DC drive systems.
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.
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...
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.
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.
Formation mechanism of bifurcation in mode-locked class-B laser
International Nuclear Information System (INIS)
The random oscillations of many longitudinal modes are inevitable in both class −A and −B lasers due to their broadened atomic bandwidths. The destructive superposition of electric field components that are incoherently oscillating at the different longitudinal modes can be converted into a constructive one by using the mode-locking technique. Here, the Maxwell—Bloch equations of motion are solved for a three-mode class-B laser under the mode-locking conditions. The results indicate that the cavity oscillating modes are shifted by changing the laser pumping rate. On the other hand, the frequency components of cavity electric field simultaneously form the various bifurcations. These bifurcations satisfy the well-known mode-locking conditions as well. The atomic population inversion forms only one bifurcation, which is responsible for shaping the cavity electric field bifurcations. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Analysis and control of the bifurcation of Hodgkin-Huxley model
Energy Technology Data Exchange (ETDEWEB)
Wang Jiang [School of Electrical and Automation Engineering, Tianjin University, 300072 Tianjin (China)]. E-mail: jiangwang@tju.edu.cn; Chen Liangquan [School of Electrical and Automation Engineering, Tianjin University, 300072 Tianjin (China); Fei Xianyang [School of Electrical and Automation Engineering, Tianjin University, 300072 Tianjin (China)
2007-01-15
The Hodgkin-Huxley (HH) equations are parameterized by a number of parameters and show a variety of qualitatively different behaviors depending on the various parameters. This paper finds the bifurcation would occur when the leakage conductance g {sub l} is lower than a special value. The Hopf bifurcation of HH model is controlled by applying a simple and unified state-feedback method and the bifurcation point is moved to an unreachable physiological point at the same time, so in this way an absolute bifurcation control is achieved. The simulation results demonstrate the validity of such theoretic analysis and control method. This new method could be a great help to the design of new closed-loop electrical stimulation systems for patients suffering from different nerve system dysfunctions.
Stability switches and Hopf bifurcations in a pair of identical tri-neuron network loops
International Nuclear Information System (INIS)
The dynamical behavior of a delayed neural network coupled by a pair of identical tri-neuron loops is considered. Conditional/absolute stability, stability switches and Hopf bifurcations induced by time delay are investigated.
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 in a simplified four-neuron BAM neural network with multiple delays
Directory of Open Access Journals (Sweden)
Wan-Tong Li
2006-02-01
Full Text Available We first study the distribution of the zeros of a fourth-degree exponential polynomial. Then we apply the obtained results to a simplified bidirectional associated memory (BAM neural network with four neurons and multiple time delays. By taking the sum of the delays as the bifurcation parameter, it is shown that under certain assumptions the steady state is absolutely stable. Under another set of conditions, there are some critical values of the delay, when the delay crosses these critical values, the Hopf bifurcation occurs. Furthermore, some explicit formulae determining the stability and the direction of periodic solutions bifurcating from Hopf bifurcations are obtained by applying the normal form theory and center manifold reduction. Numerical simulations supporting the theoretical analysis are also included.
Local stability and Hopf bifurcation in small-world delayed networks
International Nuclear Information System (INIS)
The notion of small-world networks, recently introduced by Watts and Strogatz, has attracted increasing interest in studying the interesting properties of complex networks. Notice that, a signal or influence travelling on a small-world network often is associated with time-delay features, which are very common in biological and physical networks. Also, the interactions within nodes in a small-world network are often nonlinear. In this paper, we consider a small-world networks model with nonlinear interactions and time delays, which was recently considered by Yang. By choosing the nonlinear interaction strength as a bifurcation parameter, we prove that Hopf bifurcation occurs. We determine the stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation by applying the normal form theory and the center manifold theorem. Finally, we show a numerical example to verify the theoretical analysis
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
Sufficient conditions for a period incrementing big bang bifurcation in one-dimensional maps
International Nuclear Information System (INIS)
Typically, big bang bifurcation occurs for one (or higher)-dimensional piecewise-defined discontinuous systems whenever two border collision bifurcation curves collide transversely in the parameter space. At that point, two (feasible) fixed points collide with one boundary in state space and become virtual, and, in the one-dimensional case, the map becomes continuous. Depending on the properties of the map near the codimension-two bifurcation point, there exist different scenarios regarding how the infinite number of periodic orbits are born, mainly the so-called period adding and period incrementing. In our work we prove that, in order to undergo a big bang bifurcation of the period incrementing type, it is sufficient for a piecewise-defined one-dimensional map that the colliding fixed points are attractive and with associated eigenvalues of different signs
Controlling the onset of Hopf bifurcation in the Hodgkin-Huxley model
Xie, Yong; Chen, Luonan; Kang, Yan Mei; Aihara, Kazuyuki
2008-06-01
It is a challenging problem to establish safe and simple therapeutic methods for various complicated diseases of the nervous system, particularly dynamical diseases such as epilepsy, Alzheimer’s disease, and Parkinson’s disease. From the viewpoint of nonlinear dynamical systems, a dynamical disease can be considered to be caused by a bifurcation induced by a change in the values of one or more regulating parameter. Therefore, the theory of bifurcation control may have potential applications in the diagnosis and therapy of dynamical diseases. In this study, we employ a washout filter-aided dynamic feedback controller to control the onset of Hopf bifurcation in the Hodgkin-Huxley (HH) model. Specifically, by the control scheme, we can move the Hopf bifurcation to a desired point irrespective of whether the corresponding steady state is stable or unstable. In other words, we are able to advance or delay the Hopf bifurcation, so as to prevent it from occurring in a certain range of the externally applied current. Moreover, we can control the criticality of the bifurcation and regulate the oscillation amplitude of the bifurcated limit cycle. In the controller, there are only two terms: the linear term and the nonlinear cubic term. We show that while the former determines the location of the Hopf bifurcation, the latter regulates the criticality of the Hopf bifurcation. According to the conditions of the occurrence of Hopf bifurcation and the bifurcation stability coefficient, we can analytically deduce the linear term and the nonlinear cubic term, respectively. In addition, we also show that mixed-mode oscillations (MMOs), featuring slow action potential generation, which are frequently observed in both experiments and models of chemical and biological systems, appear in the controlled HH model. It is well known that slow firing rates in single neuron models could be achieved only by type-I neurons. However, the controlled HH model is still classified as a type
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.
Zhang, Dong; Xu, Bo; Yin, Dong; Li, Yiping; He, Yuan; You, Shijie; Qiao, Shubin; Wu, Yongjian; Yan, Hongbing; Yang, Yuejin; Gao, Runlin; Dou, Kefei
2015-01-01
Abstract Occlusion of small side branch (SB) may result in significant adverse clinical events. We aim to characterize the predictors of small SB occlusion and incidence of periprocedural myocardial injury (PMI) in coronary bifurcation intervention. Nine hundred twenty-five consecutive patients with 949 bifurcation lesions (SB ≤ 2.0 mm) treated with percutaneous coronary intervention (PCI) were studied. All clinical characteristics, coronary angiography findings, PCI procedural factors, and q...
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...
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...
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.
Energy Technology Data Exchange (ETDEWEB)
Saha, Debajyoti, E-mail: debajyoti.saha@saha.ac.in; Kumar Shaw, Pankaj; Janaki, M. S.; Sekar Iyengar, A. N.; Ghosh, Sabuj; Mitra, Vramori, E-mail: vramorimitra@yahoo.com; Michael Wharton, Alpha [Plasma Physics Division, Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Kolkata 700064 (India)
2014-03-15
Order-chaos-order was observed in the relaxation oscillations of a glow discharge plasma with variation in the discharge voltage. The first transition exhibits an inverse homoclinic bifurcation followed by a homoclinic bifurcation in the second transition. For the two regimes of observations, a detailed analysis of correlation dimension, Lyapunov exponent, and Renyi entropy was carried out to explore the complex dynamics of the system.
Stability and Hopf Bifurcation in an Hexagonal Governor System With a Spring
Sotomayor, Jorge; Mello, Luis Fernando; Braga, Denis de Carvalho
2006-01-01
In this paper we study the Lyapunov stability and the Hopf bifurcation in a system coupling an hexagonal centrifugal governor with a steam engine. Here are given sufficient conditions for the stability of the equilibrium state and of the bifurcating periodic orbit. These conditions are expressed in terms of the physical parameters of the system, and hold for parameters outside a variety of codimension two.
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.
International Nuclear Information System (INIS)
For a higher order linear ordinary differential operator P, its Stokes curve bifurcates in general when it hits another turning point of P. This phenomenon is most neatly understandable by taking into account Stokes curves emanating from virtual turning points, together with those from ordinary turning points. This understanding of the bifurcation of a Stokes curve plays an important role in resolving a paradox recently found in a system of linear differential equations associated with the fourth Painleve equation
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)).
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.
Stability and bifurcation of equilibria for the axisymmetric averaged mean curvature flow
LeCrone, Jeremy
2012-01-01
We study the averaged mean curvature flow, also called the volume preserving mean curvature flow, in the particular setting of axisymmetric surfaces embedded in R^3 satisfying periodic boundary conditions. We establish analytic well--posedness of the flow within the space of little-H\\"older continuous surfaces, given rough initial data. We also establish dynamic properties of equilibria, including stability, instability, and bifurcation behavior of cylinders, where the radius acts as a bifurc...
Hopf Bifurcation of an SIQR Computer Virus Model with Time Delay
2015-01-01
A delayed SIQR computer virus model is considered. It has been observed that there exists a critical value of delay for the stability of virus prevalence by choosing the delay as a bifurcation parameter. Furthermore, the properties of the Hopf bifurcation such as direction and stability are investigated by using the normal form method and center manifold theory. Finally, some numerical simulations for supporting our theoretical results are also performed.
Jianguo Ren; Yonghong Xu
2014-01-01
A new computer virus propagation model with delay and incomplete antivirus ability is formulated and its global dynamics is analyzed. The existence and stability of the equilibria are investigated by resorting to the threshold value R0. By analysis, it is found that the model may undergo a Hopf bifurcation induced by the delay. Correspondingly, the critical value of the Hopf bifurcation is obtained. Using Lyapunov functional approach, it is proved that, under suitable conditions, the unique v...
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...
Bifurcations and sudden current change in ensembles of classically chaotic ratchets
Kenfack, A.; Sweetnam, S.; Pattanayak, A.K.
2007-01-01
In \\prl 84, 258 (2000), Mateos conjectured that current reversal in a classical deterministic ratchet is associated with bifurcations from chaotic to periodic regimes. This is based on the comparison of the current and the bifurcation diagram as a function of a given parameter for a periodic asymmetric potential. Barbi and Salerno, in \\pre 62, 1988 (2000), have further investigated this claim and argue that, contrary to Mateos' claim, current reversals can occur also in the absence of bifurca...
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...
Chalal, Hocine; ABED-MERAIM, Farid
2015-01-01
The localization of deformation into planar bands is often considered as the ultimate stage of strain prior to ductile fracture. In this study, ductility limits of metallic materials are predicted using the Gurson–Tvergaard–Needleman (GTN) damage model combined with the bifurcation approach. Both the GTN constitutive equations and the Rice bifurcation criterion are implemented into the finite element (FE) code ABAQUS/Standard within the framework of large plastic strains and a fully three-dim...
