关于耦合混沌系统完全同步的参数选择

以系统的瞬间特征值作为高质量同步的指标 ,讨论了两个耦合的混沌系统完全同步时参数选择的问题 .当运用线性定常系统稳定性的理论判定耦合后混沌吸引子的线性化同步系统的瞬间特征值时 ,即使其处处有负实部 ,混沌完全同步也会失去 .但是 ,使用线性时变连续系统的稳定性理论分析其瞬间特征值 ,给出耦合函数参数的选择范围 ,耦合的混沌吸引子完全同步的状态就能够达到稳定 .将该分析方法分别应用于R¨ossler和Lorenz混沌系统 ,通过数值仿真 ,发现其结果与理论分析相符 ,从而表明了该分析方法的有效性     

Grouping synchronization in a pulse-coupled network of chaotic spiking oscillators

This paper studies a pulse-coupled network consisting of simple chaotic spiking oscillators (CSOs). If a unit oscillator and its neighbor(s) have (almost) the same parameter values, they exhibit in-phase synchronization of chaos. As the parameter values differ, they exhibit asynchronous phenomena. Based on such behavior, some synchronous groups appear partially in the network. Typical phenomena are verified in the laboratory via a simple test circuit. These phenomena can be evaluated numerically by using an effective mapping procedure. We then apply the proposed network to image segmentation. Using a lattice pulse-coupled network via grouping synchronous phenomena, the input image data can be segmented into some sub-regions.     

Clustering in diffusively coupled networks

This paper shows how different mechanisms may lead to clustering behavior in connected networks consisting of diffusively coupled agents. In contrast to the widely studied synchronization processes, in which the states of all the coupled agents converge to the same value asymptotically, in the cluster synchronization problem studied in this paper, we require all the interconnected agents to evolve into several clusters and each agent only to synchronize within its cluster. The first mechanism is that agents have different self-dynamics, and those agents having the same self-dynamics may evolve into the same cluster. When the agents’ self-dynamics are identical, we present two other mechanisms under which cluster synchronization might be achieved. One is the presence of delays and the other is the existence of both positive and negative couplings between the agents. Some sufficient and/or necessary conditions are constructed to guarantee n-cluster synchronization. Simulation results are presented to illustrate the effectiveness of the theoretical analysis.     

Distributed filtering and synchronization of diffusively state‐coupled heterogeneous systems

This paper studies distributed filtering‐based ssynchronization of diffusively state‐coupled heterogeneous systems. For given heterogeneous subsystems and a network topology, sufficient conditions for the filtering‐based synchronization are developed with a guaranteed performance. The estimation and synchronization error dynamics are obtained in a decoupled form, and it is shown that the filter and the controller can be designed separately by LMIs. The feasibility of the proposed design method using LMIs is discussed, and the main results are validated through examples with various setup. Copyright © 2016 John Wiley & Sons, Ltd.     

Pixel clustering by adaptive pixel moving and chaotic synchronization

In this paper, a network of coupled chaotic maps for pixel clustering is proposed. Time evolutions of chaotic maps in the network corresponding to a pixel cluster are synchronized with each other. Those synchronized trajectories are desynchronized with respect to the time evolutions of chaotic maps corresponding to other pixel clusters in the same image. A pixel motion mechanism is also introduced, which makes each group of pixels more compact and, consequently, makes the model robust enough to classify ambiguous pixels. Another feature of the proposed model is that the number of pixel clusters does not need to be previously known.     

时变耦合神经振子集群刺激依赖性相响应同步

考虑时变耦合情形下,利用相位响应曲线建立谐波刺激作用下耦合神经振子集群活动的动力学模型.引入相位概率密度函数导出描述神经振子集群活动序参数的演化方程.数值模拟结果表明高频谐波刺激可产生相位同步周期振荡,同步振荡周期与刺激频率有关,刺激频率越高神经振子群同步振荡频率也越高;同步强度与刺激强度有关,刺激越强同步程度越高.     

统一混沌系统的自适应控制同步

基于Pecora-Carroll混沌同步原理和参数自适应控制策略,提出一种单参数统一混沌系统的自适应同步控制方法;推导出实现不同参数、不同初值的两统一混沌系统同步的参数自适应控制律和同步条件;研究了确定控制常数边界和范围的方法,并讨论了控制常数对同步性能的影响.理论分析和数值仿真表明,选择合适的控制常数,可实现两统一混沌系统的大范围渐近稳定同步.     

Hybrid projective synchronization in a chaotic complex nonlinear system

Hybrid projective synchronization (HPS), in which the different state variables can synchronize up to different scaling factors, is numerically observed in coupled partially linear chaotic complex nonlinear systems without adding any control term in the present paper. The scaling factors of HPS are hardly predictable. Linear feedback control method is thus adopted to control them onto any desired values based on Lyapunov stability theory. Moreover, numerical simulations are given to illustrate and verify the analytical results.     

Large-dimension image clustering by means of fragmentary synchronization in chaotic systems

The paper describes chaotic neural network improvements to enhance the quality of n-dimensional image clustering. New synchronization type—cluster fragmentary synchronization was found. To reveal fragmentary synchronization a new method is proposed. Benderskaya Elena Nikolaevna was born in 1969. She graduated from Automation and Computer Systems department of the St. Petersburg State Polytechnical University in 1993. In 1996 she received her candidate’s degree in the field of mathematical and computer modeling. Since 1996, she delivers lectures at the Faculty of computer science, SPbSPU. Her scientific interests include different aspects of artificial intelligence, namely, neural networks and adjacent fields (pattern recognition, fuzzy logic, evolution computations, and synergetics). She is the winner of the Informica 2006 All-Russian Grant Contest (FGU GNII ITT)—a contest between the leaders of scientific teams working in the field of telecommunication technology. Zhukova Sofya Vitalyevna was born in 1981. She graduated from Automation and Computer Systems department of St. Petersburg State Polytechnical University in 2004. In 2007, under E.N. Benderskaya’s supervision she defended her PhD thesis in the field of system analysis, control, and information processing (informatics). Since 2008 she holds the appointment of associate professor at the Graduate School of Management, St. Petersburg State University. Her scientific interests include control theory, internet technologies, self-organization theory, the theory of nonlinear systems, and the theory of neural networks. She was awarded a grant from the Government of the Russian Federation as a result of the All-Russia Contest of 2006–2007 for Postgraduates.     

