耦合混沌系统的相同步：从高维混沌到低维混沌

混沌系统的相同步现象是近几年混沌同步研究的热点,它反映了混沌运动中的有序行为.用分岔树来研究耦合系统相同步的进程,并用Lyapunov指数谱来探讨系统动力学在相同步时从高维混沌向低维混沌过渡的进程.发现了从多个有理同步的时间交替到完全相同步的道路.还 发现了相同步中的混沌抑制及通过倍周期分岔向混沌同步的恢复.此外,研究表明,非对称 耦合可以大大加强耦合系统的相同步,这对实际应用有重要的意义. 关键词： 相同步 分岔树 李指数     

Synchronization and control of chaos in coupled chaotic multimode Nd:YAG lasers

In this Letter we numerically investigate the dynamics of a system of two coupled chaotic multimode Nd:YAG lasers with two mode and three mode outputs. Unidirectional and bidirectional coupling schemes are adopted; intensity time series plots, phase space plots and synchronization plots are used for studying the dynamics. Quality of synchronization is measured using correlation index plots. It is found that for laser with two mode output bidirectional direct coupling scheme is found to be effective in achieving complete synchronization, control of chaos and amplification in output intensity. For laser with three mode output, bidirectional difference coupling scheme gives much better chaotic synchronization as compared to unidirectional difference coupling but at the cost of higher coupling strength. We also conclude that the coupling scheme and system properties play an important role in determining the type of synchronization exhibited by the system.     

From low-dimensional synchronous chaos to high-dimensional desynchronous spatiotemporal chaos in coupled systems

The dynamic behavior of coupled chaotic oscillators is investigated. For small coupling, chaotic state undergoes a transition from a spatially disordered phase to an ordered phase with an orientation symmetry breaking. For large coupling, a transition from full synchronization to partial synchronization with translation symmetry breaking is observed. Two bifurcation branches, one in-phase branch starting from synchronous chaos and the other antiphase branch bifurcated from spatially random chaos, are identified by varying coupling strength epsilon. Hysteresis, bistability, and first-order transitions between these two branches are observed.     

Chaos suppression through asymmetric coupling

We study pairs of identical coupled chaotic oscillators. In particular, we have used Roessler (in the funnel and no funnel regimes), Lorenz, and four-dimensional chaotic Lotka-Volterra models. In all four of these cases, a pair of identical oscillators is asymmetrically coupled. The main result of the numerical simulations is that in all cases, specific values of coupling strength and asymmetry exist that render the two oscillators periodic and synchronized. The values of the coupling strength for which this phenomenon occurs is well below the previously known value for complete synchronization. We have found that this behavior exists for all the chaotic oscillators that we have used in the analysis. We postulate that this behavior is presumably generic to all chaotic oscillators. In order to complete the study, we have tested the robustness of this phenomenon of chaos suppression versus the addition of some Gaussian noise. We found that chaos suppression is robust for the addition of finite noise level. Finally, we propose some extension to this research.     

Chaos control in a discrete time system through asymmetric coupling

We study a pair of asymmetrically coupled identical chaotic quadratic maps. We investigate, via numerical simulations, chaos suppression associated with the variation of both parameters, the coupling parameter and the parameter which measures the asymmetry. This is a new technique recently introduced for chaos suppression in continuous systems and, as far we know, not yet tested for discrete systems. Parameter-space regions where the chaotic dynamics is driven towards regular dynamics are shown. Lyapunov exponents and phase-space plots are also used to characterize the phenomenon observed as the parameters are changed.     

