新型四维超混沌系统广义投影同步及自适应同步

基于Lyapunov稳定性理论,设计合适的非线性反馈控制器以及参数更新规则,实现一类混沌系统的自适应广义投影同步.该控制器既可以适用于不包含未知参数的广义投影同步,又适用于包含未知参数的自适应广义投影同步.以新型四维超混沌系统为例,考虑含有未知参数和不含有未知参数的两种情况,从而实现驱动系统和响应系统渐近地达到所有状态向量的按照不同比例广义投影同步,同时辨识出系统的未知参数.数值模拟结果表明了所设计控制器的有效性.     

基于模糊模型的不确定时变时滞混沌系统同步

针对存在参数摄动、外扰动等不确定因素的时变时滞混沌系统的同步问题,基于Lyapunov-计的模糊控制器结构简单,且该方法适用于绝大多数变时滞混沌系统的同步控制.仿真结果表明所提出的控制方法是有效的.     

基于时变延迟混沌神经网络的H∞同步保密通信

针对一类含保密信息的时变延迟混沌神经网络,提出了同结构H_∞同步控制方案, 在实现同步后能有效恢复出隐藏的多路明文信号。利用线性矩阵不等式方法为同结构时变延迟混沌神经网络设计了H_∞同步控制器,在此基础上应用Lyapunov方法分析了同步误差的收敛性。当同步误差收敛时,可根据被动系统状态恢复出所传输的隐藏信号。仿真结果表明,该控制方案可以实现变时延混沌神经网络同步,并能恢复出多路明文信号。     

时变时滞统一混沌系统的脉冲同步控制

对参数不确定时变时滞统一混沌系统的脉冲同步控制问题进行了理论分析,利用脉冲控制方法、 李雅普诺夫稳定理论和矩阵不等式技术,给出了在驱动系统和响应系统的时滞不相同时, 其脉冲一致渐近同步的充分条件,并由此设计了一个与时滞和初值有关的脉冲控制器. 最后,通过数值示例仿真对所得结果进行了验证.     

一类混合时滞系统的混沌同步与应用

针对一类混合时滞系统的同步性问题,提出了这类系统混沌同步的一般化结果.利用Lyapunov函数,结合不等式技巧及驱动-响应方法,通过一个控制律来实现两个可辨识混合时滞系统的状态同步,并获得了实用的构造性代数条件,使得混沌同步的研究结果一般化,推广了已有结果.讨论了所获得的结果在生物学及神经网络中的应用,得到相应的同步控制充分性条件,进一步扩展了已有结果.     

时滞混沌系统的脉冲同步

针对时滞混沌系统的同步问题,利用脉冲控制方法,提出了新的渐进同步的充分条件。利用脉冲状态反馈控制,在系统矩阵为Hurwitz矩阵和正定矩阵两种情况下,得到了时滞混沌系统同步的充分条件;进一步,为便于工程应用,利用脉冲输出反馈,在系统矩阵为上述两种情况下,得到了时滞混沌系统同步的充分条件。该同步条件使时滞混沌同步系统快速地达到10-2误差。最后,以一个多重时滞混沌系统为例,进行了数值仿真,验证了该方法的有效性。     

广义离散时滞复杂动态网络的同步控制

讨论了一类广义离散时滞复杂动态网络的同步稳定性和牵制控制问题.针对此类系统,首先得到了弱保守性的离散时滞复杂动态网络系统的同步稳定性条件.其次,通过对部分节点设计牵制控制器,使得整个复杂动态网络系统达到同步,从而保证了整个系统的同步稳定性.随后,将控制器的设计问题转化为求解线性矩阵不等式(LM I)的凸优化问题,便于利用现有的优化软件求解.同时,大大降低了问题求解的复杂性.仿真结果验证了方法的有效性.     

生物神经网络系统的动力学研究进展及展望

生物神经网络系统是复杂的非线性动力学系统,其动力学研究是国内外关注的一个重要课题.本文概括性地介绍神经网络系统的动态特性及影响因素,包括时滞和噪声对神经元网络的同步,同步转迁和随机共振的影响,并且介绍神经网络系统的建模问题.由于生物神经网络通常是动态的系统,因此建立模型要考虑网络如何受时变连接方式的影响,最后对今后研究给出一些展望.     

