Analysis of stochastic bifurcation and chaos in stochastic Duffing--van der Pol system via Chebyshev polynomial approximation

The Chebyshev polynomial approximation is applied to investigate the stochastic period-doubling bifurcation and chaos problems of a stochastic Duffing--van der Pol system with bounded random parameter of exponential probability density function subjected to a harmonic excitation. Firstly the stochastic system is reduced into its equivalent deterministic one, and then the responses of stochastic system can be obtained by numerical methods. Nonlinear dynamical behaviour related to stochastic period-doubling bifurcation and chaos in the stochastic system is explored. Numerical simulations show that similar to its counterpart in deterministic nonlinear system of stochastic period-doubling bifurcation and chaos may occur in the stochastic Duffing--van der Pol system even for weak intensity of random parameter. Simply increasing the intensity of the random parameter may result in the period-doubling bifurcation which is absent from the deterministic system.     

The bifurcation threshold value of the chaos detection system for a weak signal

Recently, it has become an important problem to confirm the bifurcation threshold value of a chaos detection system for a weak signal in the fields of chaos detection. It is directly related to whether the results of chaos detection are correct or not. In this paper, the discrimination system for the dynamic behaviour of a chaos detection system for a weak signal is established by using the theory of linear differential equation with periodic coefficients and computing the Lyapunov exponents of the chaos detection system; and then, the movement state of the chaos detection system is defined. The simulation experiments show that this method can exactly confirm the bifurcation threshold value of the chaos detection system.     

The bifurcation threshold value of the chaos detection system for a weak signal＊

Recently, it has become an important problem to confirm the bifurcation threshold value of a chaos detectionsystem for a weak signal in the fields of chaos detection. It is directly related to whether the results of chaos detectionare correct or not. In this paper, the discrimination system for the dynamic behaviour of a chaos detection system fora weak signal is established by using the theory of linear differential equation with periodic coefficients and computingthe Lyapunov exponents of the chaos detection system; and then, the movement state of the chaos detection system isdefined. The simulation experiments show that this method can exactly confirm the bifurcation threshold value of thechaos detection svstem.     

Effect of metal oxide arrester on the chaotic oscillations in the voltage transformer with nonlinear core loss model using chaos theory

In this paper, controlling chaos when chaotic ferroresonant oscillations occur in a voltage transformer with nonlinear core loss model is performed. The effect of a parallel metal oxide surge arrester on the ferroresonance oscillations of voltage transformers is studied. The metal oxide arrester(MOA) is found to be effective in reducing ferroresonance chaotic oscillations. Also the multiple scales method is used to analyze the chaotic behavior and different types of fixed points in ferroresonance of voltage transformers considering core loss. This phenomenon has nonlinear chaotic dynamics and includes sub-harmonic, quasi-periodic, and also chaotic oscillations. In this paper, the chaotic behavior and various ferroresonant oscillation modes of the voltage transformer is studied. This phenomenon consists of different types of bifurcations such as period doubling bifurcation(PDB), saddle node bifurcation(SNB), Hopf bifurcation(HB), and chaos. The dynamic analysis of ferroresonant circuit is based on bifurcation theory. The bifurcation and phase plane diagrams are illustrated using a continuous method and linear and nonlinear models of core loss. To analyze ferroresonance phenomenon, the Lyapunov exponents are calculated via the multiple scales method to obtain Feigenbaum numbers. The bifurcation diagrams illustrate the variation of the control parameter. Therefore, the chaos is created and increased in the system.     

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.     

Phase Desynchronization as a Mechanism for Transitions to High—Dimensional Chaos

Phase is an important degree of freedom in studies of chaotic oscillations.Phase coherence and localization in coupled chaotic elements are studied.It is shown that phase desynchronization is a key mechanism responsible for the transitions from low-to high-dimensional chaos.The route from low-dimensional chaos to high-dimensional toroidal chaos is accompanied by a cascade of phase desynchronizations.Phase synchronization tree is adopted to exhibit the entrainment process.This bifurcation tree implies an intrinsic cascade of order embedded in irregular motions.     