Two chaos synchronization schemes and public-channel message transmission in a mutually coupled semiconductor lasers system

Chaos synchronization and message transmission of a mutually coupled system consisting of two semiconductor lasers (SLs) and a partially transparent mirror (PTM) in between are investigated theoretically. Analytical results show that two types of chaos synchronization schemes, named as isochronal synchronization (IS) and leader/laggard synchronization (LLS), can be achieved by adjusting the reflectivity and position of PTM. By establishing SIMULINK model, numerical simulations illustrate that as the PTM is positioned at the center of two lasers, IS is available when the reflectivity of PTM is moderate. The LLS is achieved when the reflectivity of PTM equals to 0.5, which means feedback strength equals to coupling strength. Its lag time is just determined by the difference of feedback delay time. The investigations of mutual chaos pass filtering (MCPF) effects and the secure chaotic communication simulations indicate that IS allows real-time bidirectional message transmission on a public-channel, while LLS can achieve higher security chaotic communication by using its lag time as cryptography key. The demonstrated system can be used as a rudiment of array chaos communications system.     

Phase locking and chaotic synchronization in an array of three lasers

A linear array of three lasers that are coupled mutually in space is investigated. It is shown that the phase of the laser fields is locked with intermediate coupling while the laser intensities are totally chaotic and chaotically synchronized. When the intensities of lasers reenter the regime of chaotic synchronization at smaller coupling constant, the laser fields show low degree of phase locking. The phase differences in the fields between three lasers show rich patterns when the coupling is changed. Received 3 August 2001 and Received in final form 27 September 2001     

Noise enhanced phase synchronization and coherence resonance in sets of chaotic oscillators with weak global coupling

The effect of noise on phase synchronization in small sets and larger populations of weakly coupled chaotic oscillators is explored. Both independent and correlated noise are found to enhance phase synchronization of two coupled chaotic oscillators below the synchronization threshold; this is in contrast to the behavior of two coupled periodic oscillators. This constructive effect of noise results from the interplay between noise and the locking features of unstable periodic orbits. We show that in a population of nonidentical chaotic oscillators, correlated noise enhances synchronization in the weak coupling region. The interplay between noise and weak coupling induces a collective motion in which the coherence is maximal at an optimal noise intensity. Both the noise-enhanced phase synchronization and the coherence resonance numerically observed in coupled chaotic R?ssler oscillators are verified experimentally with an array of chaotic electrochemical oscillators.     

Entanglement production in quantized chaotic systems

Quantum chaos is a subject whose major goal is to identify and to investigate different quantum signatures of classical chaos. Here we study entanglement production in coupled chaotic systems as a possible quantum indicator of classical chaos. We use coupled kicked tops as a model for our extensive numerical studies. We find that, in general, chaos in the system produces more entanglement. However, coupling strength between two subsystems is also a very important parameter for entanglement production. Here we show how chaos can lead to large entanglement which is universal and describable by random matrix theory (RMT). We also explain entanglement production in coupled strongly chaotic systems by deriving a formula based on RMT. This formula is valid for arbitrary coupling strengths, as well as for sufficiently long time. Here we investigate also the effect of chaos on the entanglement production for the mixed initial state. We find that many properties of the mixed-state entanglement production are qualitatively similar to the pure state entanglement production. We however still lack an analytical understanding of the mixed-state entanglement production in chaotic systems.     

Phase—Locking Dynamics in Coupled Circle—Map Lattices

The phase-locking dynamics in 1D and 2D lattices of non-identical coupled circle maps is explored.A global phase locking can be attained via a cascade of clustering processes with the increase of the coupling strength.Collective spatiotemporal dynamics is observed when a global phase locking is reached.Crisis-induced desynchronization is found,and its consequent spatiotemporal chaos is studied.     

耦合系统的混沌相位同步

通过引入混沌运动的相位定义分析了线性和非线性耦合参数对两个主共振子系统之间的混沌相位同步的影响.讨论了在近似于主共振条件下,两子系统不同步、不完全相位同步和完全相位同步之间的演化过程,揭示了不同状态相互转化与Lyapunov指数变化之间的关系,指出随着线性耦合力的增加,相位同步效应增强,然而随着非线性耦合力的增加,相位同步效应减弱. 关键词： 相位同步 Rssler振子 耦合 Lyapunov指数     

Synchronization with an arbitrary phase shift in a pair of synaptically coupled neural oscillators

The phase dynamics of a pair of spiking neural oscillators coupled by a unidirectional nonlinear connection has been studied. The synchronization effect with the controlled relative phase of spikes has been obtained for various coupling strengths and depolarization parameters. It has been found that the phase value is determined by the difference between the depolarization levels of neurons and is independent of the synaptic coupling strength. The synchronization mechanism has been studied by means of the construction and analysis of one-dimensional phase maps. The phase locking effect for spikes has been interpreted in application to the synaptic plasticity in neurobiology.     

