Hopf Bifurcation Control of a Hyperchaotic Circuit System

This paper is concerned with the Hopf bifurcation control of a new hyperchaotic circuit system. The stability of the hyperchaotie circuit system depends on a selected control parameter is studied, and the critical value of the system parameter at which Hopf bifurcation occurs is investigated. Theoretical analysis give the stability of the Hopf bifurcation. In particular, washout filter aided feedback controllers are designed for delaying the bifurcation point and ensuring the stability of the bifurcated limit cycles. An important feature of the control laws is that they do not result in any change in the set of equilibria. Computer simulation results are presented to confirm the analytical predictions.     

Hopf Bifurcation Control of a Hyperchaotic Circuit System

This paper is concerned with the Hopf bifurcation control of a newhyperchaotic circuit system. The stability of the hyperchaotic circuit system depends on a selected control parameter is studied, and the critical value of the system parameter at which Hopf bifurcation occurs is investigated. Theoretical analysis give the stability of the Hopf bifurcation. In particular, washout filter aided feedback controllers are designed for delaying the bifurcation point and ensuring the stability of the bifurcated limit cycles. Animportant feature of the control laws is that they do not result in any change in the set of equilibria. Computer simulation results are presented to confirm the analytical predictions.     

平移法控制离散系统的倍周期分岔和混沌

利用平移系统的方法,实现了对离散非线性动力学系统的倍周期分岔的控制和混沌吸引子不稳定周期轨道的控制.只要选择适当的平移参数,使系统平移到不同位置,就可将系统控制在不同的预期轨道.将此方法应用到Logistic映射和Henon映射中取得了很好的控制效果.     

Hopf Bifurcation in a New Four-Dimensional Hyperchaotic System

In this paper, the Hopf bifurcation in a new hyperchaotic system is studied. Based on the first Lya-punov 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.     

基于状态反馈控制的无线网络拥塞控制流体流模型的Hopf分岔

针对控制无线网络拥塞控制系统中流体流模型的Hopf分岔的问题,提出一种状态反馈控制器.通过选择通信时延作为分岔参数,验证模型在加入状态反馈控制器后,①增加了分岔参数的临界值,扩大了稳定性区域,使系统的Hopf分岔延迟;②通过选择合适的参数,可以容易地改变分岔周期解的稳定性及其分岔方向.理论分析和数据仿真验证了该方法能够有效地控制系统的Hopf分岔.     

Bifurcation analysis and control of periodic solutions changing into invariant tori in Langford system

Bifurcation characteristics of the Langford system in a general form are systematically analysed, and nonlinear controls of periodic solutions changing into invariant tori in this system are achieved. Analytical relationship between control gain and bifurcation parameter is obtained. Bifurcation diagrams are drawn, showing the results of control for secondary Hopf bifurcation and sequences of bifurcations route to chaos. Numerical simulations of quasi-periodic tori validate analytic predictions.     

忆阻器混沌电路产生的共存吸引子与Hopf分岔

利用荷控忆阻器和一个电感串联设计一种新型浮地忆阻混沌电路.用常规动力学分析方法研究该系统的基本动力学特性,发现系统可以产生一对关于原点对称的"心"型吸引子.将观察混沌吸引子时关注的电压、电流推广到功率和能量信号,观察到蝴蝶结型奇怪吸引子的产生.理论分析Hopf分岔行为并通过数值仿真进行验证,结果表明系统随电路参数变化能产生Hopf分岔、反倍周期分岔两种分岔行为.相对于其它忆阻混沌电路该电路采用的是一个浮地型忆阻器,并且在初始状态改变时,能产生共存吸引子和混沌吸引子与周期极限环共存现象.     

Numerical Approximation of Hopf Bifurcation for Tumor-Immune System Competition Model with Two Delays

This paper is concerned with the Hopf bifurcation analysis of tumor-immune system competition model with two delays. First, we discuss the stability of state points with different kinds of delays. Then, a sufficient condition to the existence of the Hopf bifurcation is derived with parameters at different points. Furthermore, under this condition, the stability and direction of bifurcation are determined by applying the normal form method and the center manifold theory. Finally, a kind of Runge-Kutta methods is given out to simulate the periodic solutions numerically. At last, some numerical experiments are given to match well with the main conclusion of this paper.     

二维正弦离散映射的分岔和吸引子

由一个正弦映射和一个三次方映射通过非线性耦合,构成一个新的二维正弦离散映射. 基于此二维正弦离散映射得到系统的不动点以及相应的特征值,分析了系统的稳定性,研究了系统的复杂非线性动力学行为及其吸引子的演变过程. 研究结果表明：此二维正弦离散映射中存在复杂的对称性破缺分岔、Hopf分岔、倍周期分岔和周期振荡快慢效应等非线性物理现象. 进一步根据控制变量变化时系统的分岔图、Lyapunov指数图和相轨迹图分析了系统的分岔模式共存、快慢周期振荡及其吸引子的演变过程,通过数值仿真验证了理论分析的正确性. 关键词： 正弦离散映射 对称性破缺分岔 Hopf分岔 吸引子     

Bifurcation and stability of an improved time-delayed fluid flow model in internet congestion control

Based on the fluid flow time-delayed model proposed by Misra et al in internet congestion control, one modified time-delayed model is presented, where the influence of the communication delay on the router queue length is investigated in detail. The main advantage of the new model is that its stability domain is larger even without an extra controller. By linear stability analysis and numerical simulation, the effectiveness and feasibility of the novel model in internet congestion control are verified.     

