Controlling Chaos with Rectificative Feedback Injections in 2D Coupled Complex Ginzburg-Landau Oscillators

A model of two-dimensional coupled complex Ginzburg-Landau oscillators driven by a rectificative feedback controller is used to study controlling spatiotemporal chaos without gradient force items. By properly selecting the signal injecting position with considering the maximum gap between signals and targets, and adjusting the control time interval,we have finally obtained the efficient chaos control via numerical simulations.     

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.     

Spatiotemporal Chaos Control with Pinning Signals in Distributed Systems

We suggest a local pinning feedback control for stabilizing periodic pattern in spatially extended systems. Analytical and numerical investigations of this method for a system described by the one-dimensional complex Ginzburg-Landau equation are carried out. We found that it is possible to suppress spatiotemporal chaos by using a few pinning signals in the presence of a large gradient force. Our analytical predictions well coincide with numerical observations.     

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.     

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 dynamicM variables of all lattice sites are equM 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.     

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     

耦合双稳映象格子模型的时空混沌控制

变量反馈技术实现了耦合双稳映象格子模型的时空混沌控制.数值实验结果表明,利用不同的反馈技术和不同的反馈强度,可以将双稳映象系统的混沌及耦合双稳映象格子模型的时空混沌控制到不动点或周期轨道.变量反馈控制法除了局域双稳映象系统的定态点外,不需要先获取耦合双稳映象格子时空系统的动力学信息,它对抑制耦合双稳映象系统中的湍流具有一定的指导作用.     

A Cryptographic Scheme Based on Spatiotemporal Chaos of Coupled Map Lattices

We propose a cryptographic scheme based on spatiotemporal chaos of coupled map lattices (CML) ,which is based on one-time pad. The structure of the cryptosystem determines that the progress in decryption implies the progress in exploring the dynamical behavior of spatiotemporal chaos in CML. A part of the initial condition of CML is used as a secret key, and the recovery of the secret key by exhaustive search is impossible due to the sensitivity to the initial condition in spatiotemporal chaos system. Specially the software implementation of the scheme is easy.     

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.     

Transport for Stochastic System with Infinite Locally Coupled Oscillators

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

环域反馈下复Ginzburg-Landau系统的螺旋波动力学行为

针对自激振荡系统的复金兹伯格-朗道(Complex Ginzbury-Landau, 简称CGL)方程, 研究圆形环域与方形环域两种反馈控制下的螺旋波动力学。结果表明: 圆形环域反馈控制下, 螺旋波波头通常经过一段过渡漂移后进入圆形吸引子, 圆形吸引子的半径以及反馈刚启动时波头的漂移方向随环域参数呈周期性变化, 过渡漂移阶段波头轨道的平缓程度与复反馈信号模的时间函数中钟形部分的陡度有关, 且反馈增益的正负与大小也会影响受控螺旋波的动力学行为。方形环域反馈控制下的螺旋波波头的吸引子更为丰富, 主要包括方形吸引子、小的极限环吸引子、菱形吸引子以及点吸引子, 点吸引子通常位于方形环域的两条对角线上, 且波头运动随环域控制参数呈现规律性变换。     

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.     

复Ginzburg-Landau方程时空混沌的网络同步与参量辨识

研究了参量未知的时空混沌系统构成复杂网络的同步与参量辨识问题. 设计的参量辨识律可以有效地辨识复杂网络中所有节点时空混沌系统中的未知参量. 基于稳定性定理, 通过构造适当的Lyapunov函数, 确定了网络完全同步的条件. 以参量未知的一维复Ginzburg-Landau方程作为网络节点为例, 通过仿真模拟检验了参量辨识律以及同步方法的有效性.     

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。     

非线性反馈法控制相位共轭波的光学时空混沌

相位共轭振荡器由一个标准镜和一个具有快速响应的无损耗Kerr介质作为相位共轭介质的相位共轭镜组成.利用非线性反馈方法，对相位共轭振荡器中的时间混沌和耦合相位共轭波映象系统中的时空混沌进行了控制，得到了稳定的控制结果.数值实验表明，该控制方法不需预先了解动力学系统，只需调整反馈系数，在实际系统中容易实现.控制结果为相位共轭波的混沌研究提供了理论依据. 关键词： 非线性反馈控制 相位共轭振荡器 混沌 时空混沌     

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 Chaos in Neuron Based on LasalleInvariance Principle

A new control law is proposed to asymptotically stabilize the chaotic neuron system based on LaSalle invariant principle. The control technique does not
require analytical knowledge of the system dynamics and operates without an explicit knowledge of the desired steady-state position. The well-known modified Hodgkin-Huxley (MHH) andHindmarsh-Rose (HR) model neurons are taken as examples to verify the implementation of our method. Simulation results show the proposed control law is effective. The outcome of this study is significant since it is helpful to understand the learning process
of a human brain towards the information processing, memory and abnormal discharge of the brain neurons.