Abed-Meraim, F Farid; Peerlings, RHJ Ron; Geers, MGD Marc
2014-01-01
The present contribution deals with the prediction of diffuse necking in the context of forming and stretching of metal sheets. For this purpose, two approaches are investigated, namely bifurcation and the maximum force principle, with a systematic comparison of their respective ability to predict necking. While the bifurcation approach is of quite general applicability, some restrictions are shown for the application of maximum force conditions. Although the predictions of the two approaches...
Impact of third-order dispersion on nonlinear bifurcations in optical resonators
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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.
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.
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...
Energy Technology Data Exchange (ETDEWEB)
Agliari, Anna [Dipartimento di Scienze Economiche e Sociali, Universita Cattolica del Sacro Cuore, Via Emilia Parmense, 84, 29100 Piacenza (Italy)]. E-mail: anna.agliari@unicatt.it
2006-08-15
In this paper we study some global bifurcations arising in the Puu's oligopoly model when we assume that the producers do not adjust to the best reply but use an adaptive process to obtain at each step the new production. Such bifurcations cause the appearance of a pair of closed invariant curves, one attracting and one repelling, this latter being involved in the subcritical Neimark bifurcation of the Cournot equilibrium point. The aim of the paper is to highlight the relationship between the global bifurcations causing the appearance/disappearance of two invariant closed curves and the homoclinic connections of some saddle cycle, already conjectured in [Agliari A, Gardini L, Puu T. Some global bifurcations related to the appearance of closed invariant curves. Comput Math Simul 2005;68:201-19]. We refine the results obtained in such a paper, showing that the appearance/disappearance of closed invariant curves is not necessarily related to the existence of an attracting cycle. The characterization of the periodicity tongues (i.e. a region of the parameter space in which an attracting cycle exists) associated with a subcritical Neimark bifurcation is also discussed.
International Nuclear Information System (INIS)
In this paper we study some global bifurcations arising in the Puu's oligopoly model when we assume that the producers do not adjust to the best reply but use an adaptive process to obtain at each step the new production. Such bifurcations cause the appearance of a pair of closed invariant curves, one attracting and one repelling, this latter being involved in the subcritical Neimark bifurcation of the Cournot equilibrium point. The aim of the paper is to highlight the relationship between the global bifurcations causing the appearance/disappearance of two invariant closed curves and the homoclinic connections of some saddle cycle, already conjectured in [Agliari A, Gardini L, Puu T. Some global bifurcations related to the appearance of closed invariant curves. Comput Math Simul 2005;68:201-19]. We refine the results obtained in such a paper, showing that the appearance/disappearance of closed invariant curves is not necessarily related to the existence of an attracting cycle. The characterization of the periodicity tongues (i.e. a region of the parameter space in which an attracting cycle exists) associated with a subcritical Neimark bifurcation is also discussed
Homoclinic bifurcations in low-Prandtl-number Rayleigh-B\\'{e}nard convection with uniform rotation
Maity, P; Pal, P
2014-01-01
We present results of direct numerical simulations on homoclinic gluing and ungluing bifurcations in low-Prandtl-number ($ 0 \\leq Pr \\leq 0.025 $) Rayleigh-B\\'{e}nard system rotating slowly and uniformly about a vertical axis. We have performed simulations with \\textit{stress-free} top and bottom boundaries for several values of Taylor number ($5 \\leq Ta \\leq 50$) near the instability onset. We observe a single homoclinic ungluing bifurcation, marked by the spontaneous breaking of a larger limit cycle into two limit cycles with the variation of the reduced Rayleigh number $r$ for smaller values of $Ta (< 25)$. A pair of homoclinic bifurcations, instead of one bifurcation, is observed with variation of $r$ for slightly higher values of $Ta$ ($25 \\leq Ta \\leq 50$) in the same fluid dynamical system. The variation of the bifurcation threshold with $Ta$ is also investigated. We have also constructed a low-dimensional model which qualitatively captures the dynamics of the system near the homoclinic bifurcations...
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.
Bifurcations and sudden current change in ensembles of classically chaotic ratchets
Kenfack, Anatole; Sweetnam, Sean M.; Pattanayak, Arjendu K.
2007-05-01
Mateos [Phys. Rev. Lett. 84, 258 (2000)] conjectured that current reversal in a classical deterministic ratchet is associated with bifurcations from chaotic to periodic regimes. This is based on the comparison of the current and the bifurcation diagram as a function of a given parameter for a periodic asymmetric potential. Barbi and Salerno [Phys. Rev. E 62, 1988 (2000)] have further investigated this claim and argue that, contrary to Mateos’ claim, current reversals can occur also in the absence of bifurcations. Barbi and Salerno’s studies are based on the dynamics of one particle rather than the statistical mechanics of an ensemble of particles moving in the chaotic system. The behavior of ensembles can be quite different, depending upon their characteristics, which leaves their results open to question. In this paper we present results from studies showing how the current depends on the details of the ensemble used to generate it, as well as conditions for convergent behavior (that is, independent of the details of the ensemble). We are then able to present the converged current as a function of parameters, in the same system as Mateos as well as Barbi and Salerno. We show evidence for current reversal without bifurcation, as well as bifurcation without current reversal. We conjecture that it is appropriate to correlate abrupt changes in the current with bifurcation, rather than current reversals, and show numerical evidence for our claims.
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.
Multistability and gluing bifurcation to butterflies in coupled networks with non-monotonic feedback
International Nuclear Information System (INIS)
Neural networks with a non-monotonic activation function have been proposed to increase their capacity for memory storage and retrieval, but there is still a lack of rigorous mathematical analysis and detailed discussions of the impact of time lag. Here we consider a two-neuron recurrent network. We first show how supercritical pitchfork bifurcations and a saddle-node bifurcation lead to the coexistence of multiple stable equilibria (multistability) in the instantaneous updating network. We then study the effect of time delay on the local stability of these equilibria and show that four equilibria lose their stability at a certain critical value of time delay, and Hopf bifurcations of these equilibria occur simultaneously, leading to multiple coexisting periodic orbits. We apply centre manifold theory and normal form theory to determine the direction of these Hopf bifurcations and the stability of bifurcated periodic orbits. Numerical simulations show very interesting global patterns of periodic solutions as the time delay is varied. In particular, we observe that these four periodic solutions are glued together along the stable and unstable manifolds of saddle points to develop a butterfly structure through a complicated process of gluing bifurcations of periodic solutions
Climate tipping as a noisy bifurcation: a predictive technique
Thompson, J M T
2010-01-01
It is often known, from modelling studies, that a certain mode of climate tipping (of the oceanic thermohaline circulation, for example) is governed by an underlying fold bifurcation. For such a case we present a scheme of analysis that determines the best stochastic fit to the existing data. This provides the evolution rate of the effective control parameter, the variation of the stability coefficient, the path itself and its tipping point. By assessing the actual effective level of noise in the available time series, we are then able to make probability estimates of the time of tipping. This new technique is applied, first, to the output of a computer simulation for the end of greenhouse Earth about 34 million years ago when the climate tipped from a tropical state into an icehouse state with ice caps. Second, we use the algorithms to give probabilistic tipping estimates for the end of the most recent glaciation of the Earth using actual archaeological ice-core data.
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.
Bifurcation in epigenetics: Implications in development, proliferation, and diseases
Jost, Daniel
2014-01-01
Cells often exhibit different and stable phenotypes from the same DNA sequence. Robustness and plasticity of such cellular states are controlled by diverse transcriptional and epigenetic mechanisms, among them the modification of biochemical marks on chromatin. Here, we develop a stochastic model that describes the dynamics of epigenetic marks along a given DNA region. Through mathematical analysis, we show the emergence of bistable and persistent epigenetic states from the cooperative recruitment of modifying enzymes. We also find that the dynamical system exhibits a critical point and displays, in the presence of asymmetries in recruitment, a bifurcation diagram with hysteresis. These results have deep implications for our understanding of epigenetic regulation. In particular, our study allows one to reconcile within the same formalism the robust maintenance of epigenetic identity observed in differentiated cells, the epigenetic plasticity of pluripotent cells during differentiation, and the effects of epigenetic misregulation in diseases. Moreover, it suggests a possible mechanism for developmental transitions where the system is shifted close to the critical point to benefit from high susceptibility to developmental cues.
Bifurcation and catastrophe of seepage flow system in broken rock
Institute of Scientific and Technical Information of China (English)
MIAO Xie-xing; LI Shun-cai; CHEN Zhan-qing
2009-01-01
The study of dynamical behavior of water or gas flows in broken rock is a basic research topic among a series of key projects about stability control of the surrounding rocks in mines and the prevention of some disasters such as water inrush or gas outburst and the protection of the groundwater resource. It is of great theoretical and engineering importance in respect of promo-tion of security in mine production and sustainable development of the coal industry. According to the non-Darcy property of seepage flow in broken rock dynamic equations of non-Darcy and non-steady flows in broken rock are established. By dimensionless transformation, the solution diagram of steady-states satisfying the given boundary conditions is obtained. By numerical analysis of low relaxation iteration, the dynamic responses corresponding to the different flow parameters have been obtained. The stability analysis of the steady-states indicate that a saddle-node bifurcaton exists in the seepage flow system of broken rock. Consequently, using catastrophe theory, the fold catastrophe model of seepage flow instability has been obtained. As a result, the bifurcation curves of the seepage flow systems with different control parameters are presented and the standard potential function is also given with respect to the generalized state variable for the fold catastrophe of a dynamic system of seepage flow in broken rock.
Bifurcations of lunisolar secular resonances for space debris orbits
Celletti, Alessandra; Pucacco, Giuseppe
2015-01-01
Using bifurcation theory, we study the secular resonances induced by Sun and Moon on space debris orbits around the Earth. In particular, we concentrate on a special class of secular resonances, which depends just on the debris' orbital inclination. This class is typically subdivided into three distinct types of secular resonances: those occurring at the critical inclination, those corresponding to polar orbits and a third type resulting from a linear combination of the rates of variation of the argument of perigee and the longitude of the ascending node. The model describing the dynamics of space debris includes the effects of the geopotential, as well as Sun's and Moon's attractions, and it is defined in terms of suitable action-angle variables. We consider the system averaged over both the mean anomaly of the debris and those of Sun and Moon. Such multiply-averaged Hamiltonian is used to study the lunisolar resonances which depend just on the inclination. Borrowing the technique from the theory of bifurcat...
