利用蜂拥控制算法的反馈方法控制时空混沌

以一维复数Ginzburg-Landau方程系统为模型,研究时空混沌系统的可控性.基于蜂拥控制算法思想,提出了一种反馈控制方法.数值模拟结果表明,无论是选择空间均匀周期解,还是选择行波解为控制目标态,只要选择合适的控制强度,被研究的时空混沌系统都能被控制到有序的状态.最后,利用空间的关联函数解析其控制机制. 关键词： Ginzburg-Landau方程 时空混沌 关联函数     

CO2激光器对相位共轭波时空混沌系统控制和同步的研究

以一维耦合映象格子为对象,研究了相位共轭波时空混沌系统特性. 基于Lyapunov稳定性定理,通过选取耦合参数,实现了CO₂激光器对相位共轭波时空混沌系统的控制,以及驱动多个相位共轭波时空系统达到并行同步. 数值模拟结果显示,耦合参数对相位共轭波时空混沌系统的控制和同步速度有影响,即耦合参数越大同步时间越短. 关键词： 2激光器')" href="#">CO₂激光器 相位共轭波 时空混沌 控制和同步     

时空混沌的单向耦合同步

以耦合映象格子模型为例,提出利用单向耦合驱动时空混沌的同步方案,并进行了数值分析.结果表明,适当地选择耦合驱动强度因子和均衡系数,两个时空混沌系统可以达到准确同步.通过计算最大条件Lyapunov指数,给出了可实现时空混沌同步的最小耦合强度以及最小耦合强度与系统参数之间的关系曲线.数值模拟还证明,此方法工作鲁棒 关键词： 时空混沌 同步 单向耦合 最大条件Lyapunov指数 数值模拟     

节点结构互异的复杂网络的时空混沌反同步

研究了节点结构互异的离散型时空混沌系统构成复杂网络的反同步问题. 通过构造合适的Lyapunov函数, 确定了复杂网络中连接节点之间的耦合函数的结构以及控制增益的取值范围. 以物理中具有时空混沌行为的激光相位共轭波空间扩展系统、Gibbs电光时空混沌 模型、Bragg声光时空混沌模型以及一维对流方程的离散形式作为 网络节点构成的复杂网络为例进行了仿真模拟, 发现整个网络存在稳定的混沌反同步现象.     

耦合映像格子模型时空混沌的控制

采用非线性反馈方法研究耦合电光双稳映像格子混沌系统的控制。画出空间振幅变化图。数值模拟的结构表明:在一定的相空间压缩参数区域内,控制时空混沌到均匀稳定状态时,控制结果与控制参数之间存在关系。同时利用计算机模拟了相应参数下的时序图,格点处于稳定状态,从而证明常数偏移法的有效性。     

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     

光折变振荡器中的模式锁定及阵发混沌

用数值模拟的方法研究了光折变振荡器的一些时空行为，结果表明在简并或准简并条件下的横模空间耦合将使得光折变振荡器表现出与普通激光器相似的时空现象，例如不同横向模式间的合作频率锁定，时空周期行为及多模振荡时的阵发混沌现象等等。     

一种时延范德波尔电磁系统中的复杂行为(Ⅱ)——时空混沌图案动态

对于一个由线性无损传输线加非线性边界条件组成的简单无穷维电磁系统，应用行波理论确定了电压反射波的局部映射关系.数值仿真结果表明，当系统参数发生变化时，传输线沿线电压存在着非常丰富的时空非线性现象.通过描绘出空间振幅变化图和时空行为发展图，定性分析了传输线沿线电压的时空混沌图案动态，为研究和理解时空混沌提供了一种良好的可求解模型. 关键词： 图案 时空混沌 无穷维系统 时延范德波尔电磁系统     

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.     

耦合映象格子中时空混沌的控制

采用相同的相空间压缩方法,有效地控制了均匀及非均匀耦合映象格子中的时空混沌.数值模拟结果表明,在一定的相空间压缩参数区域内,控制时空混沌到均匀稳定状态时,控制结果与控制参数之间存在确定的函数关系.利用这个控制方程,选择不同的相空间压缩参数控制耦合映象格子中的时空混沌,获得了各种所需要的稳定斑图 关键词： 时空混沌 耦合映象格子     

Bubbling transition to spatial mode excitation in an extended dynamical system

We investigated the transition to spatio-temporal chaos in spatially extended nonlinear dynamical systems possessing an invariant subspace with a low-dimensional attractor. When the latter is chaotic and the subspace is transversely stable we have a spatially homogeneous state only. The onset of spatio-temporal chaos, i.e. the excitation of spatially inhomogeneous modes, occur through the loss of transversal stability of some unstable periodic orbit embedded in the chaotic attractor lying in the invariant subspace. This is a bubbling transition, since there is a switching between spatially homogeneous and nonhomogeneous states with statistical properties of on-off intermittency. Hence the onset of spatio-temporal chaos depends critically both on the existence of a chaotic attractor in the invariant subspace and its being transversely stable or unstable.     

Optical patterns in spatially coupled phase-conjugate systems

Various pattern evolutions are presented in one-and two-dimensional spatially coupled phase-conjugate systems (SCPCSs).As the system parameters change,different patterns are obtained from the period-doubling of kink-antikinks in space to the spatiotemporal chaos in a one-dimensional SCPCS.The homogeneous symmetric states induce symmetry breaking from the four corners and the boundaries,finally leading to spatiotemporal chaos with the increase of the iteration time in a two-dimensional SCPCS.Numerical simulations are very helpful for understanding the complex optical phenomena.     