Bifurcation,chaotic phenomena and control of chaos in a one—dimensional discrete Josephson lattice

We have investigated the fluxon dynamical behaviour in a one-dimensional parallel array of small Josephson junctions in the presence of an externally applied magnetic field. In the case of high damping,the system is in stable state. On the contrary, in the case of low damping, bifurcation and chaotic phenomena have been observed. Control of chaos is achieved by a delayed feedback mechanism, which drives the chaotic system into a selected unstable periodic orbit embadded within the associated strange attractor. It is attractive to control chaos to a periodic state, rather than operating always outside the device parameter space where chaos dominates.     

Hyperchaos--chaos--Hyperchaos Transition in a Class of On--Off Intermittent Systems Driven by a Family of Generalized Lorenz Systems

Blowout bifurcation in nonlinear systems occurs when a chaotic attractor lying in some symmetric subspace becomes transversely unstable. A class of five-dimensional continuous autonomous systems is considered, in which a two-dimensional subsystem is driven by a family of generalized Lorenz systems. The systems have some common dynamical characters. As the coupling parameter changes, blowout bifurcations occur in these systems and brings on change of the systems＇ dynamics. After the bifurcation the phenomenon of on-off intermittency appears. It is observed that the systems undergo a symmetric hyperchaos-chaos-hyperchaos transition via or after blowout bifurcations. An example of the systems is given, in which the drive system is the Chen system. We investigate the dynamical behaviour before and after the blowout bifurcation in the systems and make an analysis of the transition process. It is shown that in such coupled chaotic continuous systems, blowout bifurcation leads to a transition from chaos to hyperchaos for the whole systems, which provides a route to hyperchaos.     

Effect of metal oxide arrester on the chaotic oscillations in the voltage transformer with nonlinear core loss model using chaos theory Effect of metal oxide arrester on the chaotic oscillations in the voltage transformer with nonlinear core loss model using chaos theory

In this paper, controlling chaos when chaotic ferroresonant oscillations occur in a voltage transformer with nonlin- ear core loss model is performed. The effect of a parallel metal oxide surge arrester on the ferroresonance oscillations of voltage transformers is studied. The metal oxide arrester （MOA） is found to be effective in reducing ferroresonance chaotic oscillations. Also the multiple scales method is used to analyze the chaotic behavior and different types of fixed points in ferroresonance of voltage transformers considering core loss. This phenomenon has nonlinear chaotic dynamics and includes sub-harmonic, quasi-periodic, and also chaotic oscillations. In this paper, the chaotic behavior and various ferroresonant oscillation modes of the voltage transformer is studied. This phenomenon consists of different types of bifur- cations such as period doubling bifurcation （PDB）, saddle node bifurcation （SNB）, Hopf bifurcation （HB）, and chaos. The dynamic analysis of ferroresonant circuit is based on bifurcation theory. The bifurcation and phase plane diagrams are il- lustrated using a continuous method and linear and nonlinear models of core loss. To analyze ferroresonance phenomenon, the Lyapunov exponents are calculated via the multiple scales method to obtain Feigenbaum numbers. The bifurcation diagrams illustrate the variation of the control parameter. Therefore, the chaos is created and increased in the system.     

Characteristics of Period-Adding Bursting Bifurcation Without Chaos in the Chay Neuron Model

A period-adding bursting sequence without bursting-chaos in the Chay neuron model is studied by bifurcation analysis. The genesis of each periodic bursting is separately evoked by the corresponding periodic spiking patterns through two period-doubling bifurcations, except for the period-1 bursting occurring via Hopf bifurcation. Hence,it is concluded that this period-adding bursting bifurcation without chaos has a compound bifurcation structure closely related to period-doubling bifurcations of periodic spiking in essence.     