Endovascular coil embolization in internal carotid artery bifurcation aneurysms
International Nuclear Information System (INIS)
Aim: To present the clinical and radiological results of coil embolization in internal carotid artery (ICA) bifurcation aneurysms (BA). Materials and methods: The records of 65 patients with 66 ICA BA were retrieved from data prospectively accrued between September 1999 and July 2013. Clinical and morphological outcomes of the aneurysms were assessed, including technical aspects of treatment. Results: The aneurysms under study were directed either superiorly (41/66, 62.1%), anteriorly (24/66, 36.4%), or posteriorly (1/66, 1.5%), and all were devoid of perforators. Aneurysmal necks were situated symmetrically at the terminal ICA (37/66, 56.1%) or slightly deviated to the proximal A1 segment (29/66, 43.9%). The steam-shaped S microcatheter (73.8%) was most commonly used to select the aneurysms, and the single microcatheter technique was most commonly applied (56.1%) to perform coil embolization, followed by balloon remodelling (21.2%), multiple microcatheter (15.1%), and stent-protection (7.6%). Successful aneurysmal occlusion was achieved in 100% of cases, with no procedure-related morbidity or mortality. Imaging performed in the course of follow-up (mean duration 27.3 months) confirmed stable occlusion of most lesions (47/53, 88.7%). Conclusion: Through tailored technical strategies, ICA BA are amenable to safe and effective endovascular coil embolization, with a tendency for stable occlusion long-term
Directory of Open Access Journals (Sweden)
Yi Zhang
2014-01-01
Full Text Available The objective of this paper is to study systematically the bifurcation and control of a single-species fish population logistic model with the invasion of alien species based on the theory of singular system and bifurcation. It regards Spartina anglica as an invasive species, which invades the fisheries and aquaculture. Firstly, the stabilities of equilibria in this model are discussed. Moreover, the sufficient conditions for existence of the trans-critical bifurcation and the singularity induced bifurcation are obtained. Secondly, the state feedback controller is designed to eliminate the unexpected singularity induced bifurcation by combining harvested effort with the purification capacity. It obviously inhibits the switch of population and makes the system stable. Finally, the numerical simulation is proposed to show the practical significance of the bifurcation and control from the biological point of view.
Width bifurcation and dynamical phase transitions in open quantum systems.
Eleuch, Hichem; Rotter, Ingrid
2013-05-01
The states of an open quantum system are coupled via the environment of scattering wave functions. The complex coupling coefficients ω between system and environment arise from the principal value integral and the residuum. At high-level density where the resonance states overlap, the dynamics of the system is determined by exceptional points. At these points, the eigenvalues of two states are equal and the corresponding eigenfunctions are linearly dependent. It is shown in the present paper that Im(ω) and Re(ω) influence the system properties differently in the surrounding of exceptional points. Controlling the system by a parameter, the eigenvalues avoid crossing in energy near an exceptional point under the influence of Re(ω) in a similar manner as it is well known from discrete states. Im(ω), however, leads to width bifurcation and finally (when the system is coupled to one channel, i.e., to one common continuum of scattering wave functions), to a splitting of the system into two parts with different characteristic time scales. The role of observer states is discussed. Physically, the system is stabilized by this splitting since the lifetimes of some states are longer than before, while that of one state is shorter. In the cross section the short-lived state appears as a background term in high-resolution experiments. The wave functions of the long-lived states are mixed in those of the original ones in a comparably large parameter range. Numerical results for the eigenvalues and eigenfunctions are shown for N=2,4, and 10 states coupled mostly to one channel. PMID:23767516
Post-Treatment Hemodynamics of a Basilar Aneurysm and Bifurcation
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Ortega, J; Hartman, J; Rodriguez, J; Maitland, D
2008-01-16
Aneurysm re-growth and rupture can sometimes unexpectedly occur following treatment procedures that were initially considered to be successful at the time of treatment and post-operative angiography. In some cases, this can be attributed to surgical clip slippage or endovascular coil compaction. However, there are other cases in which the treatment devices function properly. In these instances, the subsequent complications are due to other factors, perhaps one of which is the post-treatment hemodynamic stress. To investigate whether or not a treatment procedure can subject the parent artery to harmful hemodynamic stresses, computational fluid dynamics simulations are performed on a patient-specific basilar aneurysm and bifurcation before and after a virtual endovascular treatment. The simulations demonstrate that the treatment procedure produces a substantial increase in the wall shear stress. Analysis of the post-treatment flow field indicates that the increase in wall shear stress is due to the impingement of the basilar artery flow upon the aneurysm filling material and to the close proximity of a vortex tube to the artery wall. Calculation of the time-averaged wall shear stress shows that there is a region of the artery exposed to a level of wall shear stress that can cause severe damage to endothelial cells. The results of this study demonstrate that it is possible for a treatment procedure, which successfully excludes the aneurysm from the vascular system and leaves no aneurysm neck remnant, to elevate the hemodynamic stresses to levels that are injurious to the immediately adjacent vessel wall.
STABILITY, BIFURCATIONS AND CHAOS IN UNEMPLOYMENT NON-LINEAR DYNAMICS
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Pagliari Carmen
2013-07-01
Full Text Available The traditional analysis of unemployment in relation to real output dynamics is based on some empirical evidences deducted from Okun’s studies. In particular the so called Okun’s Law is expressed in a linear mathematical formulation, which cannot explain the fluctuation of the variables involved. Linearity is an heavy limit for macroeconomic analysis and especially for every economic growth study which would consider the unemployment rate among the endogenous variables. This paper deals with an introductive study about the role of non-linearity in the investigation of unemployment dynamics. The main idea is the existence of a non-linear relation between the unemployment rate and the gap of GDP growth rate from its trend. The macroeconomic motivation of this idea moves from the consideration of two concatenate effects caused by a variation of the unemployment rate on the real output growth rate. These two effects are concatenate because there is a first effect that generates a secondary one on the same variable. When the unemployment rate changes, the first effect is the variation in the level of production in consequence of the variation in the level of such an important factor as labour force; the secondary effect is a consecutive variation in the level of production caused by the variation in the aggregate demand in consequence of the change of the individual disposal income originated by the previous variation of production itself. In this paper the analysis of unemployment dynamics is carried out by the use of the logistic map and the conditions for the existence of bifurcations (cycles are determined. The study also allows to find the range of variability of some characteristic parameters that might be avoided for not having an absolute unpredictability of unemployment dynamics (deterministic chaos: unpredictability is equivalent to uncontrollability because of the total absence of information about the future value of the variable to
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Shaoyong Li
2013-01-01
Full Text Available Using bifurcation method of dynamical systems, we investigate the nonlinear waves for the generalized Zakharov equations utt-cs2uxx=β(|E|2xx, iEt+αExx-δ1uE+δ2|E|2E+δ3|E|4E=0, where α,β,δ1,δ2,δ3, and cs are real parameters, E=E(x,t is a complex function, and u=u(x,t is a real function. We obtain the following results. (i Three types of explicit expressions of nonlinear waves are obtained, that is, the fractional expressions, the trigonometric expressions, and the exp-function expressions. (ii Under different parameter conditions, these expressions represent symmetric and antisymmetric solitary waves, kink and antikink waves, symmetric periodic and periodic-blow-up waves, and 1-blow-up and 2-blow-up waves. We point out that there are two sets of kink waves which are called tall-kink waves and low-kink waves, respectively. (iii Five kinds of interesting bifurcation phenomena are revealed. The first kind is that the 1-blow-up waves can be bifurcated from the periodic-blow-up and 2-blow-up waves. The second kind is that the 2-blow-up waves can be bifurcated from the periodic-blow-up waves. The third kind is that the symmetric solitary waves can be bifurcated from the symmetric periodic waves. The fourth kind is that the low-kink waves can be bifurcated from four types of nonlinear waves, the symmetric solitary waves, the 1-blow-up waves, the tall-kink waves, and the antisymmetric solitary waves. The fifth kind is that the tall-kink waves can be bifurcated from the symmetric periodic waves. We also show that the exp-function expressions include some results given by pioneers.
International Nuclear Information System (INIS)
This is the abstracts of the Mini-Symposium on Stability and Bifurcation in Fluid Motions held on September 9-10, 1994 at the Tokai Establishment of JAERI and the Tokai Kaikan. Sixteen talks were given on various important subjects related with stability and bifurcation phenomena in fluids. All of them are theoretical and numerical analyses involving linear stability analysis, weakly nonlinear analysis, bifurcation analysis, and direct computation of nonlinearly equilibrium solutions. (author)
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Fujimura, Kaoru [ed.] [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment
1995-01-01
This is the abstracts of the Mini-Symposium on Stability and Bifurcation in Fluid Motions held on September 9-10, 1994 at the Tokai Establishment of JAERI and the Tokai Kaikan. Sixteen talks were given on various important subjects related with stability and bifurcation phenomena in fluids. All of them are theoretical and numerical analyses involving linear stability analysis, weakly nonlinear analysis, bifurcation analysis, and direct computation of nonlinearly equilibrium solutions. (author).
International Nuclear Information System (INIS)
A delay-differential modelling with stage-structure for prey is investigated. Its dynamics are studied in terms of local analysis and Hopf bifurcation theory, and its linear stability and Hopf bifurcation are demonstrated by studying the characteristic equation. The stability and direction of Hopf bifurcation are determined by applying the normal form theory and the center manifold argument, and numerical simulations are given to illustrate the analytical result
International Nuclear Information System (INIS)
Objective: To investigate variation in the carotid bifurcation geometry of adults of different age by MR angiography images combining image post-processing technique. Methods: Images of the carotid bifurcations of 27 young adults (≤40 years old) and 30 older subjects ( > 40 years old) were acquired via contrast-enhanced MR angiography. Three dimensional (3D) geometries of the bifurcations were reconstructed and geometric parameters were measured by post-processing technique. Results: The geometric parameters of the young versus older groups were as follows: bifurcation angle (70.268 degree± 16.050 degree versus 58.857 degree±13.294 degree), ICA angle (36.893 degree±11.837 degree versus 30.275 degree±9.533 degree), ICA planarity (6.453 degree ± 5.009 degree versus 6.263 degree ±4.250 degree), CCA tortuosity (0.023±0.011 versus 0.014± 0.005), ICA tortuosity (0.070±0.042 versus 0.046±0.022), ICA/CCA diameter ratio (0.693± 0.132 versus 0.728±0.106), ECA/CCA diameter ratio (0.750±0.123 versus 0.809±0.122), ECA/ ICA diameter ratio (1.103±0.201 versus 1.127±0.195), bifurcation area ratio (1.057±0.281 versus 1.291±0.252). There was significant statistical difference between young group and older group in-bifurcation angle, ICA angle, CCA tortuosity, ICA tortuosity, ECA/CCA and bifurcation area ratio (F= 17.16, 11.74, 23.02, 13.38, 6.54, 22.80, respectively, P<0.05). Conclusions: MR angiography images combined with image post-processing technique can reconstruct 3D carotid bifurcation geometry and measure the geometric parameters of carotid bifurcation in vivo individually. It provides a new and convenient method to investigate the relationship of vascular geometry and flow condition with atherosclerotic pathological changes. (authors)
Investigation of homoclinic bifurcation of plasma fireball in a double plasma device
International Nuclear Information System (INIS)
Plasma fire balls are generated due to localized discharge and it is a sharp boundary of the glow region, which suggests a localized electric field such as an electrical sheath or double layer structure. In this paper, homoclinic bifurcation phenomena in the plasma fireball dynamics which is produced in the target chamber of double plasma device have been explored. Homoclinic bifurcation is noticed in the plasma fireball as the system evolving from large time period oscillation to small time period oscillation. The control parameters of this observations are density ratio of target to source chamber (nT/nS), applied electrode voltage to produce fireball, grid bias voltage etc. The dynamical transition of plasma fire balls have been investigated by recurrence quantification analysis (RQA) and by different statistical measures. The gradual increment of kurtosis and decrement of skewness with the change of nT has been observed which are strongly indicative of homoclinic bifurcation in the system. The visual changes of recurrence plot and the gradual changes in recurrence quantifiers reflect the bifurcation with the variation in the control parameter of the double plasma device. The combination of RQA and statistical measures like 1/f power spectrum, clearly conjectured the homoclinic bifurcation due to plasma fire ball in the experimental conditions. (author)
The Formation of Ion Concentration Polarization Layer Induced by Bifurcated Current Path
Kim, Junsuk; Lee, Hyomin; Cho, Inhee; Kim, Ho-Young; Kim, Sung Jae; EES Team; MFM Team
2015-11-01
Ion Concentration Polarization (ICP) is a fundamental electrokinetic phenomenon that occurs near a perm-selective membrane and, thus, the characteristics can be significantly altered by the current path through the Nafion nanoporous membrane. In this work, a new ICP device that bifurcated the current path was fabricated using micro/micro-nano/nano/micro hybrid channel connection, while a conventional ICP device has employed micro/nano/micro channel connection. The propagation of ICP layer was initiated from the nano-channel at high concentration regime and from micro-nano connection at low concentration regime. Interestingly, the reverse propagation was observed at low concentration regime as well. These combined effects conveyed a competition between two distinguishable propagations at intermediate concentration regime, caused by singularity of the bifurcated current path. Experiments and an equivalent circuit analysis were conducted for this bifurcation. As a result, the conductance ratio of electrolyte to Nafion governed the bifurcation. Conclusively, the bifurcation-induced ICP layer formation was able to be characterized by analyzing current-time characteristic which have two distinct RC delay times. 2013R1A1A1008125, CISS- 2011-0031870 and 2012-0009563 by the Ministry of Science, ICT & Future Planning and HI13C1468, HI14C0559.