异结构不确定混沌系统的广义投影同步

针对一类参数随时间变化的不确定混沌系统,用鲁棒自适应方法实现异结构混沌系统的广义投影同步和参数辨识。基于李亚普诺夫稳定性理论,设计了鲁棒自适应控制器和参数自适应律。通过改变广义投影同步的比例矩阵,获得所有状态变量任意比例于原驱动系统的混沌信号,并辨识出系统所有未知参数。以R-ssler超混沌系统和Lü超混沌系统为例,数值仿真验证了所设计方法的有效性和可行性。     

新型超混沌系统的改进自适应广义投影同步

基于Lyapunov稳定性理论,设计合适的非线性控制器以及参数更新规则,实现一类混沌系统以及超混沌系统的改进自适应广义投影同步。该方法可以使得驱动系统和响应系统渐近地达到所有对应状态向量,按照不同的比例进行同相位或者反相位投影同步,同时既可以对响应系统中的未知参数进行辨识,也可以对驱动系统中的未知参数进行辨识,当然,该方法也可以适用于不包含未知参数的混沌系统广义投影同步。以新型的四维超混沌Lorenz系统和超混沌Chen系统为例,数值模拟结果表明了所设计控制器的有效性。     

Finite-Time and Fixed-Time Synchronization of Inertial Neural Networks with Mixed Delays

This paper considers the drive-response synchronization in finite-time and fixed-time of inertial neural networks with time-varying and distributed delays(mixed delays). First, by constructing a proper variable substitution, the original inertial neural networks can be rewritten as a first-order differential system. Second, by constructing Lyapunov functions and using differential inequalities,some new and effective criteria are obtained for ensuring the finite-time synchronization. Finally, three numerical examples are also given at the end of this paper to show the effectiveness of the results.     

New results on the robust stability analysis of neural networks with discrete and distributed time delays

Delay-dependent robust stability of cellular neural networks with time-varying discrete and distributed time-varying delays is considered. Based on Lyapunov stability theory and the linear matrix inequality （LMIs） technique, delay-dependent stability criteria are derived in terms of LMIs avoiding bounding certain cross terms, which often leads to conservatism. The effectiveness of the proposed stability criteria and the improvement over the existing results are illustrated in the numerical examples.     

Passivity analysis for uncertain stochastic neural networks with discrete interval and distributed time-varying delays

The problem of passivity analysis is investigated for uncertain stochastic neural networks with discrete interval and distributed time-varying delays. The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time-varying and belongs to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. By constructing proper Lyapunov-Krasovskii functional and employing a combination of the free-weighting matrix method and stochastic analysis technique, new delay dependent passivity conditions are derived in terms of linear matrix inequalities (LMIs). Finally, numerical examples are given to show the less conservatism of the proposed conditions.     

变时滞广义神经网络的指数稳定性

讨论具有可变时滞的Cohen Grossberg广义神经网络平衡态的稳定性问题。以推广的Halanay微分不等式为工具,通过构造合适的Lyapunov函数,结合Dini导数和不等式技巧,对具有可变时滞(适合于任何时滞有界情况)的广义神经网络平衡态的指数稳定性进行分析。在适当的假设条件下,得到了系统渐近指数稳定的几个充分性判据,与此同时也给出了相应的Lyapunov指数。     

一类新的离散时延递归RBF神经网络

提出了一类带有离散时间 FIR/ IIR滤波器的递归 RBF神经网络 ,用离散时间 FIR/ IIR滤波器代替通常的 RBF神经网络中的线性输出权值 ,以适用于离散动力学系统的辨识和控制以及混沌时间序列预测 .本文给出的学习算法简单 ,可以避免传统的递归算法的不稳定性 .将该类神经网络用于动力学系统的建模 ,收到很好的效果 .     

Global Asymptotic Synchronization of a Class of BAM Neural Networks with Time Delays via Integrating Inequality Techniques

In this paper, the authors are concerned with global asymptotic synchronization for a class of BAM neural networks with time delays. Instead of using Lyapunov functional method, LMI method and matrix measure method which are recently widely applied to investigating global exponential/asymptotic synchronization for neural networks, two novel sufficient conditions on global asymptotic synchronization of above BAM neural networks are established by using a kind of new study method of global synchronization: Integrating inequality techniques. The method and results extend the study of global synchronization of neural networks.     

Adaptive NN stabilization for stochastic systems with discrete and distributed time-varying delays

A new adaptive neural network(NN) output-feedback stabilization controller is investigated for a class of uncertain stochastic nonlinear strict-feedback systems with discrete and distributed time-varying delays and unknown nonlinear functions in both drift and diffusion terms.First,an extensional stability notion and the related criterion are introduced.Then,a nonlinear observer to estimate the unmeasurable states is designed,and a systematic backstepping procedure to design an adaptive NN output-feedback controller is proposed such that the closed-loop system is stable in probability.The effectiveness of the proposed control scheme is demonstrated via a numerical example.     

Pinning Synchronization of Discrete-Time Complex Networks with Different Time-Varying Delays

This paper investigates pinning synchronization of discrete-time complex networks with different time-varying delays. An important lemma is presented and proved, then detailed analysis is given to yield some synchronization criteria for this kind of networks. The results provide an effective way to synchronize discrete-time complex networks by reducing control cost. Furthermore, these theoretical results are illustrated by a complex network via two kinds of pinning schemes. Numerical simulations verify the feasibility of the proposed methods.