基于共振参数微扰法的SEPIC变换器的混沌控制

本文以SEPIC变换器中前置电感电流为控制对象, 采用共振参数微扰法对电流模式控制SEPIC 变换器中的混沌现象进行控制. 该方法通过对电路参数的微小扰动实现了对SEPIC变换器中混沌现象的控制, 并通过时域波形、功率谱及分岔图等对结果进行了分析. 最后实验结果表明, 以前置电感电流为控制对象, 利用共振参数微扰法可以实现SEPIC变换器的混沌控制. 关键词： SEPIC变换器 混沌 混沌控制 共振参数微扰     

基于符号序列描述的一类分段光滑系统中分岔现象与混沌分析

从拓扑序列出发，提出了描述DC/DC变换器一类分段光滑系统中的分岔现象和混沌行为的符号序列方法，根据最大子序列的性态判别分岔的类型，以及检测边界碰撞分岔的发生.例如,当发生倍周期分岔时，最大子序列保持不变；当发生边界碰撞分岔时，最大子序列发生变化；混沌态则没有最大子序列.研究表明，占空比是表征DC/DC变换器一类分段光滑系统动力学行为的一个最本质的量，“饱和非线性”是引起边界碰撞分岔产生的根本原因. 关键词： 符号序列 分岔 混沌 分段光滑系统     

一类新的混沌神经放电的动力学特征的实验和数学模型研究

神经元电活动理论模型Hindmarsh-Rose(HR)模型提示有位于周期1和周期2放电模式之间的一类特殊的混沌放电,但长期以来对其没有获得足够认识.依据回归映射的确定性结构和非线性预报的短期可预报性,确认了在大鼠的实验性神经起步点的实验中发现的位于周期1和周期2放电模式之间的非周期放电是混沌放电模式,还将该混沌放电模式区分为3个不同表观样式.其中1个表观形式与HR模型的仿真结果相类似,验证了HR模型的理论预期;其余2个样式与仿真结果并不相似.进一步揭示了3个表观样式的动力学特征以及相互之间的区别与联系,并与位于周期2和周期3节律之间、周期3和周期4节律之间的混沌比较了异同,也区别了从周期1到混沌再到周期2放电模式的节律转迁历程与其他的从周期1到周期2节律的分岔过程的不同.研究结果确认了该类特殊混沌节律和相应分岔过程的新特征,丰富了混沌放电节律和节律分岔序列的种类.还对仿真该混沌的多样性和非光滑特性,以及揭示该类混沌的产生途径等进行了讨论. 关键词： 混沌 神经放电模式 分岔 节律     

基于开关电感结构的混合升压变换器非线性现象研究

将开关电感结构嵌入到传统Boost变换器中可以显著提高Boost变换器的电压传输比, 同时减少开关器件的电流应力, 降低损耗, 提高效率, 具有广阔的应用前景. 本文首次研究了基于开关电感结构的混合升压变换器的分岔和混沌现象, 导出了连续电流模式下的离散迭代映射模型, 采用分岔图分析了电路参数对系统性能的影响, 发现此变换器不仅发生了倍周期分岔、边界碰撞分岔、切分岔和阵发混沌, 还存在一种特殊的现象: 随着电容C和电感L₂的减小, 电路的运行状态并非严格经历1倍周期、2倍周期和4倍周期, 而是在4倍周期期间发生了分岔轨迹相交的情况, 在相交的一点, 变换器工作于周期3. 最后通过典型的时域波形和相轨图验证了这种特殊现象的存在. 研究结果表明, 当电路参数变化时, 基于开关电感结构的混合升压变换器比传统低维Boost变换器具有更加复杂、多样化的非线性现象. 关键词： 开关电感 混合升压变换器 离散迭代映射 混沌     

脉冲作用下Chen系统的非光滑分岔分析

研究了脉冲作用下Chen系统的复杂动力学行为. 对脉冲作用下的Chen系统进行了非光滑分岔分析. 该系统可经级联倍周期分岔到达混沌, 也可由周期解经鞍结分岔直接到达混沌. 最后通过Floquet理论揭示了该系统周期解的非光滑分岔机理.