Synchronization of Spatiotemporal Chaos in Coupled Complex Ginzburg-Landau Oscillators

Synchronization of spatiotemporal distributed system is investigated by considering the model of 1D dif-fusively coupled complex Ginzburg-Landau oscillators. An itinerant approach is suggested to randomly move turbulentsignal injections in the space of spatiotemporal chaos. Our numerical simulations show that perfect turbulence synchro-nization can be achieved with properly selected itinerant time and coupling intensity.     

Controlling Spatiotemporal Chaos in Coupled Map Lattices to Periodic Orbits

Two methods are presented for controlling spatiotemporal chaotic motion in coupled map lattices to a kind of periodic orbit where the dynamical variables of all lattice sites are equal and act periodically as time evolves. Stability analysis of the periodic orbits is presented. We prove that especially the second controlling method can stabilize all the periodic orbits we concern. Basin of attraction and noise problem are discussed.     

用直线稳定方法控制耦合哈密顿系统的混沌运动

讨论了不稳定不动点邻域的不稳定轨道的稳定问题．通过对系统施加外部的控制信号,将直线稳定方法推广到控制高维保守系统一耦合标准映象的混沌运动．通过对外加控制信号的调整,使系统不稳定不动点邻域的不稳定轨道沿着连接任意时刻轨道点和该不动点的直线趋向不动点,从而使难于控制的高维保守系统的不稳定轨道趋于稳定．这种方法不需要事先掌握系统动力行为,而且具有较强的抗干扰能力。     

Transition to Amplitude Death in Coupled System with Small Number of Nonlinear Oscillators

In this work, we investigate the amplitude death in coupled system with small number of nonlinear oscillators. We show how the transitions to the partial and the complete amplitude deathes happen. We also show that the partial amplitude death can be found in globally coupled oscillators either.     

Transport for Stochastic System with Infinite Locally Coupled Oscillators

We consider the transport of particles for spatially periodic system with infinite locally coupled oscillatorsdriven by additive and multiplicative noises. A formula of the probability current derived by us shows that the couplingamong the infinite oscillators is an ingredient for transport. This coupling of the oscillators can induce transport ofparticles in the absence of the correlation of the additive and multiplicative noises, even without the multiplicative noise.     

利用速度反馈方法控制时空混沌

以空间一维的复Ginzburg-Landau方程为模型,研究了利用系统变量随时间的变化率作为反馈控制信号控制偏微分方程系统中时空混沌的可能性.通过理论分析和数值模拟方法讨论了控制参数与可控性所满足的关系,解释了不同目标态时临界控制参数的尺寸效应.关键词：混沌控制时空混沌速度反馈复Ginzburg-Landau方程     

Controlling Chaos in a Semiconductor Laser via Weak Optical Positive Feedback and Modulating Amplitude

Numerical analysis of weak optical positive feedback (OPF) controlling chaos is studied in a semiconductor laser.The physical model of controlling chaos produced via modulating the current of semiconductor laser is presented under the condition of OPF.We find the physical mechanism that the nonlinear gain coefficient and linewidth enhancement factor of the laser are affected by OPF so that the dynamical behaviour of the system can be efficiently controlled.Chaos is controlled into a single-periodic state,a dual-periodic state,a fri-periodic state,a quadr-periodic state,a pentaperiodic state,and the laser emitting powers are increased by OPF in simulations.Lastly,another chaos-control method with modulating the amplitude of the feedback light is presented and numerically simulated to control chaotic laser into multi-periodic states.     

用常数周期脉冲方法控制耦合标准映象的混沌

将用常数周期脉冲方法控制保守系统的混沌运动的方法,用于控制高维系统耦合标准映象的混沌运动,计算了系统参数k=0.8和耦合常数β=0.04的有限时间李雅普诺夫指数,考察了不同系统参数和耦合常数下的有限时间李雅普诺夫指数随迭代次数的演化规律,从各次迭代的有限时间收敛区选择满足期望动力学特征的轨道片段,施加适当的脉冲强度找出其对应的周期不动点,从而得到期望的周期转道。     

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.     

Controlling Chaotic Behavior in a Bose-Einstein Condensate with Linear Feedback

The spatial structure of a Bose-Einstein condensate （BEC） loaded into an optical lattice potential is investigated and the spatially chaotic distributions of the condensates are revealed. A method of chaos control with linear feedback is presented in this paper. By using the method, we propose a scheme of controlling chaotic behavior in a BEC with atomic mirrors. The results of the computer simulation show that controlling the chaos into the stable states could be realized by adjusting the coefficient of feedback only if the maximum Lyapunov exponent of the system is negative.     