Controlling chaos in spatially extended beam-plasma system by the continuous delayed feedback

In this paper we discuss the control of complex spatio-temporal dynamics in a spatially extended nonlinear system (fluid model of Pierce diode) based on the concepts of controlling chaos in the systems with few degrees of freedom. A presented method is connected with stabilization of unstable homogeneous equilibrium state and the unstable spatio-temporal periodical states analogous to unstable periodic orbits of chaotic dynamics of the systems with few degrees of freedom. We show that this method is effective and allows to achieve desired regular dynamics chosen from a number of possible in the considered system.     

Emergence of spatiotemporal chaos arising from far-field breakup of spiral waves in the plankton ecological systems

It has been reported that the minimal spatially extended phytoplankton--zooplankton system exhibits both temporal regular/chaotic behaviour, and spatiotemporal chaos in a patchy environment. As a further investigation by means of computer simulations and theoretical analysis, in this paper we observe that the spiral waves may exist and the spatiotemporal chaos emerge when the parameters are within the mixed Turing--Hopf bifurcation region, which arises from the far-field breakup of the spiral waves over a large range of diffusion coefficients of phytoplankton and zooplankton. Moreover, the spatiotemporal chaos arising from the far-field breakup of spiral waves does not gradually invade the whole space of that region. Our results are confirmed by nonlinear bifurcation of wave trains. We also discuss ecological implications of these spatially structured patterns.     

Traveling waves and chaotic properties in cellular automata

Traveling wave solutions of cellular automata (CA) with two states and nearest neighbors interaction on one-dimensional (1-D) infinite lattice are computed. Space and time periods and the number of distinct waves have been computed for all representative rules, and each velocity ranging from 2 to 22. This computation shows a difference between spatially extended systems, generating only temporal chaos and those producing as well spatial complexity. In the first case wavelengths are simply related to the velocity of propagation and the dispersivity is an affine function, while in the second case (which coincides with Wolfram class 3), the dispersivity is multiform and its dependence on the velocities is highly random and discontinuous. This property is typical of space-time chaos in CA. (c) 1999 American Institute of Physics.     

A coupled map lattice model for rheological chaos in sheared nematic liquid crystals

A variety of complex fluids under shear exhibit complex spatiotemporal behavior, including what is now termed rheological chaos, at moderate values of the shear rate. Such chaos associated with rheological response occurs in regimes where the Reynolds number is very small. It must thus arise as a consequence of the coupling of the flow to internal structural variables describing the local state of the fluid. We propose a coupled map lattice model for such complex spatiotemporal behavior in a passively sheared nematic liquid crystal using local maps constructed so as to accurately describe the spatially homogeneous case. Such local maps are coupled diffusively to nearest and next-nearest neighbors to mimic the effects of spatial gradients in the underlying equations of motion. We investigate the dynamical steady states obtained as parameters in the map and the strength of the spatial coupling are varied, studying local temporal properties at a single site as well as spatiotemporal features of the extended system. Our methods reproduce the full range of spatiotemporal behavior seen in earlier one-dimensional studies based on partial differential equations. We report results for both the one- and two-dimensional cases, showing that spatial coupling favors uniform or periodically time-varying states, as intuitively expected. We demonstrate and characterize regimes of spatiotemporal intermittency out of which chaos develops. Our work indicates that similar simplified lattice models of the dynamics of complex fluids under shear should provide useful ways to access and quantify spatiotemporal complexity in such problems, in addition to representing a fast and numerically tractable alternative to continuum representations.     

Globally coupled maps with sequential updating

A system of globally coupled logistic maps with sequential updating is analyzed numerically. It is found that deterministic asynchronous updating schemes may have dramatic influences on the dynamical behaviors of globally coupled systems. Transitions from spatio–temporal chaos to spatially organized states are observed as the coupling parameter varies. It is shown that the model system may exhibit a variety of collective properties such as the clustering, traveling wave patterns, and spatial bifurcation cascades.     

Scaling properties of spatially extended chaotic systems

We investigate the scaling properties of Lyapunov eigenvectors and exponents in coupled-map lattices exhibiting space-time chaos. A deep interrelation between spatiotemporal chaos and kinetic roughening of surfaces is postulated. We show that the logarithm of unstable eigenvectors exhibits scale-invariance with roughness exponents that can be predicted by a simple scaling conjecture. We argue that these scaling properties should be generic in spatially homogeneous extended systems with local diffusive-like couplings.     

Blowout bifurcation and spatial mode excitation in the bubbling transition to turbulence

The transition to turbulence (spatio-temporal chaos) in a wide class of spatially extended dynamical system is due to the loss of transversal stability of a chaotic attractor lying on a homogeneous manifold (in the Fourier phase space of the system), causing spatial mode excitation. Since the latter manifests as intermittent spikes this has been called a bubbling transition. We present numerical evidences that this transition occurs due to the so-called blowout bifurcation, whereby the attractor as a whole loses transversal stability and becomes a chaotic saddle. We used a nonlinear three-wave interacting model with spatial diffusion as an example of this transition.