Invariants, Attractors and Bifurcation in Two Dimensional Maps with Polynomial Interaction
Hacinliyan, Avadis Simon; Aybar, Orhan Ozgur; Aybar, Ilknur Kusbeyzi
This work will present an extended discrete-time analysis on maps and their generalizations including iteration in order to better understand the resulting enrichment of the bifurcation properties. The standard concepts of stability analysis and bifurcation theory for maps will be used. Both iterated maps and flows are used as models for chaotic behavior. It is well known that when flows are converted to maps by discretization, the equilibrium points remain the same but a richer bifurcation scheme is observed. For example, the logistic map has a very simple behavior as a differential equation but as a map fold and period doubling bifurcations are observed. A way to gain information about the global structure of the state space of a dynamical system is investigating invariant manifolds of saddle equilibrium points. Studying the intersections of the stable and unstable manifolds are essential for understanding the structure of a dynamical system. It has been known that the Lotka-Volterra map and systems that can be reduced to it or its generalizations in special cases involving local and polynomial interactions admit invariant manifolds. Bifurcation analysis of this map and its higher iterates can be done to understand the global structure of the system and the artifacts of the discretization by comparing with the corresponding results from the differential equation on which they are based.
Fixed-point bifurcation analysis in biological models using interval polynomials theory.
Rigatos, Gerasimos G
2014-06-01
The paper proposes a systematic method for fixed-point bifurcation analysis in circadian cells and similar biological models using interval polynomials theory. The stages for performing fixed-point bifurcation analysis in such biological systems comprise (i) the computation of fixed points as functions of the bifurcation parameter and (ii) the evaluation of the type of stability for each fixed point through the computation of the eigenvalues of the Jacobian matrix that is associated with the system's nonlinear dynamics model. Stage (ii) requires the computation of the roots of the characteristic polynomial of the Jacobian matrix. This problem is nontrivial since the coefficients of the characteristic polynomial are functions of the bifurcation parameter and the latter varies within intervals. To obtain a clear view about the values of the roots of the characteristic polynomial and about the stability features they provide to the system, the use of interval polynomials theory and particularly of Kharitonov's stability theorem is proposed. In this approach, the study of the stability of a characteristic polynomial with coefficients that vary in intervals is equivalent to the study of the stability of four polynomials with crisp coefficients computed from the boundaries of the aforementioned intervals. The efficiency of the proposed approach for the analysis of fixed-point bifurcations in nonlinear models of biological neurons is tested through numerical and simulation experiments. PMID:24817437
Forced phase-locked response of a nonlinear system with time delay after Hopf bifurcation
International Nuclear Information System (INIS)
The trivial equilibrium of a nonlinear autonomous system with time delay may become unstable via a Hopf bifurcation of multiplicity two, as the time delay reaches a critical value. This loss of stability of the equilibrium is associated with two coincident pairs of complex conjugate eigenvalues crossing the imaginary axis. The resultant dynamic behaviour of the corresponding nonlinear non-autonomous system in the neighbourhood of the Hopf bifurcation is investigated based on the reduction of the infinite-dimensional problem to a four-dimensional centre manifold. As a result of the interaction between the Hopf bifurcating periodic solutions and the external periodic excitation, a primary resonance can occur in the forced response of the system when the forcing frequency is close to the Hopf bifurcating periodic frequency. The method of multiple scales is used to obtain four first-order ordinary differential equations that determine the amplitudes and phases of the phase-locked periodic solutions. The first-order approximations of the periodic solutions are found to be in excellent agreement with those obtained by direct numerical integration of the delay-differential equation. It is also found that the steady state solutions of the nonlinear non-autonomous system may lose their stability via either a pitchfork or Hopf bifurcation. It is shown that the primary resonance response may exhibit symmetric and asymmetric phase-locked periodic motions, quasi-periodic motions, chaotic motions, and coexistence of two stable motions
Correlation analysis of the North Equatorial Current bifurcation and the Indonesian Throughflow
Institute of Scientific and Technical Information of China (English)
ZHAO Yunxia; WEI Zexun; WANG Yonggang; XU Tengfei; FENG Ying
2015-01-01
Based on monthly mean Simple Ocean Data Assimilation (SODA) products from 1958 to 2007, this study analyzes the seasonal and interannual variability of the North Equatorial Current (NEC) bifurcation latitude and the Indonesian Throughflow (ITF) volume transport. Further, Empirical Mode Decomposition (EMD) method and lag-correlation analysis are employed to reveal the relationships between the NEC bifurcation location, NEC and ITF volume transport and ENSO events. The analysis results of the seasonal variability show that the annual mean location of NEC bifurcation in upper layer occurs at 14.33°N and ITF volume transport has a maximum value in summer, a minimum value in winter and an annual mean transport of 7.75×106 m3/s. The interannual variability analysis indicates that the variability of NEC bifurcation location can be treated as a precursor of El Niño. The correlation coefficient between the two reaches the maximum of 0.53 with a time lag of 2 months. The ITF volume transport is positively related with El Niño events with a maximum coefficient of 0.60 by 3 months. The NEC bifurcation location is positively correlated with the ITF volume transport with a correlation coefficient of 0.43.
Bioresorbable Scaffolds for the Management of Coronary Bifurcation Lesions.
Kawamoto, Hiroyoshi; Ruparelia, Neil; Tanaka, Akihito; Chieffo, Alaide; Latib, Azeem; Colombo, Antonio
2016-05-23
The use of bioresorbable scaffolds (BRS) may be associated with benefits including restoration of endothelial function, positive vessel remodeling, and reduced risk for very late (stent) thrombosis compared with metallic stents by virtue of their complete absorption within 3 to 4 years of implantation. When treating bifurcation lesions, these advantages may be even more pronounced. The aim of this review is to summarize current experiences and technical considerations of bifurcation treatment with BRS. Because of the physical properties of current-generation BRS, there are concerns with regard to the efficacy and safety of this novel technology for the treatment of bifurcations, with the potential for increased rates of scaffold thrombosis and side-branch occlusions, and as a consequence, bifurcations have been excluded from the major BRS trials. Nevertheless, BRS have been used for this indication in clinical practice, as evidenced by "real-world" registries. Considering the potential limitations, specific technical considerations and modified bifurcation strategies should be used in an attempt to attenuate problems and achieve optimal procedural and clinical outcomes. PMID:27198679
Von Bertalanffy's dynamics under a polynomial correction: Allee effect and big bang bifurcation
Leonel Rocha, J.; Taha, A. K.; Fournier-Prunaret, D.
2016-02-01
In this work we consider new one-dimensional populational discrete dynamical systems in which the growth of the population is described by a family of von Bertalanffy's functions, as a dynamical approach to von Bertalanffy's growth equation. The purpose of introducing Allee effect in those models is satisfied under a correction factor of polynomial type. We study classes of von Bertalanffy's functions with different types of Allee effect: strong and weak Allee's functions. Dependent on the variation of four parameters, von Bertalanffy's functions also includes another class of important functions: functions with no Allee effect. The complex bifurcation structures of these von Bertalanffy's functions is investigated in detail. We verified that this family of functions has particular bifurcation structures: the big bang bifurcation of the so-called “box-within-a-box” type. The big bang bifurcation is associated to the asymptotic weight or carrying capacity. This work is a contribution to the study of the big bang bifurcation analysis for continuous maps and their relationship with explosion birth and extinction phenomena.
Does the principle of minimum work apply at the carotid bifurcation: a retrospective cohort study
International Nuclear Information System (INIS)
There is recent interest in the role of carotid bifurcation anatomy, geometry and hemodynamic factors in the pathogenesis of carotid artery atherosclerosis. Certain anatomical and geometric configurations at the carotid bifurcation have been linked to disturbed flow. It has been proposed that vascular dimensions are selected to minimize energy required to maintain blood flow, and that this occurs when an exponent of 3 relates the radii of parent and daughter arteries. We evaluate whether the dimensions of bifurcation of the extracranial carotid artery follow this principle of minimum work. This study involved subjects who had computed tomographic angiography (CTA) at our institution between 2006 and 2007. Radii of the common, internal and external carotid arteries were determined. The exponent was determined for individual bifurcations using numerical methods and for the sample using nonlinear regression. Mean age for 45 participants was 56.9 ± 16.5 years with 26 males. Prevalence of vascular risk factors was: hypertension-48%, smoking-23%, diabetes-16.7%, hyperlipidemia-51%, ischemic heart disease-18.7%. The value of the exponent ranged from 1.3 to 1.6, depending on estimation methodology. The principle of minimum work (defined by an exponent of 3) may not apply at the carotid bifurcation. Additional factors may play a role in the relationship between the radii of the parent and daughter vessels
Degenerate Bogdanov-Takens bifurcations in a one-dimensional transport model of a fusion plasma
de Blank, H. J.; Kuznetsov, Yu. A.; Pekkér, M. J.; Veldman, D. W. M.
2016-09-01
Experiments in tokamaks (nuclear fusion reactors) have shown two modes of operation: L-mode and H-mode. Transitions between these two modes have been observed in three types: sharp, smooth and oscillatory. The same modes of operation and transitions between them have been observed in simplified transport models of the fusion plasma in one spatial dimension. We study the dynamics in such a one-dimensional transport model by numerical continuation techniques. To this end the MATLAB package CL_MATCONTL was extended with the continuation of (codimension-2) Bogdanov-Takens bifurcations in three parameters using subspace reduction techniques. During the continuation of (codimension-2) Bogdanov-Takens bifurcations in 3 parameters, generically degenerate Bogdanov-Takens bifurcations of codimension-3 are detected. However, when these techniques are applied to the transport model, we detect a degenerate Bogdanov-Takens bifurcation of codimension 4. The nearby 1- and 2-parameter slices are in agreement with the presence of this codimension-4 degenerate Bogdanov-Takens bifurcation, and all three types of L-H transitions can be recognized in these slices. The same codimension-4 situation is observed under variation of the additional parameters in the model, and under some modifications of the model.