Transitions to Long-Resident States in Coupled Chaotic Oscillators

The behaviour of coupled chaotic oscillators before complete synchronization is investigated. Long-time residence of trajectories appears besides one of the saddle foci. The tendency that orbits of the two oscillators get closer becomes faster with the increasing coupling strength. The diffusion of phase difference between the two oscillators is first enhanced and then suppressed. There are exact correspondences among these phenomena. The mechanism of these correspondences is explored. These phenomena uncover the route to synchronization of coupled chaotic oscillators.     

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.     

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.     

Chaotic phase synchronization in small-world networks of bursting neurons

We investigate the chaotic phase synchronization in a system of coupled bursting neurons in small-world networks. A transition to mutual phase synchronization takes place on the bursting time scale of coupled oscillators, while on the spiking time scale, they behave asynchronously. It is shown that phase synchronization is largely facilitated by a large fraction of shortcuts, but saturates when it exceeds a critical value. We also study the external chaotic phase synchronization of bursting oscillators in the small-world network by a periodic driving signal applied to a single neuron. It is demonstrated that there exists an optimal small-world topology, resulting in the largest peak value of frequency locking interval in the parameter plane, where bursting synchronization is maintained, even with the external driving. The width of this interval increases with the driving amplitude, but decrease rapidly with the network size. We infer that the externally applied driving parameters outside the frequency locking region can effectively suppress pathologically synchronized rhythms of bursting neurons in the brain.     

Experiments on chaos synchronization in two separate microchip lasers

Synchronization of chaos generated in two Nd:YVO(4) microchip lasers is experimentally demonstrated with master-slave coupling schemes. For synchronization of chaos, precise locking of the sustained relaxation-oscillation frequency is required, as is optical frequency locking. One needs to match both the pump-modulation parameters for chaos generation and the laser parameters of the two lasers to generate perfectly synchronized chaotic spectra in the master-slave type I coupling scheme.     

Transition to complete synchronization via near-synchronization in two coupled chaotic neurons

The synchronization transition in two coupled chaotic Morris-Lecar （ML） neurons with gap junction is studied with the coupling strength increasing. The conditional Lyapunov exponents, along with the synchronization errors are calculated to diagnose synchronization of two coupled chaotic ML neurons. As a result, it is shown that the increase in the coupling strength leads to incoherence, then induces a transition process consisting of three different synchronization states in succession, namely, burst synchronization, near-synchronization and embedded burst synchronization, and achieves complete synchronization of two coupled neurons finally. These sequential transitions to synchronization reveal a new transition route from incoherence to complete synchronization in coupled systems with multi-time scales.     

耦合Hindmarsh-Rose神经元的放电模式和完全同步

通过数值模拟和分岔分析的方法研究了Hindmarsh-Rose（HR）神经元的放电模式。当外加直流激励变化时，单个的神经元表现为静息态、周期性峰放电、周期性簇放电以及混沌的放电模式。利用快慢动力学分析的方法研究了HR神经元的动力学行为。当每个神经元表现为静息态、周期性放电和混沌时，两个耦合的神经元在一定的耦合强度下均会达到完全同步。神经元的耦合方式模拟神经元之间缝隙连接的电耦合。理论分析了完全同步的判断准则，并给出相应的数值模拟结果。电耦合HR神经元耦合系统的峰峰间期的分岔结构在耦合的作用下仍然能保持未耦合时的分岔结构。