Collapse of spatiotemporal chaos

The transient nature of spatiotemporal chaos is examined in reaction-diffusion systems with coexisting stable states. We find the apparent asymptotic spatiotemporal chaos of the Gray-Scott system to be transient, with the average transient lifetime increasing exponentially with medium size. The collapse of spatiotemporal chaos arises when statistical spatial correlations produce a quasihomogeneous medium, and the system obeys its zero-dimensional dynamics to relax to its stable asymptotic state.     

Self-replicating holes in a vertically vibrated dense suspension

We find self-replicating holes on the surface of a vertically vibrated potato starch suspension. Above certain acceleration, the finite-amplitude deformation of the surface grows to form a hole that penetrates the fluid layer. The circular shape of the hole is not stable, and the hole begins to replicate just like the self-replicating spots in chemical reaction-diffusion systems. At high acceleration, these holes exhibit spatiotemporal chaos. By assessing the statistical properties in a steady state, we show that fluctuation in the number of holes can be understood by a master equation.     

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     

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.     

Propagation dynamics on the Fermi-Pasta-Ulam lattices

The spatiotemporal propagation of a momentum excitation on the finite Fermi-Pasta-Ulam lattices is investigated. The competition between the solitary wave and phonons gives rise to interesting propagation behaviors. For a moderate nonlinearity, the initially excited pulse may propagate coherently along the lattice for a long time in a solitary wave manner accompanied by phonon tails. The lifetime of the long-transient propagation state exhibits a sensitivity to the nonlinear parameter. The solitary wave decays exponentially during the final loss of stability, and the decay rate varying with the nonlinear parameter exhibits two different scaling laws. This decay is found to be related to the largest Lyapunov exponent of the corresponding Hamiltonian system, which manifests a transition from weak to strong chaos. The mean-free-path of the solitary waves is estimated in the strong chaos regime, which may be helpful to understand the origin of anomalous conductivity in the Fermi-Pasta-Ulam lattice.     

Origin of transient and intermittent dynamics in spatiotemporal chaotic systems

Nonattracting chaotic sets (chaotic saddles) are shown to be responsible for transient and intermittent dynamics in an extended system exemplified by a nonlinear regularized long-wave equation, relevant to plasma and fluid studies. As the driver amplitude is increased, the system undergoes a transition from quasiperiodicity to temporal chaos, then to spatiotemporal chaos. The resulting intermittent time series of spatiotemporal chaos displays random switching between laminar and bursty phases. We identify temporally and spatiotemporally chaotic saddles which are responsible for the laminar and bursty phases, respectively. Prior to the transition to spatiotemporal chaos, a spatiotemporally chaotic saddle is responsible for chaotic transients that mimic the dynamics of the post-transition attractor.     

Elimination of spiral waves and spatiotemporal chaos by the pulse with a specific spatiotemporal configuration

Spiral waves and spatiotemporal chaos are sometimes harmful and should be controlled. In this paper spiral waves and spatiotemporal chaos are successfully eliminated by the pulse with a very specific spatiotemporal configuration. The excited position D of spiral waves or spatiotemporal chaos is first recorded at an arbitrary time （to）. When the system at the domain D enters a recovering state, the external pulse is injected into the domain. If the intensity and the working time of the pulse are appropriate, spiral waves and spatiotemporal chaos can finally be eliminated because counter-directional waves can be generated by the pulse. There are two advantages in the method. One is that the tip can be quickly eliminated together with the body of spiral wave, and the other is that the injected pulse may be weak and the duration can be very short so that the original system is nearly not affected, which is important for practical applications.     

基于模糊模型的耦合时空混沌H_\infty$跟踪控制

由于子系统的时空耦合作用，实现耦合时空混沌的跟踪控制比较困难。然而模型未知的耦合时空混沌的子系统可由一系列模糊逻辑模型逼近，每个模糊逻辑模型代表子系统在特定运行点的局部线性化模型。基于该系列模糊模型，采用模糊跟踪控制方法实现了耦合时空混沌的模型参考跟踪控制，并用线性矩阵不等式的凸优化方法求解控制器参数，确保系统的全局渐近稳定性。仿真验证了方案的有效性。     