Turing-Hopf bifurcation in the reaction-diffusion equations and its applications
Song, Yongli; Zhang, Tonghua; Peng, Yahong
2016-04-01
In this paper, we consider the Turing-Hopf bifurcation arising from the reaction-diffusion equations. It is a degenerate case and where the characteristic equation has a pair of simple purely imaginary roots and a simple zero root. First, the normal form theory for partial differential equations (PDEs) with delays developed by Faria is adopted to this degenerate case so that it can be easily applied to Turing-Hopf bifurcation. Then, we present a rigorous procedure for calculating the normal form associated with the Turing-Hopf bifurcation of PDEs. We show that the reduced dynamics associated with Turing-Hopf bifurcation is exactly the dynamics of codimension-two ordinary differential equations (ODE), which implies the ODE techniques can be employed to classify the reduced dynamics by the unfolding parameters. Finally, we apply our theoretical results to an autocatalysis model governed by reaction-diffusion equations; for such model, the dynamics in the neighbourhood of this bifurcation point can be divided into six categories, each of which is exactly demonstrated by the numerical simulations; and then according to this dynamical classification, a stable spatially inhomogeneous periodic solution has been found.
On period doubling bifurcations of cycles and the harmonic balance method
Energy Technology Data Exchange (ETDEWEB)
Itovich, Griselda R. [Departamento de Matematica, FAEA, Universidad Nacional del Comahue, Neuquen Q8300BCX (Argentina)] e-mail: gitovich@arnet.com.ar; Moiola, Jorge L. [Departamento de Ingenieria Electrica y de Computadoras Universidad Nacional del Sur, Bahia Blanca B8000CPB (Argentina)] e-mail: jmoiola@criba.edu.ar
2006-02-01
This works attempts to give quasi-analytical expressions for subharmonic solutions appearing in the vicinity of a Hopf bifurcation. Starting with well-known tools as the graphical Hopf method for recovering the periodic branch emerging from classical Hopf bifurcation, precise frequency and amplitude estimations of the limit cycle can be obtained. These results allow to attain approximations for period doubling orbits by means of harmonic balance techniques, whose accuracy is established by comparison of Floquet multipliers with continuation software packages. Setting up a few coefficients, the proposed methodology yields to approximate solutions that result from a second period doubling bifurcation of cycles and to extend the validity limits of the graphical Hopf method.
Hopf bifurcation in a diffusive Lotka-Volterra type system with nonlocal delay effect
Guo, Shangjiang; Yan, Shuling
2016-01-01
The dynamics of a diffusive Lotka-Volterra type model for two species with nonlocal delay effect and Dirichlet boundary conditions is investigated in this paper. The existence and multiplicity of spatially nonhomogeneous steady-state solutions are obtained by means of Lyapunov-Schmidt reduction. The stability of spatially nonhomogeneous steady-state solutions and the existence of Hopf bifurcation with the changes of the time delay are obtained by analyzing the distribution of eigenvalues of the infinitesimal generator associated with the linearized system. By the normal form theory and the center manifold reduction, the stability and bifurcation direction of Hopf bifurcating periodic orbits are derived. Finally, our theoretical results are illustrated by a model with homogeneous kernels and one-dimensional spatial domain.
Metamorphosis of plasma turbulence-shear-flow dynamics through a transcritical bifurcation
International Nuclear Information System (INIS)
The structural properties of an economical model for a confined plasma turbulence governor are investigated through bifurcation and stability analyses. A close relationship is demonstrated between the underlying bifurcation framework of the model and typical behavior associated with low- to high-confinement transitions such as shear-flow stabilization of turbulence and oscillatory collective action. In particular, the analysis evinces two types of discontinuous transition that are qualitatively distinct. One involves classical hysteresis, governed by viscous dissipation. The other is intrinsically oscillatory and nonhysteretic, and thus provides a model for the so-called dithering transitions that are frequently observed. This metamorphosis, or transformation, of the system dynamics is an important late side-effect of symmetry breaking, which manifests as an unusual nonsymmetric transcritical bifurcation induced by a significant shear-flow drive
Metamorphosis of plasma turbulence-shear flow dynamics through a transcritical bifurcation
Ball, R; Sugama, H
2002-01-01
The structural properties of an economical model for a confined plasma turbulence governor are investigated through bifurcation and stability analyses. A close relationship is demonstrated between the underlying bifurcation framework of the model and typical behavior associated with low- to high-confinement transitions such as shear flow stabilization of turbulence and oscillatory collective action. In particular, the analysis evinces two types of discontinuous transition that are qualitatively distinct. One involves classical hysteresis, governed by viscous dissipation. The other is intrinsically oscillatory and non-hysteretic, and thus provides a model for the so-called dithering transitions that are frequently observed. This metamorphosis, or transformation, of the system dynamics is an important late side-effect of symmetry-breaking, which manifests as an unusual non-symmetric transcritical bifurcation induced by a significant shear flow drive.
Symmetry-breaking bifurcations of central forced and heated convection in a spherical fluid shell
Tuckerman, L. S.; Feudel, F.; Bergemann, K.; Egbers, C.; Futterer, B.; Gellert, M.; Hollerbach, R.
2010-11-01
We study convection in a spherical shell under a gravitational force designed to mimic the GeoFlow microgravity experiment, using a combination of time-dependent simulation and path-following methods. With an outer radius which is twice that of the inner radius, the critical modes are spherical harmonics with l=4, leading generically to transcritical bifurcations involving axisymmetric and octahedral branches, in agreement with predictions by Michel, Ihrig & Golubitsky, Chossat, Matthews, and Busse & Riahi. A secondary bifurcation involving the l=5 mode leads to an additional seven-cell branch. All three steady patterns are simultaneously stable for 7 150 18 710, simulations lead to time-dependent states, some periodic and some chaotic. The period varies greatly: some of the orbits belong to different branches and a global bifurcation is suspected of delimiting the lower limit of periodic states.
DEFF Research Database (Denmark)
Yang, Li Hui; Xu, Zhao; Østergaard, Jacob;
2010-01-01
This paper first presents the Hopf bifurcation analysis for a vector-controlled doubly fed induction generator (DFIG) which is widely used in wind power conversion systems. 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. The oscillatory instability of the DFIG has been observed by simulation study. The detailed mathematical model of the DFIG 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. The eigenvalue sensitivity analysis with respect to machine and control parameters are performed to assess the impact of parameters upon system stability. Moreover, the Hopf...
DEFF Research Database (Denmark)
Yang, Lihui; Xu, Zhao; Østergaard, Jacob;
2009-01-01
This paper first presents the Hopf bifurcation analysis for a vector-controlled doubly fed induction generator (DFIG) which is widely used in wind power conversion systems. 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. The oscillatory instability of the DFIG has been observed by simulation study. The detailed mathematical model of the DFIG 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. The eigenvalue sensitivitiy analysis with respect to machine and control parameters are performed to assess the impact of parameters upon system stability. Moreover, the Hopf...
A dosimetric model for localised radon progeny accumulations at tracheobronchial bifurcations
International Nuclear Information System (INIS)
The prevalent philosophy of inhalation risk assessment protocols is based upon assumptions of uniform particle deposition patterns and homogeneous clearance processes within human lung airways. Here we discuss the effects of enhanced deposition and reduced mucociliary clearance at tracheobronchial bifurcations on the dosimetry of inhaled radon progeny. In accordance with experimental deposition and clearance findings, upper tracheobronchial airways (i.e. generations k = 1 to 6) may be divided into three distinct physical regions: tubular segments, bifurcation zones (excluding the inclusive carina), and carinal ridges. Calculations indicate that radon progeny accumulations at airway branching sites can lead to significantly higher doses delivered to epithelial cells located within bifurcations, particularly at carinal ridges, than along tubular sections. These anatomical sites of increased exposure in tracheobronchial airways, the main, lobar, and segmental bronchi, are consistent with clinically reported locations of preferential occurrence of lung carcinomas in uranium miners. (author)
Stochastic period-doubling bifurcation analysis of a Roessler system with a bounded random parameter
International Nuclear Information System (INIS)
This paper aims to study the stochastic period-doubling bifurcation of the three-dimensional Roessler system with an arch-like bounded random parameter. First, we transform the stochastic Roessler system into its equivalent deterministic one in the sense of minimal residual error by the Chebyshev polynomial approximation method. Then, we explore the dynamical behaviour of the stochastic Roessler system through its equivalent deterministic system by numerical simulations. The numerical results show that some stochastic period-doubling bifurcation, akin to the conventional one in the deterministic case, may also appear in the stochastic Roessler system. In addition, we also examine the influence of the random parameter intensity on bifurcation phenomena in the stochastic Roessler system. (general)
Symmetry-breaking bifurcation in the nonlinear Schr\\"{o}dinger equation with symmetric potentials
Kirr, E; Pelinovsky, D E
2010-01-01
We consider the focusing (attractive) nonlinear Schr\\"odinger (NLS) equation with an external, symmetric potential which vanishes at infinity and supports a linear bound state. We prove that the symmetric, nonlinear ground states must undergo a symmetry breaking bifurcation if the potential has a non-degenerate local maxima at zero. Under a generic assumption we show that the bifurcation is either subcritical or supercritical pitchfork. In the particular case of double-well potentials with large separation, the power of nonlinearity determines the subcritical or supercritical character of the bifurcation. The results are obtained from a careful analysis of the spectral properties of the ground states at both small and large values for the corresponding eigenvalue parameter. We employ a novel technique combining concentration--compactness and spectral properties of linearized Schr\\"odinger type operators to show that the symmetric ground states can either be uniquely continued for the entire interval of the ei...
Bifurcation and Stability in a Delayed Predator-Prey Model with Mixed Functional Responses
Yafia, R.; Aziz-Alaoui, M. A.; Merdan, H.; Tewa, J. J.
2015-06-01
The model analyzed in this paper is based on the model set forth by Aziz Alaoui et al. [Aziz Alaoui & Daher Okiye, 2003; Nindjin et al., 2006] with time delay, which describes the competition between the predator and prey. This model incorporates a modified version of the Leslie-Gower functional response as well as that of Beddington-DeAngelis. In this paper, we consider the model with one delay consisting of a unique nontrivial equilibrium E* and three others which are trivial. Their dynamics are studied in terms of local and global stabilities and of the description of Hopf bifurcation at E*. At the third trivial equilibrium, the existence of the Hopf bifurcation is proven as the delay (taken as a parameter of bifurcation) that crosses some critical values.
Example of a non-smooth Hopf bifurcation in an aero-elastic system
Magri, Luca
2012-01-01
We investigate a typical aerofoil section under dynamic stall conditions, the structural model is linear and the aerodynamic loading is represented by the Leishman-Beddoes semi-empirical dynamic stall model. The loads given by this model are non-linear and non-smooth, therefore we have integrated the equation of motion using a Runge-Kutta-Fehlberg algorithm equipped with event detection. The main focus of the paper is on the interaction between the Hopf bifurcation typical of aero-elastic systems, which causes flutter oscillations, and the discontinuous definition of the stall model. The paper shows how the non-smooth definition of the dynamic stall model can generate a non-smooth Hopf bifurcation. The mechanisms for the appearance of limit cycle attractors are described by using standard tools of the theory of dynamical systems such as phase plots and bifurcation diagrams.