时滞输出反馈非恒同主从耦合混沌系统一致同步的判据

当主从耦合混沌系统的参数之间非恒同时,一般意义上的混沌同步难以实现,因此,讨论了其具有一定误差界的一致同步问题.本文对一类包含Lur’e系统和Lipschitz系统在内的混沌系统,应用Lyapunov函数方法导出通过时滞输出反馈控制实现一致同步的充分条件,该判据用矩阵不等式的形式给出.进而讨论了同步的鲁棒性问题.最后结合Chua电路对结论进行了数值模拟,验证了结论的正确性与有效性.     

内共振系统的混沌同步现象

研究了两耦合混沌系统之间 2∶1内共振条件下的相位混沌同步现象 ,发现随着耦合程度的增加 ,系统会进入相位混沌同步 .当耦合程度的增加到一定值时 ,相位混沌同步现象消失 .通过计算相应的Lyapunov指数 ,发现相位混沌同步现象的产生与消失与耦合系统的Lyapunov指数之间存在一定的关系     

一个新的复混沌系统的动力学特性及其同步

提出了一个新的复数形式的混沌系统,系统的研究了其对称性、耗散性、Lyapnov指数和吸引子等基本动力学特性,接着根据无源控制原理设计控制器实现了混沌系统的同步,然后基于Lyapunov稳定性理论与无源控制原理从理论上证明了方法的有效性,最后又通过matlab软件对混沌同步系统进行数值仿真,仿真结果显示两个混沌很快很好地达到了同步,从而进一步验证了该方法的有效性和可行性.     

一个混沌系统的同步控制研究

研究了一个混沌系统的混沌同步控制问题。分别采用线性反馈控制方法、非线性反馈方法、脉冲控制方法对该混沌系统进行同步控制。基于Lyapunov稳定性理论和脉冲控制技术,对同步的充分条件进行了讨论,并给出了相应的理论证明。数值仿真证明了这三种不同方法的有效性。     

一类非线性反馈混沌系统分析和同步控制

讨论了如何由 SISO线性系统经非线性反馈构造混沌系统 ,给出了此类混沌系统采用单变量信号实现同步的控制策略 ,通过梯度下降法减少在带有噪声驱动信号下系统同步的多步误差均方差 ,得到最优耦合参数。数字仿真表明了理论分析的正确性     

基于脉冲同步的混沌保密通信系统

介绍了脉冲混沌同步的基本原理,提出了基于脉冲同步的一般化混沌保密通信系统。针对该系统存在的传输时间帧拥堵问题,提出一种“信息感应”脉冲同步系统。该系统中有用信息被嵌入在发射端的同步脉冲里,在接收端再通过这些脉冲被感应出来,解决了时间帧拥堵的问题。     

基于动态事件触发的混沌系统故障容错同步问题

针对混沌系统故障容错同步问题进行研究,设计基于动态事件触发的同步控制器以实现混沌系统的故障容错同步.首先,针对系统中存在的故障环节构造故障容错的系统模型,在此基础上采用输入-状态稳定性(ISS)的方法,将控制器求解问题转化为求解所对应故障容错系统的稳定性问题;然后,通过构造Lyapunov函数给出混沌系统故障容错同步的充分条件,通过引入动态变量,使得所设计的触发条件可以根据系统的运行状态进行动态调整,在实现系统故障容错同步的同时,最大程度地降低网络的占用率;最后,通过数值仿真验证所提出方法的有效性.     

Hermite-neural-network-based adaptive control for a coupled nonlinear chaotic system

A TSK-type Hermite neural network (THNN) is studied in this paper. Since the output weights of the THNN use a functional-type form, it provides powerful representation, high learning performance and good generalization capability. Then, a Hermite-neural-network-based adaptive control (HNNAC) system which is composed of a neural controller and a robust compensator is proposed. The neural controller utilizes a THNN to online approximate an ideal controller, and the robust compensator is designed to eliminate the effect of the approximation error introduced by the neural controller upon the system stability. Moreover, a proportional-integral (PI)-type learning algorithm is derived to speed up the convergence of the tracking error. Finally, the proposed HNNAC system is applied to synchronize a coupled nonlinear chaotic system. In the simulation study, it shows that the proposed HNNAC system can achieve favorable synchronization performance without requiring a preliminary offline tuning.

     

基于统一混沌系统的同步及其保密通信研究

针对最新提出的统一混沌系统模型,采用线性状态反馈同步方法,实现了统一混沌系统精确同步问题。在此基础上,提出了混沌保密通信方案,并将其应用于混沌掩盖与混沌扩频两种保密通信方式。基于matlab6.5的仿真结果表明了上述方法的有效性。     

线性反馈实现Liu系统的混沌同步

讨论了新混沌系统Liu系统的混沌同步问题.基于Lyapunov函数分别提出了单变量以及多变量的线性状态反馈控制方案,采用这两种线性控制方案均可实现Liu系统的混沌同步.线性反馈控制比起非线性控制具有结构简单、易于实现的特点.数值模拟结果验证了两种方案的可行性.