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.     

Feedback Induced Instability and Chaos in Semiconductor Lasers and Their Applications

Semiconductor laser with feedback is an excellent model for nonlinear optical system which shows chaotic dynamics. It is interesting not only from the fundamental physical study but also application standpoints of view. The dynamics of feedback induced instability and chaos, especially for optical feedback, and their applications are reviewed in this paper. The model of such a system is described by the laser rate equations. At first the dynamic behaviors of feedback induced instability and chaos in semiconductor lasers are discussed on the basis of the theory and experiments. Instability and chaos may be stabilized by the method of chaos control. Then we apply the method to suppress the noise induced by the feedback in a semiconductor laser. The synchronization of chaos between two similar systems is also an important issue in chaos applications and we discuss secure communications based on chaos synchronization. Some other examples of applications of feedback induced chaos are also described.     

Ehrenfest ‘phase-space’ trajectories and quantum chaos in He atom under strong,oscillating magnetic fields: an application of time-dependent quantum fluid density functional theory (TDQFDFT)

Using a dynamical signature proposed earlier from our laboratory, quantum chaos in He atom interacting with strong, oscillating magnetic fields has been studied through a comparison between the nonlinear divergence of two neighbouring Ehrenfest ‘phase-space’ (EPS) trajectories differing slightly in initial conditions and the Loschmidt echo. The dynamical EPS signature can detect quantum chaos independently of the Loschmidt echo and in agreement with the latter, even for low-lying states, in the same spirit as that of classical chaos. This time-dependent signature extends the concept of quantum chaos to systems which have no classical counterparts and brings the concept of quantum chaos closer to that of classical chaos.     

基于直接延迟反馈的混沌反控制

在混沌有益时，有目的地产生混沌已经成为混沌学研究的热点问题，本文提出直接延迟反馈实现混沌的反控制，在非混沌系统中产生了混沌.该方法与间接延迟反馈控制方法相比，控制更加简单，更易于实现.该方法与Pyragas提出的延迟反馈混沌控制方法的控制器结构相同，因此，这种直接延迟反馈控制方法可以在需要混沌时产生混沌，不需要混沌时控制混沌，实现混沌控制和反控制的统一，为设计者提供最大的灵活性.针对参数处于非混沌区的Chen系统和Lorenz系统的仿真结果表明了该混沌反控制方法的有效性. 关键词： 混沌 反控制 直接延迟反馈     

Bifurcation control and chaos in a linear impulsive system

Bifurcation control and the existence of chaos in a class of linear impulsive systems are discussed by means of both theoretical and numerical ways. Chaotic behaviour in the sense of Marotto's definition is rigorously proven. A linear impulsive controller, which does not result in any change in one period-1 solution of the original system, is proposed to control and anti-control chaos. The numerical results for chaotic attractor, route leading to chaos, chaos control, and chaos anti-control, which are illustrated with two examples, are in good agreement with the theoretical analysis.     

Controlling Chaos Probability of a Bose-Einstein Condensate in a Weak Optical Superlattice

The spatial chaos probability of a Bose-Einstein condensate perturbed by a weak optical superlattice is studied. It is demonstrated that the spatial. chaotic solution appears with a certain probability in a given parameter region under a random boundary condition. The effects of the lattice depths and wave vectors on the chaos probability are illustrated, and different regions associated with different chaos probabilities are found. This suggests a feasible scheme for suppressing and strengthening chaos by adjusting the optical superlattice experimentaJly.     

Chaos‐related Localization in Modulated Lattice Array

This paper will discuss the chaos‐related localization in a lattice array with an external periodical field acted on a boundary site that allows us to realize the controllable chaotic dynamics with a tunable driving frequency. Two types of chaos‐related localization, short‐term and long‐term localization, which are closely related to the degree of chaos are reported and may provide a way to realize switching from chaos‐related localization to chaos‐assisted tunneling. Interestingly, with the increase of nonlinearity, driving frequency or even second‐order coupling, there always exists a parameter window with sharp edges for long‐term localization which facilitates us to find the thresholds to control the system into or out of localization region. In addition, the numerical results further demonstrate that the initial phase of the driving field may greatly influence the degree of the chaos. These results can be extended to finite driven N‐site system and may deepen our understanding of chaos‐related localization in nonlinear driving system.     