Hybrid control of bifurcation and chaos in stroboscopic model of Internet congestion control system
Institute of Scientific and Technical Information of China (English)
Ding Da-Wei; Zhu Jie; Luo Xiao-Shu
2008-01-01
Interaction between transmission control protocol (TCP) and random early detection (RED) gateway in the Internet congestion control system has been modelled as a discrete-time dynamic system which exhibits complex bifurcating and chaotic behaviours.In this paper,a hybrid control strategy using both state feedback and parameter perturbation is employed to control the bifurcation and stabilize the chaotic orbits embedded in this discrete-time dynamic system of TCP/RED.Theoretical analysis and numerical simulations show that the bifurcation is delayed and the chaotic orbits are stabilized to a fixed point,which reliably achieves a stable average queue size in an extended range of parameters and even completely eliminates the chaotic behaviour in a particular range of parameters.Therefore it is possible to decrease the sensitivity of RED to parameters.By using the hybrid strategy,we may improve the stability and performance of TCP/RED congestion control system significantly.
Bifurcation of a nonlinear Schrödinger equation with a symmetrical double well
International Nuclear Information System (INIS)
The bifurcation of a one-dimensional Gross–Pitaevskii-type equation with a symmetrical double well is investigated. A general relation for the critical power, above which a kind of bifurcation transition from a supercritical pitchfork to a subcritical pitchfork occurs, is presented in terms of the ratio of the nonlinear tunneling to the nonlinear interaction. When the nonlinearity is very weak, our relation reduces to a universal power law; when the nonlinearity is strong, this universal critical power depends on the nonlinearity, the shape of the trap and even the dimension. By means of a numerical calculation, a possible bifurcation transition induced by nonlinearity is predicted for both the ground state and the first excited state. (paper)
Codimension-Two Bifurcation, Chaos and Control in a Discrete-Time Information Diffusion Model
Ren, Jingli; Yu, Liping
2016-07-01
In this paper, we present a discrete model to illustrate how two pieces of information interact with online social networks and investigate the dynamics of discrete-time information diffusion model in three types: reverse type, intervention type and mutualistic type. It is found that the model has orbits with period 2, 4, 6, 8, 12, 16, 20, 30, quasiperiodic orbit, and undergoes heteroclinic bifurcation near 1:2 point, a homoclinic structure near 1:3 resonance point and an invariant cycle bifurcated by period 4 orbit near 1:4 resonance point. Moreover, in order to regulate information diffusion process and information security, we give two control strategies, the hybrid control method and the feedback controller of polynomial functions, to control chaos, flip bifurcation, 1:2, 1:3 and 1:4 resonances, respectively, in the two-dimensional discrete system.
Homoclinic bifurcation in a Hodgkin-Huxley model of thermally sensitive neurons
International Nuclear Information System (INIS)
We study global bifurcations of the chaotic attractor in a modified Hodgkin-Huxley model of thermally sensitive neurons. The control parameter for this model is the temperature. The chaotic behavior is realized over a wide range of temperatures and is visualized using interspike intervals. We observe an abrupt increase of the interspike intervals in a certain temperature region. We identify this as a homoclinic bifurcation of a saddle-focus fixed point which is embedded in the chaotic attractors. The transition is accompanied by intermittency, which obeys a universal scaling law for the average length of trajectory segments exhibiting only short interspike intervals with the distance from the onset of intermittency. We also present experimental results of interspike interval measurements taken from the crayfish caudal photoreceptor, which qualitatively demonstrate the same bifurcation structure. (c) 2000 American Institute of Physics
Energy Technology Data Exchange (ETDEWEB)
Nagata, Shun-ichi; Kazekawa, Kiyoshi; Matsubara, Shuko [Fukuoka University Chikushi Hospital, Department of Neurosurgery, Chikushino, Fukuoka (Japan); Sugata, Sei [Bironoki Neurosurgical Hospital, Shibushi, Kagoshima (Japan)
2006-08-15
Obstructions of the supraaortic vessels are an important cause of morbidity associated with a variety of symptoms. Percutaneous transluminal angioplasty has evolved as an effective and safe treatment modality for occlusive lesions of the supraaortic vessels. However, the endovascular management of an innominate bifurcation has not previously been reported. A 53-year-old female with a history of systematic hypertension, diabetes mellitus and hypercholesterolemia presented with left hemiparesis and dysarthria. Angiography of the innominate artery showed a stenosis of the innominate bifurcation. The lesion was successfully treated using the retrograde kissing stent technique via a brachial approach and an exposed direct carotid approach. The retrograde kissing stent technique for the treatment of a stenosis of the innominate bifurcation was found to be a safe and effective alternative to conventional surgery. (orig.)
International Nuclear Information System (INIS)
Obstructions of the supraaortic vessels are an important cause of morbidity associated with a variety of symptoms. Percutaneous transluminal angioplasty has evolved as an effective and safe treatment modality for occlusive lesions of the supraaortic vessels. However, the endovascular management of an innominate bifurcation has not previously been reported. A 53-year-old female with a history of systematic hypertension, diabetes mellitus and hypercholesterolemia presented with left hemiparesis and dysarthria. Angiography of the innominate artery showed a stenosis of the innominate bifurcation. The lesion was successfully treated using the retrograde kissing stent technique via a brachial approach and an exposed direct carotid approach. The retrograde kissing stent technique for the treatment of a stenosis of the innominate bifurcation was found to be a safe and effective alternative to conventional surgery. (orig.)
Resonance near border-collision bifurcations in piecewise-smooth, continuous maps
International Nuclear Information System (INIS)
Mode-locking regions (resonance tongues) formed by border-collision bifurcations of piecewise-smooth, continuous maps commonly exhibit a distinctive sausage-like geometry with pinch points called 'shrinking points'. In this paper we extend our unfolding of the piecewise-linear case [Simpson and Meiss (2009 Nonlinearity 22 1123–44)] to show how shrinking points are destroyed by nonlinearity. We obtain a codimension-three unfolding of this shrinking point bifurcation for N-dimensional maps. We show that the destruction of the shrinking points generically occurs by the creation of a curve of saddle-node bifurcations that smooth one boundary of the sausage, leaving a kink in the other boundary
Phase-flip bifurcation in a coupled Josephson junction neuron system
Segall, Kenneth; Guo, Siyang; Crotty, Patrick; Schult, Dan; Miller, Max
2014-12-01
Aiming to understand group behaviors and dynamics of neural networks, we have previously proposed the Josephson junction neuron (JJ neuron) as a fast analog model that mimics a biological neuron using superconducting Josephson junctions. In this study, we further analyze the dynamics of the JJ neuron numerically by coupling one JJ neuron to another. In this coupled system we observe a phase-flip bifurcation, where the neurons synchronize out-of-phase at weak coupling and in-phase at strong coupling. We verify this by simulation of the circuit equations and construct a bifurcation diagram for varying coupling strength using the phase response curve and spike phase difference map. The phase-flip bifurcation could be observed experimentally using standard digital superconducting circuitry.
Voltage Stability Bifurcation Analysis for AC/DC Systems with VSC-HVDC
Directory of Open Access Journals (Sweden)
Yanfang Wei
2013-01-01
Full Text Available A voltage stability bifurcation analysis approach for modeling AC/DC systems with VSC-HVDC is presented. The steady power model and control modes of VSC-HVDC are briefly presented firstly. Based on the steady model of VSC-HVDC, a new improved sequential iterative power flow algorithm is proposed. Then, by use of continuation power flow algorithm with the new sequential method, the voltage stability bifurcation of the system is discussed. The trace of the P-V curves and the computation of the saddle node bifurcation point of the system can be obtained. At last, the modified IEEE test systems are adopted to illustrate the effectiveness of the proposed method.
Bifurcations and degenerate periodic points in a 3D chaotic fluid flow
Smith, Lachlan D; Lester, Daniel R; Metcalfe, Guy
2016-01-01
Analysis of the periodic points of a conservative periodic dynamical system uncovers the basic kinematic structure of the transport dynamics, and identifies regions of local stability or chaos. While elliptic and hyperbolic points typically govern such behaviour in 3D systems, degenerate (parabolic) points play a more important role than expected. 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, ...
Phase-flip bifurcation in a coupled Josephson junction neuron system
Energy Technology Data Exchange (ETDEWEB)
Segall, Kenneth, E-mail: ksegall@colgate.edu [Department of Physics and Astronomy, Colgate University, Hamilton, NY 13346 (United States); Guo, Siyang; Crotty, Patrick [Department of Physics and Astronomy, Colgate University, Hamilton, NY 13346 (United States); Schult, Dan [Department of Mathematics, Colgate University, Hamilton, NY 13346 (United States); Miller, Max [Department of Physics and Astronomy, Colgate University, Hamilton, NY 13346 (United States)
2014-12-15
Aiming to understand group behaviors and dynamics of neural networks, we have previously proposed the Josephson junction neuron (JJ neuron) as a fast analog model that mimics a biological neuron using superconducting Josephson junctions. In this study, we further analyze the dynamics of the JJ neuron numerically by coupling one JJ neuron to another. In this coupled system we observe a phase-flip bifurcation, where the neurons synchronize out-of-phase at weak coupling and in-phase at strong coupling. We verify this by simulation of the circuit equations and construct a bifurcation diagram for varying coupling strength using the phase response curve and spike phase difference map. The phase-flip bifurcation could be observed experimentally using standard digital superconducting circuitry.
Directory of Open Access Journals (Sweden)
Randhir Singh Baghel
2012-02-01
Full Text Available In this article, we propose a three dimensional mathematical model of phytoplankton dynamics with the help of reaction-diffusion equations that studies the bifurcation and pattern formation mechanism. We provide an analytical explanation for understanding phytoplankton dynamics with three population classes: susceptible, incubated, and infected. This model has a Holling type II response function for the population transformation from susceptible to incubated class in an aquatic ecosystem. Our main goal is to provide a qualitative analysis of Hopf bifurcation mechanisms, taking death rate of infected phytoplankton as bifurcation parameter, and to study further spatial patterns formation due to spatial diffusion. Here analytical findings are supported by the results of numerical experiments. It is observed that the coexistence of all classes of population depends on the rate of diffusion. Also we obtained the time evaluation pattern formation of the spatial system.
Resonance near Border-Collision Bifurcations in Piecewise-Smooth, Continuous Maps
Simpson, D J W
2010-01-01
Mode-locking regions (resonance tongues) formed by border-collision bifurcations of piecewise-smooth, continuous maps commonly exhibit a distinctive sausage-like geometry with pinch points called "shrinking points". In this paper we extend our unfolding of the piecewise-linear case [{\\em Nonlinearity}, 22(5):1123-1144, 2009] to show how shrinking points are destroyed by nonlinearity. We obtain a codimension-three unfolding of this shrinking point bifurcation for $N$-dimensional maps. We show that the destruction of the shrinking points generically occurs by the creation of a curve of saddle-node bifurcations that smooth one boundary of the sausage, leaving a kink in the other boundary.