相空间压缩实现时空混沌系统的广义同步

提出了一种通过相空间压缩实现时空混沌系统广义同步的方法. 以Fitzhugh-Nagumo反应扩散时空混沌系统为例,仿真模拟说明了该方法的有效性与实用性. 通过研究有界噪声作用下该系统的同步效果,表明这种同步方法具有较强的抗干扰能力. 此方法可以实现任意时空混沌系统的广义同步,具有普适性. 同步控制器结构简单、易于应用. 关键词： 时空混沌 广义同步 相空间压缩     

局域反馈抑制心脏中的螺旋波和时空混沌

采用LuoRud91模型研究了螺旋波和时空混沌的抑制,提出用局域反馈控制方法抑制螺旋波和时空混沌,采用静止和运动控制器两种控制策略.结果表明:适当选择控制参数,静止控制器的局域反馈方法能很好抑制螺旋波,但不能有效抑制时空混沌;采用运动控制器的局域反馈方法能有效抑制螺旋波和时空混沌,抑制速度与控制器移动的速度有关,在选择适当的控制参数下,螺旋波和时空混沌能在很短的时间内被抑制.     

An image encryption scheme based on the MLNCML system using DNA sequences

We propose a new image scheme based on the spatiotemporal chaos of the Mixed Linear–Nonlinear Coupled Map Lattices (MLNCML). This spatiotemporal chaotic system has more cryptographic features in dynamics than the system of Coupled Map Lattices (CML). In the proposed scheme, we employ the strategy of DNA computing and one time pad encryption policy, which can enhance the sensitivity to the plaintext and resist differential attack, brute-force attack, statistical attack and plaintext attack. Simulation results and theoretical analysis indicate that the proposed scheme has superior high security.     

An image encryption scheme based on new spatiotemporal chaos

Spatiotemporal chaos is chaotic dynamics in spatially extended system, which has attracted much attention in the image encryption field. The spatiotemporal chaos is often created by local nonlinearity dynamics and spatial diffusion, and modeled by coupled map lattices (CML). This paper introduces a new spatiotemporal chaotic system by defining the local nonlinear map in the CML with the nonlinear chaotic algorithm (NCA) chaotic map, and proposes an image encryption scheme with the permutation-diffusion mechanism based on these chaotic maps. The encryption algorithm diffuses the plain image with the bitwise XOR operation between itself pixels, and uses the chaotic sequence generated by the NCA map to permute the pixels of the resulting image. Finally, the constructed spatiotemporal chaotic sequence is employed to diffuse the shuffled image. The experiments demonstrate that the proposed encryption scheme is of high key sensitivity and large key space. In addition, the scheme is secure enough to resist the brute-force attack, entropy attack, differential attack, chosen-plaintext attack, known-plaintext attack and statistical attack.     

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     

Segmented waves from a spatiotemporal transverse wave instability

We observe traveling waves emitted from Turing spots in the chlorine dioxide-iodine-malonic acid reaction. The newborn waves are continuous, but they break into segments as they propagate, and the propagation of these segments ultimately gives rise to spatiotemporal chaos. We model the wave-breaking process and the motion of the chaotic segments. We find stable segmented spirals as well. We attribute the segmentation to an interaction between front rippling via a transverse instability and front symmetry breaking by a fast-diffusing inhibitor far from the codimension-2 Hopf-Turing bifurcation, and the chaos to a secondary instability of the periodic segmentation.     

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.     

Security analysis of a one-way hash function based on spatiotemporal chaos

The collision and statistical properties of a one-way hash function based on spatiotemporal chaos are investigated. Analysis and simulation results indicate that collisions exist in the original algorithm and, therefore, the original algorithm is insecure and vulnerable. An improved algorithm is proposed to avoid the collisions.     

基于时空混沌系统的单向Hash函数构造

提出了一种基于时空混沌系统的Hash函数构造方法.以线性变换后的消息数作为一组初值来驱动单向耦合映像格子的时空混沌系统，产生时空混沌序列，取其空间最后一组混沌序列的适当项，线性映射为Hash值要求的128bit值.研究结果表明，这种基于时空混沌系统的Hash函数具有很好的单向性、弱碰撞性、初值敏感性，较基于低维混沌映射的Hash函数具有更强的保密性能，且实现简单. 关键词： 时空混沌 Hash函数 单向耦合映像格子     

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.     

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.