最近邻耦合网络的时空混沌同步研究

本文进行了最近邻网络的时空混沌同步研究.以时空混沌系统作为网络的节点,基于Lyapunov稳定性定理,通过确定网络的最大Lyapunov指数,得到了实现网络完全同步的条件.采用Fisher-Kolmogorov时空混沌系统作为网络节点实例进行了仿真模拟,获得了理想的同步效果.进一步研究了有界噪声影响下网络的同步性能,结果显示它具有较强的抗干扰能力.     

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.     

环形加权网络的时空混沌延迟同步

研究了环形加权网络的时空混沌延迟同步问题.以随时间和空间演化均呈现混沌行为的时空混沌系统作为网络的节点,通过环形加权连接使所有节点建立关联.基于线性稳定性定理,通过确定网络的最大Lyapunov指数,得到了实现网络延迟同步的条件.在最大Lyapunov指数小于零的区域内,任取节点之间耦合强度的权重值,均可以使整个网络实现延迟同步.采用具有时空混沌行为的自催化反应扩散系统作为网络节点,仿真模拟验证了该方法的有效性. 关键词： 延迟同步 加权网络 时空混沌 Lyapunov指数     

时空混沌中的序图样研究

通过分段单调映射和线性耦合研究时空混沌中的序图样.理论分析发现,混沌映射的时不变性质导致映射曲线交点减少,为序图样缺失的一个重要原因.证明了线性耦合可以破坏映射的时不变性质,并给出曲线交点增加的条件.分析了耦合系统的映射、耦合系数和耦合次数对序图样的影响,并以实例和仿真实验验证了上述理论结果.     

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     

Control of spatiotemporal chaos: A study with an autocatalytic reaction-diffusion system

The characterization of chaotic spatiotemporal dynamics has been studied for a representative nonlinear autocatalytic reaction mechanism coupled with diffusion. This has been carried out by an analysis of the Lyapunov spectrum in spatiallylocalised regions. The linear scaling relationships observed in the invariant measures as a function of thesub-system size have been utilized to assess the controllability, stability and synchronization properties of the chaotic dynamics. The dynamical synchronization properties of this high-dimensional system has been analyzed using suitable Lyapunov functionals. The possibility of controlling spatiotemporal chaos for relevant objectives using available noisy scalar time-series data with simultaneous self-adaptation of the control parameter(s) has also been discussed.     

A novel approach for the potential parameters selection of Peyrard-Bishop model

The selection of the potential parameters is a very difficult question because the potentials entering the model are effective potentials. In this Letter, an approach for selecting potential parameters of the Peyrard-Bishop model by mean Lyapunov exponent is presented. Using the theory introduced by Shibata [H. Shibata, Physica A 264 (1999) 226] on the Peyrard-Bishop model shows that, the system is very sensitive to the parameters selection. The obtained results demonstrate that the best range for parameters are where the mean Lyapunov exponent has low values. Furthermore, there is a good correspondence between our results and other reports.     

Lorenz系统驱动声光双稳时空混沌系统并行同步的研究

研究了一个时间混沌系统驱动多个时空混沌系统的并行同步问题.以单模激光Lorenz系统和一维耦合映像格子为例,在单模激光Lorenz系统中提取一个混沌序列,通过与一维耦合映像格子中的状态变量耦合使单模激光Lorenz系统和多个同结构一维耦合映像格子同时达到广义同步,并且多个一维耦合映像格子之间实现完全并行同步.通过计算条件Lyapunov指数,可以得到并行同步所需反馈系数的取值范围.数值模拟证明了此方法的可行性和有效性.     

Mean Lyapunov exponent approach for the helicoidal Peyrard-Bishop model

In this Letter, the ordered and disordered regions of the field variable of an oscillator chain are studied. For this purpose, the mean Lyapunov exponent (MLE) theory is applied to the helicoidal Peyrard-Bishop (hPB) model. Applying mean Lyapunov exponent theory introduced by Shibata [H. Shibata, Physica A 264 (1999) 226] on the model shows that, the system is very sensitive to the potential parameters. By analyzing the behavior of the MLE with respect to the harmonic helicoidal coupling (K), it can be found that, it is not possible to set the Morse potential parameters of the hPB model in good qualitative agreement with other experimental and theoretical studies. Furthermore, the results show that the MLE is independent of length of the DNA chain. This achievement is important since it can be used to overcome the computational difficulties.     

Chronotopic Lyapunov analysis: II. Toward a unified approach

From the analyticity properties of the equation governing infinitesimal perturbations, it is conjectured that all types of Lyapunov exponents introduced in spatially extended 1D systems can be derived from a single function that we call the entropy potential. The general consequences of its very existence on the Kolmogorov-Sinai entropy of generic spatiotemporal patterns are discussed.     

激光Maxwell-Bloch 方程时空混沌网络的同步研究

研究了激光Maxwell-Bloch 方程时空混沌网络的同步问题.对单模激光Maxwell-Bloch方程进行了修正. 以N个修正后具有时空混沌特性的单模激光Maxwell-Bloch方程作为网络节点构成复杂网络. 在考虑到网络连接过程中,节点时空混沌系统中的参量可能受到某种干扰而与实际值产生微小偏差的情况下,采用网络第一个节点的时空混沌系统同时并行驱动其余N-1个时空混沌系统达到同步. 进一步通过仿真模拟验证了同步方案的有效性.     