Chaotic dynamic behavior analysis and control for a financial risk system

According to the risk management process of financial markets,a financial risk dynamic system is constructed in this paper.Through analyzing the basic dynamic properties,we obtain the conditions for stability and bifurcation of the system based on Hopf bifurcation theory of nonlinear dynamic systems.In order to make the system’s chaos disappear,we select the feedback gain matrix to design a class of chaotic controller.Numerical simulations are performed to reveal the change process of financial market risk.It is shown that,when the parameter of risk transmission rate changes,the system gradually comes into chaos from the asymptotically stable state through bifurcation.The controller can then control the chaos effectively.     

Chaos Control in a New Three-Dimensional Chaotic T System

In this paper, we study chaos control of the new 3D chaotic system. We use three feedback methods （the linear, speed, doubly-periodic function controller） to suppress the chaos to unstable equilibrium. As a result, some controllers are obtained. Moreover, numerical simulations are used to verify the effectiveness of the obtained controllers.     

Amplitude control of limit cycle in a van der Pol Duffing system

This paper applies washout filter technology to amplitude control of limit cycles emerging from Hopf bifurcation of the van der Pol--Duffing system. The controlling parameters for the appearance of Hopf bifurcation are given by the Routh--Hurwitz criteria. Noticeably, numerical simulation indicates that the controllers control the amplitude of limit cycles not only of the weakly nonlinear van der Pol--Duffing system but also of the strongly nonlinear van der Pol--Duffing system. In particular, the emergence of Hopf bifurcation can be controlled by a suitable choice of controlling parameters. Gain-amplitude curves of controlled systems are also drawn.     

Bifurcation and chaos analysis of a nonlinear electromechanical coupling relative rotation system

Hopf bifurcation and chaos of a nonlinear electromechanical coupling relative rotation system are studied in this paper. Considering the energy in air-gap field of AC motor, the dynamical equation of nonlinear electromechanical coupling relative rotation system is deduced by using the dissipation Lagrange equation. Choosing the electromagnetic stiffness as a bifurcation parameter, the necessary and sufficient conditions of Hopf bifurcation are given, and the bifurcation characteristics are studied. The mechanism and conditions of system parameters for chaotic motions are investigated rigorously based on the Silnikov method, and the homoclinic orbit is found by using the undetermined coefficient method. Therefore, Smale horseshoe chaos occurs when electromagnetic stiffness changes. Numerical simulations are also given, which confirm the analytical results.     

状态反馈控制声光双稳系统的倍周期分岔和混沌

设计了一种动力学状态反馈(DSF)方法控制非线性混沌系统.介绍了DSF方法的控制原理,并用此方法控制声光双稳(AOB)系统的混沌,以此验证其有效性.仿真模拟显示,通过选择恰当的控制参数,有效地实现了声光双稳(AOB)系统中倍周期分岔的延迟控制和混沌吸引子中原不稳定周期轨道的稳定控制,同时,还可以将系统控制在2np、3mp 和2np×3mp这样其它任意所需的周期轨道上.     

一个三时滞生物捕食被捕食系统分岔的混合控制

针对多时滞捕食被捕食系统的Hopf分岔控制问题,提出一种基于状态反馈和参数调节的混合控制方法,这种混合控制方法可以延迟有害Hopf分岔的发生或使Hopf分岔消失.分析了该控制系统的稳定性和Hopf分岔的存在性,并通过规范型理论和中心流形定理,给出了分岔周期解的稳定性和分岔方向的计算公式.最后通过数值模拟验证了该理论的正确性. 关键词： 时滞 捕食被捕食系统 Hopf分岔 混合控制     

一类惯性神经网络的分岔与控制

本文讨论了一类三阶惯性神经网络的稳定性和分岔问题. 利用灵敏度理论,确定了合适的Hopf 分岔参数. 基于Routh-Hurwitz判据和分岔理论,给出了系统稳定性、发生Hopf分岔以及产生静态分岔的条件. 数值模拟不仅验证了理论分析的正确性,还说明了所设计的单节点时滞反馈控制器不仅能延迟网络分岔的发生,还能改变极限环的振幅. 关键词： 惯性神经网络 稳定性 时滞反馈控制 Hopf分岔     

具有对应分段系统和指数系统的新混沌系统的Hopf分岔控制研究

为进一步了解一个复杂的有不稳定奇点的三维动力系统在Hopf分岔点附近的非线性特性,采用非线性控制器,提出了相应的控制系统,使得受控系统可能发生余维一、余维二和余维三的Hopf分岔.通过严格的数学推导给出了受控系统发生分岔的参数条件,证明了可控制系统在指定区域内发生退化分岔和可调控分岔的稳定性.     

Hopf bifurcations in time-delay systems with band-limited feedback

We investigate the steady-state solution and its bifurcations in time-delay systems with band-limited feedback. This is a first step in a rigorous study concerning the effects of AC-coupled components in nonlinear devices with time-delayed feedback. We show that the steady state is globally stable for small feedback gain and that local stability is lost, generically, through a Hopf bifurcation for larger feedback gain. We provide simple criteria that determine whether the Hopf bifurcation is supercritical or subcritical based on the knowledge of the first three terms in the Taylor-expansion of the nonlinearity. Furthermore, the presence of double-Hopf bifurcations of the steady state is shown, which indicates possible quasiperiodic and chaotic dynamics in these systems. As a result of this investigation, we find that AC-coupling introduces fundamental differences to systems of Ikeda-type [K. Ikeda, K. Matsumoto, High-dimensional chaotic behavior in systems with time-delayed feedback, Physica D 29 (1987) 223–235] already at the level of steady-state bifurcations, e.g. bifurcations exist in which limit cycles are created with periods other than the fundamental “period-2” mode found in Ikeda-type systems.