Chaotic temperature dependence in a model of spin glasses

We address the problem of chaotic temperature dependence in disordered glassy systems at equilibrium by following states of a random-energy random-entropy model in temperature; of particular interest are the crossings of the free-energies of these states. We find that this model exhibits strong, weak or no temperature chaos depending on the value of an exponent. This allows us to write a general criterion for temperature chaos in disordered systems, predicting the presence of temperature chaos in the Sherrington-Kirkpatrick and Edwards-Anderson spin glass models, albeit when the number of spins is large enough. The absence of chaos for smaller systems may justify why it is difficult to observe chaos with current simulations. We also illustrate our findings by studying temperature chaos in the naıve mean field equations for the Edwards-Anderson spin glass. Received 27 March 2002 Published online 19 July 2002     

Chaotic dynamics on large networks

Many systems in nature are governed by a large number of agents that interact nonlinearly through complex feedback loops. When the networks are sufficiently large and interconnected, they typically exhibit self-organization and chaos. This paper examines the prevalence and degree of chaos on large unweighted recurrent networks of ordinary differential equations with sigmoidal nonlinearities and unit coupling. The largest Lyapunov exponent is used as the signature and measure of the chaos, and the study includes the effects of damping, asymmetries in the distribution of coupling strengths, network symmetry, and sparseness of connections. Minimum conditions and optimal network architectures are determined for the existence of chaos. The results have implications for the design of social and other networks in the real world in which weak chaos is deemed desirable or as a way of understanding why certain networks might exist on "the edge of chaos."     

基于粒子群优化的混沌系统比例-积分-微分控制

基于比例-积分-微分(PID)控制算法的简单性和实用性,但对于复杂非线性系统控制时参数的难以确定问题,运用集群智能中的改进粒子群算法进行PID控制器的优化,并应用于若干混沌系统的控制.对Hénon混沌、Duffing混沌、六辊UC 轧机混沌、Nagumo-sato神经元混沌、Chen氏混沌以及永磁同步电动机混沌的控制进行了仿真研究.研究结果表明： 用PID进行混沌系统的输出反馈控制是有效的,从而拓宽了PID控制的应用范围; 用简单方法控制复杂混沌系统是完全可能的,对混沌系统的控制具有较好的参考价值; 粒子 关键词： 混沌 比例-积分-微分控制 粒子群优化算法     

Maintenance and suppression of chaos by weak harmonic perturbations: a unified view

General results concerning maintenance or enhancement of chaos are presented for dissipative systems subjected to two harmonic perturbations (one chaos inducing and the other chaos enhancing). The connection with previous results on chaos suppression is also discussed in a general setting. It is demonstrated that, in general, a second harmonic perturbation can reliably play an enhancer or inhibitor role by solely adjusting its initial phase. Numerical results indicate that general theoretical findings concerning periodic chaos-inducing perturbations also work for aperiodic chaos-inducing perturbations, and in arrays of identical chaotic coupled oscillators.     

Chaos control and synchronization in Bragg acousto-optic bistable systems driven by a separate chaotic system

In this paper we propose a new scheme to achieve chaos control and synchronization in Bragg acousto-optic bistable systems. In the scheme, we use the output of one system to drive two identical chaotic systems. Using the maximal conditional Lyapunov exponent (MCLE) as the criterion, we analyze the conditions for realizing chaos synchronization. Numerical calculation shows that the two identical systems in chaos with negative MCLEs and driven by a chaotic system can go into chaotic synchronization whether or not they were in chaos initially. The two systems can go into different periodic states from chaos following an inverse period-doubling bifurcation route as well when driven by a periodic system.     

An Improved Calculation Formula of the Extended Entropic Chaos Degree and Its Application to Two-Dimensional Chaotic Maps

The Lyapunov exponent is primarily used to quantify the chaos of a dynamical system. However, it is difficult to compute the Lyapunov exponent of dynamical systems from a time series. The entropic chaos degree is a criterion for quantifying chaos in dynamical systems through information dynamics, which is directly computable for any time series. However, it requires higher values than the Lyapunov exponent for any chaotic map. Therefore, the improved entropic chaos degree for a one-dimensional chaotic map under typical chaotic conditions was introduced to reduce the difference between the Lyapunov exponent and the entropic chaos degree. Moreover, the improved entropic chaos degree was extended for a multidimensional chaotic map. Recently, the author has shown that the extended entropic chaos degree takes the same value as the total sum of the Lyapunov exponents under typical chaotic conditions. However, the author has assumed a value of infinity for some numbers, especially the number of mapping points. Nevertheless, in actual numerical computations, these numbers are treated as finite. This study proposes an improved calculation formula of the extended entropic chaos degree to obtain appropriate numerical computation results for two-dimensional chaotic maps.     

Analysis of Chaotic Dynamics by the Extended Entropic Chaos Degree

The Lyapunov exponent is the most-well-known measure for quantifying chaos in a dynamical system. However, its computation for any time series without information regarding a dynamical system is challenging because the Jacobian matrix of the map generating the dynamical system is required. The entropic chaos degree measures the chaos of a dynamical system as an information quantity in the framework of Information Dynamics and can be directly computed for any time series even if the dynamical system is unknown. A recent study introduced the extended entropic chaos degree, which attained the same value as the total sum of the Lyapunov exponents under typical chaotic conditions. Moreover, an improved calculation formula for the extended entropic chaos degree was recently proposed to obtain appropriate numerical computation results for multidimensional chaotic maps. This study shows that all Lyapunov exponents of a chaotic map can be estimated to calculate the extended entropic chaos degree and proposes a computational algorithm for the extended entropic chaos degree; furthermore, this computational algorithm was applied to one and two-dimensional chaotic maps. The results indicate that the extended entropic chaos degree may be a viable alternative to the Lyapunov exponent for both one and two-dimensional chaotic dynamics.     

