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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
Zhusubaliyev, Zhanybai T.; Mosekilde, Erik; Yanochkina, Olga O.
2011-01-01
embedded one into the other and with their basins of attraction delineated by intervening repelling tori. The paper illustrates the coexistence of three stable tori with different resonance behaviors and shows how reconstruction of these tori takes place across the borders of different dynamical regimes....... The paper also demonstrates how pairs of attracting and repelling tori emerge through border-collision torus-birth and border-collision torus-fold bifurcations. © 2011 World Scientific Publishing Company....
Perturbed period-doubling bifurcation. I. Theory
Svensmark, Henrik; Samuelsen, Mogens Rugholm
1990-01-01
-defined way that is a function of the amplitude and the frequency of the signal. New scaling laws between the amplitude of the signal and the detuning δ are found; these scaling laws apply to a variety of quantities, e.g., to the shift of the bifurcation point. It is also found that the stability 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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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?
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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...
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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’
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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'
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
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
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
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
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
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.
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...
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
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
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
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
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.