Chaos control in the nonlinear Schrodinger equation with Kerr law nonlinearity

The nonlinear Schr6dinger equation with Kerr law nonlinearity in the two-frequency interference is studied by the numerical method. Chaos occurs easily due to the absence of damping. This phenomenon will cause the distortion in the process of information transmission. We find that fiber-optic transmit signals still present chaotic phenomena if the control intensity is smaller. With the increase of intensity, the fiber-optic signal can stay in a stable state in some regions. When the strength is suppressed to a certain value, an unstable phenomenon of the fiber-optic signal occurs. Moreover we discuss the sensitivities of the parameters to be controlled. The results show that the linear term coefficient and the environment of two quite different frequences have less effects on the fiber-optic transmission. Meanwhile the phenomena of vibration, attenuation and escape occur in some regions.     

Chaos synchronization in networks of coupled maps with time-varying topologies

Complexity of dynamical networks can arise not only from the complexity of the topological structure but also from the time evolution of the topology. In this paper, we study the synchronous motion of coupled maps in time-varying complex networks both analytically and numerically. The temporal variation is rather general and formalized as being driven by a metric dynamical system. Four network models are discussed in detail in which the interconnections between vertices vary through time randomly. These models are: 1) i.i.d. sequences of random graphs with fixed wiring probability, 2) groups of graphs with random switches between the individual graphs, 3) graphs with temporary random failures of nodes, and 4) the meet-for-dinner model where the vertices are randomly grouped. We show that the temporal variation and randomness of the connection topology can enhance synchronizability in many cases; however, there are also instances where they reduce synchronizability. In analytical terms, the Hajnal diameter of the coupling matrix sequence is presented as a measure for the synchronizability of the graph topology. In topological terms, the decisive criterion for synchronization of coupled chaotic maps is that the union of the time-varying graphs contains a spanning tree.     

Modulation Induced Low-Frequency Fluctuations in Semiconductor Lasers with Optical Feedback and Their Suppression by Synchronous Modulation

Modulation induced low-frequency fluctuations (LFFs) of a semiconductor laser in the presence of optical feedback are investigated. LFFs are controlled to a synchronous oscillation when an appropriate modulation very close to the resonance frequency of the external cavity is applied to the injection current. The dependence of the frequency locking on the modulation frequency and depth is studied.     

Critical quantum chaos in 2D disordered systems with spin-orbit coupling

We examine the validity of the recently proposed semi-Poisson level spacing distribution function P(S), which characterizes “critical quantum chaos”, in 2D disordered systems with spin-orbit coupling. At the Anderson transition we show that the semi-Poisson P(S) can describe closely the critical distribution obtained with averaged boundary conditions, over Dirichlet in one direction with periodic in the other and Dirichlet in both directions. We also obtain a sub-Poisson linear number variance , with asymptotic value . The obtained critical statistics, intermediate between Wigner and Poisson, is discussed for disordered systems and chaotic models. Received 1 September 1999     

Global firing induced by network disorder in ensembles of active rotators

We study the influence of repulsive interactions on an ensemble of coupled excitable rotators. We find that a moderate fraction of repulsive interactions can trigger global firing of the ensemble. The regime of global firing, however, is suppressed in sufficiently large systems if the network of repulsive interactions is fully random, due to self-averaging in its degree distribution. We thus introduce a model of partially random networks with a broad degree distribution, where self-averaging due to size growth is absent. In this case, the regime of global firing persists for large sizes. Our results extend previous work on the constructive effects of diversity in the collective dynamics of complex systems.     

Vehicular motion in 2D city traffic network with signals controlled by phase shift

We study the dynamic behavior of vehicular traffic through the series of traffic lights controlled by phase shift in two-dimensional (2D) city traffic network. The nonlinear-map model is presented for the vehicular traffic. The city traffic network is made of one-way perpendicular streets arranged in a square lattice with traffic signals where vertical streets are oriented upwards and horizontal streets are oriented rightwards. There are two traffic lights for the movement to north or that to east at each crossing. The traffic lights are controlled by the cycle time, split, and phase shift. The vehicle moves through the series of signals on a path selected by the driver. The city traffic with a heterogeneous density distribution is also studied. The dependence of the arrival time on cycle time, split, phase shift, selected path, and density is clarified for 2D city traffic. It is shown that the vehicular traffic is efficiently controlled by the phase shift.