Bifurcation and neck formation as a precursor to ductile fracture during high rate extension
Energy Technology Data Exchange (ETDEWEB)
Freund, L.B.; Soerensen, N.J. [Brown Univ., Providence, RI (United States)
1997-12-31
A block of ductile material, typically a segment of a plate or shell, being deformed homogeneously in simple plane strain extension commonly undergoes a bifurcation in deformation mode to nonuniform straining in the advanced stages of plastic flow. The focus here is on the influence of material inertia on the bifurcation process, particularly on the formation of diffuse necks as precursors to dynamic ductile fracture. The issue is considered from two points of view, first within the context of the theory of bifurcation of rate-independent, incrementally linear materials and then in terms of the complete numerical solution of a boundary value problem for an elastic-viscoplastic material. It is found that inertia favors the formation of relatively short wavelength necks as observed in shaped charge break-up and dynamic fragmentation.
Cortese, Bernardo; Piraino, Davide; Buccheri, Dario; Alfonso, Fernando
2016-10-01
Bifurcation lesion management still represents a challenge for interventional cardiologists and currently there is a number of different approaches/techniques involving coronary stents. The use of a drug-coated balloon for native coronary vessel management is emerging as an alternative treatment, although in selected patient populations only. In particular, this technology has been tested for the treatment of bifurcations, both for the main vessel and the side branches. Several studies have evaluated this treatment as an alternative or as a therapeutic option complementary to stents, with conflicting and debatable results. However, the perspective of leaving lower metallic burden in this type of lesions is highly appealing and should be deeply investigated. We review here the currently available scientific data and future perspectives on drug-coated balloon use for bifurcation lesions. PMID:27390995
Bifurcation of resistive wall mode dynamics predicted by magnetohydrodynamic-kinetic hybrid theory
International Nuclear Information System (INIS)
The magnetohydrodynamic-kinetic hybrid theory has been extensively and successfully applied for interpreting experimental observations of macroscopic, low frequency instabilities, such as the resistive wall mode, in fusion plasmas. In this work, it is discovered that an analytic version of the hybrid formulation predicts a bifurcation of the mode dynamics while varying certain physical parameters of the plasma, such as the thermal particle collisionality or the ratio of the thermal ion to electron temperatures. This bifurcation can robustly occur under reasonably large parameter spaces as well as with different assumptions, for instance, on the particle collision model. Qualitatively similar bifurcation features are also observed in full toroidal computations presented in this work, based on a non-perturbative hybrid formulation
Bifurcation of resistive wall mode dynamics predicted by magnetohydrodynamic-kinetic hybrid theory
Energy Technology Data Exchange (ETDEWEB)
Yang, S. X.; Wang, Z. X., E-mail: zxwang@dlut.edu.cn [Key Laboratory of Materials Modification by Beams of the Ministry of Education, School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China); Wang, S.; Hao, G. Z., E-mail: haogz@swip.ac.cn; Song, X. M.; Wang, A. K. [Southwestern Institute of Physics, P.O.Box 432, Chengdu 610041 (China); Liu, Y. Q. [Culham Centre for Fusion Energy, Culham Science Centre, Abingdon OX14 3DB (United Kingdom); Southwestern Institute of Physics, P.O.Box 432, Chengdu 610041 (China)
2015-09-15
The magnetohydrodynamic-kinetic hybrid theory has been extensively and successfully applied for interpreting experimental observations of macroscopic, low frequency instabilities, such as the resistive wall mode, in fusion plasmas. In this work, it is discovered that an analytic version of the hybrid formulation predicts a bifurcation of the mode dynamics while varying certain physical parameters of the plasma, such as the thermal particle collisionality or the ratio of the thermal ion to electron temperatures. This bifurcation can robustly occur under reasonably large parameter spaces as well as with different assumptions, for instance, on the particle collision model. Qualitatively similar bifurcation features are also observed in full toroidal computations presented in this work, based on a non-perturbative hybrid formulation.
Hybrid control of bifurcation and chaos in stroboscopic model of Internet congestion control system
International Nuclear Information System (INIS)
Interaction between transmission control protocol (TCP) and random early detection (RED) gateway in the Internet congestion control system has been modelled as a discrete-time dynamic system which exhibits complex bifurcating and chaotic behaviours. In this paper, a hybrid control strategy using both state feedback and parameter perturbation is employed to control the bifurcation and stabilize the chaotic orbits embedded in this discrete-time dynamic system of TCP/RED. Theoretical analysis and numerical simulations show that the bifurcation is delayed and the chaotic orbits are stabilized to a fixed point, which reliably achieves a stable average queue size in an extended range of parameters and even completely eliminates the chaotic behaviour in a particular range of parameters. Therefore it is possible to decrease the sensitivity of RED to parameters. By using the hybrid strategy, we may improve the stability and performance of TCP/RED congestion control system significantly
Bigoni, D; Noselli, G; Zaccaria, D
2012-01-01
Bifurcation of an elastic structure crucially depends on the curvature of the constraints against which the ends of the structure are prescribed to move, an effect which deserves more attention than it has received so far. In fact, we show theoretically and we provide definitive experimental verification that an appropriate curvature of the constraint over which the end of a structure has to slide strongly affects buckling loads and can induce: (i.) tensile buckling; (ii.) decreasing- (softening), increasing- (hardening), or constant-load (null stiffness) postcritical behaviour; (iii.) multiple bifurcations, determining for instance two bifurcation loads (one tensile and one compressive) in a single-degree-of-freedom elastic system. We show how to design a constraint profile to obtain a desired postcritical behaviour and we provide the solution for the elastica constrained to slide along a circle on one end, representing the first example of an inflexional elastica developed from a buckling in tension. These ...
Institute of Scientific and Technical Information of China (English)
ZHANG Qichang; HE Xuejun; HAO Shuying
2006-01-01
The simplest normal form of resonant double Hopf bifurcation was studied based on Lie operator.The coefficients of the simplest normal forms of resonant double Hopf bifurcation and the nonlinear transformations in terms of the original system coefficients were given explicitly.The nonlinear transformations were used for reducing the lower-and higher-order normal forms, and the rank of system matrix was used to determine the coefficient of normal form which could be reduced.These make the gained normal form simpler than the traditional one.A general program was compiled with Mathematica.This program can compute the simplest normal form of resonant double Hopf bifurcation and the non-resonant form up to the 7th order.
Nemeth, Michael P.
2010-01-01
A comprehensive development of nondimensional parameters and equations for nonlinear and bifurcations analyses of quasi-shallow shells, based on the Donnell-Mushtari-Vlasov theory for thin anisotropic shells, is presented. A complete set of field equations for geometrically imperfect shells is presented in terms general of lines-of-curvature coordinates. A systematic nondimensionalization of these equations is developed, several new nondimensional parameters are defined, and a comprehensive stress-function formulation is presented that includes variational principles for equilibrium and compatibility. Bifurcation analysis is applied to the nondimensional nonlinear field equations and a comprehensive set of bifurcation equations are presented. An extensive collection of tables and figures are presented that show the effects of lamina material properties and stacking sequence on the nondimensional parameters.
Fridjonsson, Einar O.; Seymour, Joseph D.; Cokelet, Giles R.; Codd, Sarah L.
2011-05-01
The flow and distribution of Newtonian, polymeric and colloid suspension fluids at low Reynolds numbers in bifurcations has importance in a wide range of disciplines, including microvascular physiology and microfluidic devices. A bifurcation consisting of circular capillaries laser etched into a hard polymer with inlet diameter 2.50 ± 0.01 mm, bifurcating to a small diameter outlet of 0.76 ± 0.01 mm and a large diameter outlet of 1.25 ± 0.01 mm is examined. Four distinct fluids (water, 0.25%wt xanthan gum, 8 and 22%vol hard-sphere colloidal suspensions) are flowed at flow rates from 10 to 30 ml/h corresponding to Reynolds numbers based on the entry flow from 0.001 to 8. PGSE NMR techniques are applied to obtain dynamic images of the fluids inside the bifurcation with spatial resolution of 59 × 59 μm/pixel in plane over a 200-μm-thick slice. Velocity in all three spatial directions is examined to determine the impact of secondary flows and characterize the transport in the bifurcation. The velocity data provide direct measurement of the volumetric distribution of the flow between the two channels as a function of flow rate. Water and the 8% colloidal suspension show a constant distribution with increasing flow rate, the xanthan gum shows an increase in fluid going into the larger outlet with higher flow rate, and the 22% colloidal suspension shows a decrease in fluid entering the larger channel with higher flow rate. For the colloidal particle flow, the distribution of colloid particles down the capillary is determined by examining the spectrally resolved propagator for the oil inside the core-shell particles in a direction perpendicular to the axial flow. Using dynamic magnetic resonance microscopy, the potential for using magnetic resonance for "particle counting" in a microscale bifurcation is thus demonstrated.
International Nuclear Information System (INIS)
The coexistence of a resting condition and period-1 firing near a subcritical Hopf bifurcation point, lying between the monostable resting condition and period-1 firing, is often observed in neurons of the central nervous systems. Near such a bifurcation point in the Morris—Lecar (ML) model, the attraction domain of the resting condition decreases while that of the coexisting period-1 firing increases as the bifurcation parameter value increases. With the increase of the coupling strength, and parameter and initial value dependent synchronization transition processes from non-synchronization to compete synchronization are simulated in two coupled ML neurons with coexisting behaviors: one neuron chosen as the resting condition and the other the coexisting period-1 firing. The complete synchronization is either a resting condition or period-1 firing dependent on the initial values of period-1 firing when the bifurcation parameter value is small or middle and is period-1 firing when the parameter value is large. As the bifurcation parameter value increases, the probability of the initial values of a period-1 firing neuron that lead to complete synchronization of period-1 firing increases, while that leading to complete synchronization of the resting condition decreases. It shows that the attraction domain of a coexisting behavior is larger, the probability of initial values leading to complete synchronization of this behavior is higher. The bifurcations of the coupled system are investigated and discussed. The results reveal the complex dynamics of synchronization behaviors of the coupled system composed of neurons with the coexisting resting condition and period-1 firing, and are helpful to further identify the dynamics of the spatiotemporal behaviors of the central nervous system. (general)
Onset of normal and inverse homoclinic bifurcation in a double plasma system near a plasma fireball
Mitra, Vramori; Sarma, Bornali; Sarma, Arun; Janaki, M. S.; Sekar Iyengar, A. N.
2016-03-01
Plasma fireballs are generated due to a localized discharge and appear as a luminous glow with a sharp boundary, which suggests the presence of a localized electric field such as electrical sheath or double layer structure. The present work reports the observation of normal and inverse homoclinic bifurcation phenomena in plasma oscillations that are excited in the presence of fireball in a double plasma device. The controlling parameters for these observations are the ratio of target to source chamber (nT/nS) densities and applied electrode voltage. Homoclinic bifurcation is noticed in the plasma potential fluctuations as the system evolves from narrow to long time period oscillations and vice versa with the change of control parameter. The dynamical transition in plasma fireball is demonstrated by spectral analysis, recurrence quantification analysis (RQA), and statistical measures, viz., skewness and kurtosis. The increasing trend of normalized variance reflects that enhancing nT/nS induces irregularity in plasma dynamics. The exponential growth of the time period is strongly indicative of homoclinic bifurcation in the system. The gradual decrease of skewness and increase of kurtosis with the increase of nT/nS also reflect growing complexity in the system. The visual change of recurrence plot and gradual enhancement of RQA variables DET, Lmax, and ENT reflects the bifurcation behavior in the dynamics. The combination of RQA and spectral analysis is a clear evidence that homoclinic bifurcation occurs due to the presence of plasma fireball with different density ratios. However, inverse bifurcation takes place due to the change of fireball voltage. Some of the features observed in the experiment are consistent with a model that describes the dynamics of ionization instabilities.
