连续动力系统的广义同步

讨论连续的混沌动力系统之间的广义同步．利用Liapunov稳定性理论,通过构造适当的耦合项,得到了一个关于驱动响应系统广义同步的充分条件．并通过对两个例子的数字模拟,说明了充分条件的有效性．     

广义函数多目标规划的充分条件

本文借助于广义函数的调和表示，采用非标准分析方法，给出广义函数多目标规划的几个充分条件．     

广义H-矩阵的一组充分条件

利用矩阵的连续过渡、子矩阵的谱半径估计等方法,研究了正定条件下的广义H-矩阵的判别法．给出了判定正定条件下广义H-矩阵的几个充分条件,当块矩阵退化为点矩阵时,这些条件即为非奇异H-矩阵的充分条件．     

一类广义Boussinesq型方程解的爆破

研究一类广义Boussinesq型方程的初边值问题,利用Galerkin方法证明问题局部广义解的存在性与唯一性．同时,通过使用凸性方法给出问题的解在有限时刻发生爆破的充分条件．     

基于比率的广义Holling-Tanner系统的全局渐近稳定性

本文对基于比率的广义Holling-Tanner系统进行了定性分析,给出了系统解有界的条件和平衡点局部稳定的条件．通过构造适当的Liapunov函数,得到了正平衡点全局渐近稳定性的充分条件．     

广义Liénard系统周期解的不存在性

本文建立了广义Lienard系统不存在周期解的若干充分条件．     

线性广义时滞系统的H∞输出反馈控制器

本文首先给出了广义时滞系统稳定的一个充分条件，接着讨论了线性广义时滞系统的H∞输出反馈控制，给出了控制器存在的充分条件，同时利用线性矩阵不等式(LMI)的方法，给出控制器的设计，最后举例说明本文方法的可行性．     

关于系统(x)=h(y)-F(x),(y)=-g(x) 的中心

本文给出了广义Ｌｉｅｎａｒｄ系统的原点为局部中心和全局中心的几个充分条件及原点为全局中心的充要条件,所得结果推广和改进了文献［１－６］的结果．     

广义Calderón-zygmund核的多线性振荡奇异积分算子的Lp-有界性

本文研究了关于广义Calderon-Zygmund核的多线性振荡奇异积分算子,给出了这类算子的Lp-有界性充分条件．     

离散广义系统的区间矩阵平稳振荡

利用范数理论和代数方法,研究了离散广义系统的区间平稳振荡问题．给出了两种区间矩阵平稳振荡存在的充分条件．提供了可行性的算例．     

Linearly coupled synchronization of the unified chaotic systems and the Lorenz systems

This paper investigates the synchronization of two linearly coupled unified chaotic systems and two linearly coupled Lorenz systems. Some sufficient conditions for synchronization are attained through rigorous mathematical theory. Compared with the results in the reference [Chaos, Solitons & Fractals 2002;14:529], the sufficient condition for the synchronization of two linearly coupled Lorenz systems is simpler and less conservative. Numerical simulations are provided for illustration and verification.     

Some new less conservative criteria for impulsive synchronization of a hyperchaotic Lorenz system based on small impulsive signals

In this Letter the issue of impulsive Synchronization of a hyperchaotic Lorenz system is developed. We propose an impulsive synchronization scheme of the hyperchaotic Lorenz system including chaotic systems. Some new and sufficient conditions on varying impulsive distances are established in order to guarantee the synchronizability of the systems using the synchronization method. In particular, some simple conditions are derived for synchronizing the systems by equal impulsive distances. The boundaries of the stable regions are also estimated. Simulation results show the proposed synchronization method to be effective.     

Analysis of generalized projective synchronization for a chaotic gyroscope with a periodic gyroscope

In this paper, a simple nonlinear controller is applied to investigate the generalized projective synchronization for a controlled chaotic gyroscope with a periodic gyroscope dynamical system. The necessary and sufficient conditions for generalized projective synchronization are developed through the theory of discontinuous dynamical systems. The synchronization invariant domain from the synchronization conditions is presented. The parameter maps are explored for a better understanding of the synchronicity of two gyroscopes with different motions. Finally, the partial and full generalized projective synchronizations of two nonlinear coupled gyroscope systems are carried out to verify the effectiveness of the scheme.     

Chaos synchronization for master slave piecewise linear systems: Application to Chua’s circuit

This paper deals with chaos synchronization for master slave piecewise linear systems. The synchronization problem is formulated as a global stability problem of error synchronization dynamics. New sufficient conditions are provided using a Lyapunov approach and the so-called S-procedure. We show that the synchronization problem can be solved as an optimization problem subject to a set of Linear Matrix Inequalities (LMI) for which a state feedback controller is designed efficiently. The effectiveness of the proposed solution is verified via simulation results using the original Chua’s circuit model. Furthermore, it will be proven that the new sufficient conditions relaxed the conservatism of previous existing works.     

分数阶双指数混沌系统的自适应滑模同步

研究了分数阶双指数混沌系统的自适应滑模同步问题.通过设计滑模函数和控制器,构造了平方Lyapunov函数进行稳定性分析.利用Barbalat引理证明了同步误差渐近趋于零,获得了系统取得自适应滑模同步的充分条件.数值仿真结果表明:选取适当的控制器及与滑模函数,分数阶双指数混沌系统取得自适应滑模同步.     

On the synchronization of different chaotic oscillators

The synchronization of two different chaotic oscillators is studied, based on an open-loop control – the entrainment control. We consider two types of synchronization: complete synchronization and effectively complete synchronization. The sufficient conditions that two different systems can be synchronized by this method is discussed. Furthermore, a hierarchical idea to synchronize multiple chaotic subsystems is proposed.     

A note on phase synchronization in coupled chaotic fractional order systems

The dynamic behaviors of fractional order systems have received increasing attention in recent years. This paper addresses the reliable phase synchronization problem between two coupled chaotic fractional order systems. An active nonlinear feedback control scheme is constructed to achieve phase synchronization between two coupled chaotic fractional order systems. We investigated the necessary conditions for fractional order Lorenz, Lü and Rössler systems to exhibit chaotic attractor similar to their integer order counterpart. Then, based on the stability results of fractional order systems, sufficient conditions for phase synchronization of the fractional models of Lorenz, Lü and Rössler systems are derived. The synchronization scheme that is simple and global enables synchronization of fractional order chaotic systems to be achieved without the computation of the conditional Lyapunov exponents. Numerical simulations are performed to assess the performance of the presented analysis.     

分数阶不确定多混沌系统的自适应滑模同步

研究分数阶不确定多混沌系统的自适应滑模同步,通过构造滑模面,设计控制器和适应规则,能够满足滑模面的稳定性与到达性,进而得到分数阶不确定多混沌系统取得自适应滑模同步的充分性条件,研究表明:分数阶不确定多混沌系统满足在一定条件下能够取得自适应滑模同步.     

On hyperchaos synchronization of a hyperchaotic Lü system

This work presents hyperchaos synchronization of two identical hyperchaotic Lü systems. In this study three methods are applied to achieve hyperchaos synchronization. The sufficient conditions for achieving synchronization of two identical hyperchaotic Lü systems are derived by using Lyapunov stability theory. Numerical simulations are presented to demonstrate the effectiveness of the proposed hyperchaos synchronization schemes.     

A simple criterion for impulsive chaotic synchronization

In the paper, impulsive synchronization of the two identical chaotic systems with different initial conditions is studied. The sufficient conditions on feedback strength and impulsive interval are established to guarantee the synchronization. The method is simple and the relevant mathematical proof is presented. Numerical simulations show the effectiveness of the method.