Analysis of Chaotic Dynamics by the Extended Entropic Chaos Degree

The Lyapunov exponent is the most-well-known measure for quantifying chaos in a dynamical system. However, its computation for any time series without information regarding a dynamical system is challenging because the Jacobian matrix of the map generating the dynamical system is required. The entropic chaos degree measures the chaos of a dynamical system as an information quantity in the framework of Information Dynamics and can be directly computed for any time series even if the dynamical system is unknown. A recent study introduced the extended entropic chaos degree, which attained the same value as the total sum of the Lyapunov exponents under typical chaotic conditions. Moreover, an improved calculation formula for the extended entropic chaos degree was recently proposed to obtain appropriate numerical computation results for multidimensional chaotic maps. This study shows that all Lyapunov exponents of a chaotic map can be estimated to calculate the extended entropic chaos degree and proposes a computational algorithm for the extended entropic chaos degree; furthermore, this computational algorithm was applied to one and two-dimensional chaotic maps. The results indicate that the extended entropic chaos degree may be a viable alternative to the Lyapunov exponent for both one and two-dimensional chaotic dynamics.     

An Improved Calculation Formula of the Extended Entropic Chaos Degree and Its Application to Two-Dimensional Chaotic Maps

The Lyapunov exponent is primarily used to quantify the chaos of a dynamical system. However, it is difficult to compute the Lyapunov exponent of dynamical systems from a time series. The entropic chaos degree is a criterion for quantifying chaos in dynamical systems through information dynamics, which is directly computable for any time series. However, it requires higher values than the Lyapunov exponent for any chaotic map. Therefore, the improved entropic chaos degree for a one-dimensional chaotic map under typical chaotic conditions was introduced to reduce the difference between the Lyapunov exponent and the entropic chaos degree. Moreover, the improved entropic chaos degree was extended for a multidimensional chaotic map. Recently, the author has shown that the extended entropic chaos degree takes the same value as the total sum of the Lyapunov exponents under typical chaotic conditions. However, the author has assumed a value of infinity for some numbers, especially the number of mapping points. Nevertheless, in actual numerical computations, these numbers are treated as finite. This study proposes an improved calculation formula of the extended entropic chaos degree to obtain appropriate numerical computation results for two-dimensional chaotic maps.     

Emergence of a multidomain regime and spatiotemporal chaos in Gunn diodes under impact ionization conditions

Nonlinear spatiotemporal dynamics of carrier densities in Gunn diodes under impact ionization conditions is numerically investigated using a set of model partial differential equations. Numerical results show that a multidomain regime emerges as a result of the decrease in domain size caused by impact ionization, and that the spatiotemporal evolution of the domains becomes chaotic in the presence of strong impact ionization.     

DC-DC变换器的信息熵分析

为确定不同反馈系数k下DC-DC变换器系统的行为,结合系统处于周期状态时的稳定性和系统处于混沌时不会重复经过每一点的特点,提出了一种采用极限思想和信息熵来估计DC-DC变换器非线性行为的方法.该方法能准确分析系统处于周期状态和混沌状态的熵值,量化了DC-DC变换器倍周期分叉和混沌行为.以一阶电压反馈DCM Boost变换器和DCM Buck变换器为例进行仿真.研究结果表明,所提出的信息熵可以准确反映分叉点、周期数及产生混沌的位置,完善了该类变换器非线性动力学分析的理论和方法.     

大规模富社团网络的时空混沌同步

以Plankton时空混沌系统作为网络节点,通过非线性耦合构成富社团(rich-club,RC)网络,研究其时空混沌同步规律.首先给出了RC网络中连接节点之间的非线性耦合函数的一般性选取原则.进而基于Lyapunov稳定性定理,理论分析了实现网络同步的条件.最后,通过仿真模拟检验了网络的时空混沌同步效果.仿真研究表明,RC网络中各富节点之间以及这些富节点各自星形连接的子网络中的所有节点均实现了完全同步。     

Synchronization of spatiotemporal chaos in complex networks via backstepping

A backstepping approach is proposed for the synchronization of chain networks of multi-spatiotemporal chaotic systems with topologically equivalent structures. The synchronization of multi-spatiotemporal chaotic systems is implemented by adding the control only to a terminal node, and the controller is designed via a corresponding update law. The control law is applied to spatiotemporal Gray-Scott systems. Numerical results demonstrate the effectiveness and the feasibility of the proposed approach.     

Synchronization of spatiotemporal chaos in complex networks via backstepping

A backstepping approach is proposed for the synchronization of chain networks of multi-spatiotemporal chaotic systems with topologically equivalent structures.The synchronization of multi-spatiotemporal chaotic systems is implemented by adding the control only to a terminal node,and the controller is designed via a corresponding update law.The control law is applied to spatiotemporal Gray-Scott systems.Numerical results demonstrate the effectiveness and the feasibility of the proposed approach.     

混沌系统的速度反馈同步

从线性反馈同步、广义同步、耦合同步三个方面讨论了混沌系统的速度反馈同步，计算了速度反馈同步所需要满足的反馈系数的条件，并与一般意义下的位移反馈同步系数进行了比较，结果表明速度反馈系数均大幅度减小，从而降低了同步的复杂度和代价.数值仿真表明了该方法有效可行. 关键词： 混沌 反馈 同步 最大Lyapunov指数     

Hierarchy of rational order families of chaotic maps with an invariant measure

We introduce an interesting hierarchy of rational order chaotic maps that possess an invariant measure. In contrast to the previously introduced hierarchy of chaotic maps [1–5], with merely entropy production, the rational order chaotic maps can simultaneously produce and consume entropy. We compute the Kolmogorov-Sinai entropy of these maps analytically and also their Lyapunov exponent numerically, where the obtained numerical results support the analytical calculations.