Model generation of coronary artery bifurcations from CTA and single plane angiography
Energy Technology Data Exchange (ETDEWEB)
Cardenes, Ruben; Diez, Jose L.; Duchateau, Nicolas; Pashaei, Ali; Frangi, Alejandro F. [Center for Computational Imaging and Simulation Technologies in Biomedicine (CISTIB)-Universitat Pompeu Fabra and Networking Biomedical Research Center on Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN), Barcelona 08018 (Spain); Cardiology Department, University Hospital Dr. Peset, Valencia 46017 (Spain); Hospital Clinic Provincial de Barcelona, Institut d' investigacions Biomediques August Pi i Sunyer-Universitat de Barcelona, Barcelona 08036 (Spain); Center for Computational Imaging and Simulation Technologies in Biomedicine (CISTIB)-Universitat Pompeu Fabra and Networking Biomedical Research Center on Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN), Barcelona 08018 (Spain); Center for Computational Imaging and Simulation Technologies in Biomedicine (CISTIB)-Universitat Pompeu Fabra and Networking Biomedical Research Center on Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN), Barcelona 08018, Spain and Department of Mechanical Engineering, University of Sheffield, Sheffield S1 3JD (United Kingdom)
2013-01-15
Purpose: To generate accurate and realistic models of coronary artery bifurcations before and after percutaneous coronary intervention (PCI), using information from two image modalities. Because bifurcations are regions where atherosclerotic plaque appears frequently and intervention is more challenging, generation of such realistic models could be of high value to predict the risk of restenosis or thrombosis after stent implantation, and to study geometrical and hemodynamical changes. Methods: Two image modalities have been employed to generate the bifurcation models: computer tomography angiography (CTA) to obtain the 3D trajectory of vessels, and 2D conventional coronary angiography (CCA) to obtain radius information of the vessel lumen, due to its better contrast and image resolution. In addition, CCA can be acquired right before and after the intervention in the operation room; therefore, the combination of CTA and CCA allows the generation of realistic preprocedure and postprocedure models of coronary bifurcations. The method proposed is semiautomatic, based on landmarks manually placed on both image modalities. Results: A comparative study of the models obtained with the proposed method with models manually obtained using only CTA, shows more reliable results when both modalities are used together. The authors show that using preprocedure CTA and postprocedure CCA, realistic postprocedure models can be obtained. Analysis carried out of the Murray's law in all patient bifurcations shows the geometric improvement of PCI in our models, better than using manual models from CTA alone. An experiment using a cardiac phantom also shows the feasibility of the proposed method. Conclusions: The authors have shown that fusion of CTA and CCA is feasible for realistic generation of coronary bifurcation models before and after PCI. The method proposed is efficient, and relies on minimal user interaction, and therefore is of high value to study geometric and
Institute of Scientific and Technical Information of China (English)
Nan Zhang; Tong Qiu; Bingzhen Chen
2015-01-01
The major difficulty in achieving good performance of industrial polymerization reactors lies in the lack of under-standing of their nonlinear dynamics and the lack of wel-developed techniques for the control of nonlinear pro-cesses, which are usually accompanied with bifurcation phenomenon. This work aims at investigating the nonlinear behavior of the parameterized nonlinear system of vinyl acetate polymerization and further modifying the bifurcation characteristics of this process via a washout filter-aid control er, with all the original steady state equilibria preserved. Advantages and possible extensions of the proposed methodology are discussed to provide scientific guide for further controller design and operation improvement.
Observation of bifurcation property of radial electric field using a heavy ion beam probe in CHS
International Nuclear Information System (INIS)
Bifurcation nature of potential profile of a toroidal helical plasma is investigated in the Compact Helical System (CHS), using a heavy ion beam probe. The measurements reveal that there exist three main branches of potential profiles in electron cyclotron resonance (ECR) heated plasmas with low density of ne∼0.5x1013cm-3. The branches with higher central potential exhibit a rather strong radial electric field shear that should result in fluctuation reduction and formation of transport barrier. Lissajous expression is useful to extract the bifurcation characteristics of potential structure. (author)
Jiang, Heping; Jiang, Jiao; Song, Yongli
In this paper, we firstly employ the normal form theory of delayed differential equations according to Faria and Magalhães to derive the normal form of saddle-node-Hopf bifurcation for the general retarded functional differential equations. Then, the dynamical behaviors of a Leslie-Gower predator-prey model with time delay and nonmonotonic functional response are considered. Specially, the dynamical classification near the saddle-node-Hopf bifurcation point is investigated by using the normal form and the center manifold approaches. Finally, the numerical simulations are employed to support the theoretical results.
Codimension 3 nonresonant bifurcations of homoclinic orbits with two inclination flips
Institute of Scientific and Technical Information of China (English)
SHUI; Shuliang; ZHU; Deming
2005-01-01
Homoclinic bifurcations in four-dimensional vector fields are investigated by setting up a local coordinate near a homoclinic orbit. This homoclinic orbit is principal but its stable and unstable foliations take inclination flip. The existence, nonexistence, and uniqueness of the 1-homoclinic orbit and 1-periodic orbit are studied. The existence of the two-fold 1-periodic orbit and three-fold 1 -periodic orbit are also obtained. It is indicated that the number of periodic orbits bifurcated from this kind of homoclinic orbits depends heavily on the strength of the inclination flip.
DEFF Research Database (Denmark)
Willerslev, Anne; Li, Xiao Q; Munch, Inger C;
2014-01-01
from the population-based, observational Copenhagen Child Cohort 2000 study. RESULTS: The blood stream in retinal arteries maintains a figure-of-8 SD-OCT profile consistent with a laminar flow in concentric sheets and a parabolic velocity distribution up to the point of divergence at arterial...... bifurcations. In contrast, the blood stream at the site of confluence of two retinal veins remains divided into two parallel sets of sheets with separate velocity distribution for a downstream distance of at least four trunk vessel diameters. Consequently, retinal trunk vessels near bifurcations...
Hopf bifurcation analysis and circuit implementation for a novel four-wing hyper-chaotic system
International Nuclear Information System (INIS)
In the paper, a novel four-wing hyper-chaotic system is proposed and analyzed. A rare dynamic phenomenon is found that this new system with one equilibrium generates a four-wing-hyper-chaotic attractor as parameter varies. The system has rich and complex dynamical behaviors, and it is investigated in terms of Lyapunov exponents, bifurcation diagrams, Poincaré maps, frequency spectrum, and numerical simulations. In addition, the theoretical analysis shows that the system undergoes a Hopf bifurcation as one parameter varies, which is illustrated by the numerical simulation. Finally, an analog circuit is designed to implement this hyper-chaotic system. (general)
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
investigation in the present paper is the dynamical model of a constant voltage converter which represents a three-dimensional piecewise-smooth system of nonautonomous differential equations. A specific type of phenomena that arise in the dynamics of piecewise-smooth systems are the so-called border....... 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....
Directory of Open Access Journals (Sweden)
Jianguo Ren
2014-01-01
Full Text Available A new computer virus propagation model with delay and incomplete antivirus ability is formulated and its global dynamics is analyzed. The existence and stability of the equilibria are investigated by resorting to the threshold value R0. By analysis, it is found that the model may undergo a Hopf bifurcation induced by the delay. Correspondingly, the critical value of the Hopf bifurcation is obtained. Using Lyapunov functional approach, it is proved that, under suitable conditions, the unique virus-free equilibrium is globally asymptotically stable if R01. Numerical examples are presented to illustrate possible behavioral scenarios of the mode.
Quelques problèmes de stabilité et de bifurcation des solides visqueux
ABED-MERAIM, Farid
1999-01-01
This PhD thesis is composed essentially of two main parts, of unequal sizes, which are summarized as follows: Part I: It is concerned with stability and bifurcation issues relating to strain-rate-independent solids and structures (i.e., elastic or elasto-plastic). A thorough and comprehensive review of the various investigations in this field allowed us to propose an original and compact presentation of the theory of stability and bifurcation. An illustration of this theory is then shown thro...
Hopf bifurcation control for a coupled nonlinear relative rotation system with time-delay feedbacks
Liu, Shuang; Li, Xue; Tan, Shu-Xian; Li, Hai-Bin
2014-10-01
This paper investigates the Hopf bifurcations resulting from time delay in a coupled relative-rotation system with time-delay feedbacks. Firstly, considering external excitation, the dynamical equation of relative rotation nonlinear dynamical system with primary resonance and 1:1 internal resonance under time-delay feedbacks is deduced. Secondly, the averaging equation is obtained by the multiple scales method. The periodic solution in a closed form is presented by a perturbation approach. At last, numerical simulations confirm that time-delay theoretical analyses have influence on the Hopf bifurcation point and the stability of periodic solution.
Bifurcation and chaos in a ratio-dependent predator-prey system with time delay
International Nuclear Information System (INIS)
In this paper, a ratio-dependent predator-prey model with time delay is investigated. We first consider the local stability of a positive equilibrium and the existence of Hopf bifurcations. By using the normal form theory and center manifold reduction, we derive explicit formulae which determine the stability, direction and other properties of bifurcating periodic solutions. Finally, we consider the effect of impulses on the dynamics of the above time-delayed population model. Numerical simulations show that the system with constant periodic impulsive perturbations admits rich complex dynamic, such as periodic doubling cascade and chaos.
Side-branch technique for difficult guidewire placement in coronary bifurcation lesion.
He, Xingwei; Gao, Bo; Liu, Yujian; Li, Zhuxi; Zeng, Hesong
2016-01-01
Despite tremendous advances in technology and skills, percutaneous coronary intervention (PCI) of bifurcation lesion (BL) remains a particular challenge for the interventionalist. During bifurcation PCI, safe guidewire placement in the main branch (MB) and the side branch (SB) is the first step for successful procedure. However, in certain cases, the complex pattern of vessel anatomy and the mix of plaque distribution may make target vessel wiring highly challenging. Therefore, specific techniques are required for solving this problem. Hereby, we describe a new use of side-branch technique for difficult guidewire placement in BL. PMID:25842349
Study on two-phase natural circulation flow instability by using Bifurcation Theory
International Nuclear Information System (INIS)
Through the concept of characteristic flow rate (CFR) a nonlinear analysis method--Bifurcation Theory could be used to analyze the thermo-hydraulic instability of Two-phase Natural Circulation Flow (TPNCF) systems. By constructing solution diagram of dynamic system based on CFR (Xu et al, 1994), the stable and unstable flow regimes can be described and the transition boundaries can be predicted in terms of real bifurcation method. The theoretical predictions agree fairly well with experimental results reported by Xu (1994). Further research for wider range of parameters is desirable