Synchronization and suppression of chaos in non-locally coupled map lattices

We considered coupled map lattices with long-range interactions to study the spatiotemporal behaviour of spatially extended dynamical systems. Coupled map lattices have been intensively investigated as models to understand many spatiotemporal phenomena observed in extended system, and consequently spatiotemporal chaos. We used the complex order parameter to quantify chaos synchronization for a one-dimensional chain of coupled logistic maps with a coupling strength which varies with the lattice in a power-law fashion. Depending on the range of the interactions, complete chaos synchronization and chaos suppression may be attained. Furthermore, we also calculated the Lyapunov dimension and the transversal distance to the synchronization manifold.     

一种基于混沌系统部分序列参数辨识的混沌保密通信方法

本文提出一种混沌保密通信方法,即混沌系统的部分序列用于混沌系统参数辨识其他序列用于通信保密.利用混沌蚁群优化算法对部分序列混沌系统进行参数辨识,以达到了解混沌系统全部信息的目的.在参数辨识过程中引入参数空间和蚁群空间,通过空间变换函数使参数空间与蚁群空间之间相互变换.文中使用Lorenz系统进行数值试验,其结果验证混沌系统部分序列参数辨识及混沌保密通信的可行性.     

链式互耦合半导体激光器的实时混沌同步

通过在互耦合外腔半导体激光器之间增加中继激光器,建立了一种链式互耦合半导体激光器混沌同步系统模型.理论分析了系统的实时混沌同步条件,数值研究了注入电流、互耦合条件、反馈条件等对系统实时混沌同步品质的影响,揭示了同步质量在反馈强度和互耦合强度二维参数空间的分布规律.结果表明:注入电流较大时,满足互耦合强度和反馈强度相同,互耦合延时和反馈延时相等,系统中所有激光器之间可同时实现稳定高品质实时混沌同步;中心激光器和边激光器之间的稳定实时混沌同步分布在在互耦合强度和反馈强度较小的区域以及互耦合强度和反馈强度相近的区域;边激光器之间由于同时接收到中心激光器实施的相同注入,能够较容易的实现稳定高品质的实时混沌同步.该系统可进一步扩展成为实现远距离的双向实时混沌同步或阵列激光器系统的实时混沌同步.     

Synchronization properties and effects of parameter mismatches in unidirectionally coupled chaotic vertical-cavity surface-emitting lasers

We numerically investigate the effects of parameter mismatches on chaos synchronization in vertical-cavity surfaceemitting lasers (VCSELs). We assume injection-locked chaos synchronization in a unidirectionally coupled and openloop optical feedback system. The accuracy of chaos synchronization is greatly affected by the mismatches of the device parameters and operation conditions between the two lasers. In particular, the oscillation frequency of the laser is one of the important parameters in a system of injection-locked chaos synchronization. However, the variations of the device characteristics of VCSELs are very large compared with those of other types of semiconductor lasers. We study the effects of parameter mismatches related to the oscillation frequency of VCSELs on chaos synchronization. We proved that mismatches in terms of the birefringence and the injection current play crucial roles for the quality of chaos synchronization.     

参数共振微扰法在Boost变换器混沌控制中的实现及其优化

参数共振微扰法是一种简单的非反馈混沌控制方法，它十分适合非自治系统的混沌控制.研究了这种方法在电流模式控制Boost变换器混沌控制中的应用，并通过对扰动相位进行优化 ，达到最优的混沌控制结果.同时对参数共振微扰法及其优化方法在Boost变换器混沌控制中的作用进行了理论分析，推导并计算了各种电路参数变化对有效的混沌控制所需的扰动的影响. 关键词： Boost变换器 混沌 混沌控制 参数共振微扰法     

Comparing mechanical analysis with generalized-competitive-mode analysis for the plasma chaotic system

The plasma chaotic system is a dissipative dynamical system modeled by a parametric plasma instability arising from the interaction of the whistler and ion acoustic waves with the plasma oscillation near the lower hybrid resonance. The amplitudes of these three oscillations obey a three-dimensional system of ordinary differential equations that exhibits chaos for certain parameter values. Besides the maximal Lyapunov exponent technique, a generalized-competitive-mode (GCM) technique has been proposed to evaluate parameter values associated with chaos. A mechanical analysis has also been proposed to reveal the mechanisms underlying the different dynamical modes including chaos. In a series of comparisons between the GCM analysis and mechanical analysis, chaos for the plasma chaotic system is determined. The mechanism and causes by which the plasma chaotic system produces different dynamical behaviors are interpreted. Furthermore, using the whistler-parameter variation of the Casimir function and Casimir power for the plasma system, the generating mechanisms of the different orbital modes and the different levels of chaos are uncovered.