Reliable impulsive synchronization for a class of nonlinear chaotic systems

The problem of reliable impulsive synchronization for a class of nonlinear chaotic systems has been investigated in this paper. Firstly a reliable impulsive controller is designed by using the impulsive control theory. Then by the uniform asymptotic stability criteria of systems with impulsive effects, some sufficient conditions for reliable impulsive synchronization between the drive system and the response system are obtained. Numerical simulations are given to show the effectiveness of the proposed method.     

Impulsive control of chaotic systems and its applications in synchronization

In this paper,some novel sufficient conditions for asymptotic stability of impulsive control systems are presented by comparison systems.The results are used to obtain the conditions under which the chaotic systems can be asymptotically controlled to the origin via impulsive control.Compared with some existing results,our results are more relaxed in the sense that the Lyapunov function is required to be nonincreasing only along a subsequence of switchings.Moreover,a larger upper bound of impulsive intervals for stabilization and synchronization is obtained.     

An improved impulsive control approach to nonlinear systems with time-varying delays

A scheme for the impulsive control of nonlinear systems with time-varying delays is investigated in this paper. Based on the Lyapunov-like stability theorem for impulsive functional differential equations (FDEs), some sufficient conditions are presented to guarantee the uniform asymptotic stability of impulsively controlled nonlinear systems with time-varying delays. These conditions are more effective and less conservative than those obtained. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed method.     

Stability Analysis and Design of Impulsive Control Lorenz Systems Family

Lorenz systems family unifying Lorenz system, Chen system and Lü system is a typical chaotic family. In this paper, we consider impulsive control Lorenz chaotic systems family with time-varying impulse intervals. By establishing an effective tool of a set of inequalities, we analyze the asymptotic stability of impulsive control Lorenz systems family and obtain some new less conservative conditions. Based on the stability analysis, we design a novel impulsive controller with time-varying impulse intervals. Illustrative examples are provided to show the feasibility and effectiveness of our method. The obtained results not only can be used to design impulsive control for Lorenz systems family, but also can be extended to other chaotic systems.     

Analysis and design of set-stability for impulsive control systems

This Letter studies analysis and design of set-stability for impulsive control systems. A new comparison theorem of asymptotic set-stability for impulsive differential system is presented. Based on the new result, we derive some less conservative conditions for asymptotic set-stability of impulsive control systems with impulse at fixed times, and the results are used to design impulsive control laws of nonlinear systems for set-stability. A numerical example is used to verify the theoretical result.     

Uniform stability with respect to the impulsive perturbations of the solutions of impulsive differential equations

The notions of strong uniform stability of the zero solution of systems of differential equations and uniform stability with respect to the impulsive perturbations of the zero solution of systems of impulsive differential equations are introduced. The main results are given in two theorems. The first contains sufficient conditions under which the strong uniform stability of the zero solution of the respective system without impulses implies uniform stability with respect to the impulsive perturbations of the zero solution of the initial system with impulses. In the second theorem sufficient conditions are given under which the uniform Lipschitz stability of the zero solution of the respective system without impulses implies uniform stability with respect to the impulsive perturbations of the zero solution of the initial system with impulses.     

忆阻混沌系统的脉冲同步与初值影响研究

以光滑三次型磁控忆阻器的蔡氏电路为例, 研究了两个同构忆阻混沌系统的脉冲控制同步方法.基于Lyapunov稳定性理论, 给出了忆阻混沌系统的脉冲同步渐近稳定条件; 结合误差系统的最大条件Lyapunov指数谱, 讨论了系统初值对脉冲同步性能的影响, 并进行了相应的数值仿真实验.结果表明, 在合适的脉冲控制参数条件下, 同构的忆阻混沌系统的脉冲同步是可行而有效的; 忆阻混沌系统的初值对脉冲同步性能存在一定的影响, 但可通过增大脉冲耦合强度来抑制系统初值的影响.     

Solubility and immiscibility behavior in ternary hydrothermal systems with critical phenomena in saturated solutions

Abstract

Liquid-liquid immiscibility occurs widely in water-salt systems as stable and metastable equilibria at sub- and supercritical conditions. The phase behavior of ternary mixtures complicated by metastable immiscibility and by a transition of the metastable immiscibility regions into the stable equilibria is discussed using the experimental data on water-salt systems and theoretically derived complete phase diagrams.     

Lipschitz stability of impulsive systems of differential equations

Notions ofLipschitz stability of the zero solution of impulsive systems of differential equations with fixed moments of impulse effect are introduced. Sufficient conditions for various types of uniform Lipschitz stability are obtained and the relations between these notions are investigated. The results obtained are used for the investigation of the uniform Lipschitz stability of the zero solution of linear impulsive systems of differential equations.     

Stability of sets for impulsive systems

Problems related to the stability and asymptotic stability of sets of sufficiently general type with respect to impulsive systems are considered. The research is done by means of piecewise continuous anxiliary functions which are an analogue of the classical Lyapunov functions. It is proved that the existence of such functions with certain properties is a sufficient condition for various types of stability and asymptotic stability of sets with respect to impulsive systems.     

Modified impulsive synchronization of fractional order hyperchaotic systems

In this paper, a modified impulsive control scheme is proposed to realize the complete synchronization of fractional order hyperchaotic systems. By constructing a suitable response system, an integral order synchronization error system is obtained. Based on the theory of Lyapunov stability and the impulsive differential equations, some effective sufficient conditions are derived to guarantee the asymptotical stability of the synchronization error system. In particular, some simpler and more convenient conditions are derived by taking the fixed impulsive distances and control gains. Compared with the existing results, the main results in this paper are practical and rigorous. Simulation results show the effectiveness and the feasibility of the proposed impulsive control method.     

Cylindrical MHD induction device in the “ideal pressure source” regime

The causes for the onset of a specific operating regime of MHD induction devices which arises after a loss of stability of the uniform flow are investigated. A modification of the original method of studying singularly perturbed dynamical systems in the neighborhood of a bifurcation point is used to construct the asymptotic behavior of the characteristic pressure for various limiting cases. Zh. Tekh. Fiz. 67, 5–9 (June 1997)     

基于比较系统方法的分数阶混沌系统脉冲同步控制

针对一类分数阶混沌系统的同步问题, 提出基于比较系统理论的脉冲同步方法. 通过构造新的响应系统, 可将原分数阶同步误差系统转化为整数阶同步误差系统, 基于Lyapunov稳定性理论与脉冲微分方程理论, 给出一组新的分数阶混沌系统全局渐近同步判据. 特别地, 当脉冲间距与脉冲控制增益为常数时, 可获得更为简单和实用的同步判据. 与现有结果相比, 所得充分条件更为严格和实用. 通过对分数阶Chen系统同步问题的数值仿真研究, 验证了所提方法的有效性和可行性.     

Impulsive control of nonlinear systems with time-varying delays

A whole impulsive control scheme of nonlinear systems with time-varying delays, which is an extension for impulsive control of nonlinear systems without time delay, is presented in this paper. Utilizing the Lyapunov functions and the impulsive-type comparison principles, we establish a series of different conditions under which impulsively controlled nonlinear systems with time-varying delays are asymptotically stable. Then we estimate upper bounds of impulse interval and time-varying delays for asymptotically stable control. Finally a numerical example is given to illustrate the effectiveness of the method.     

Impulsive control of time-delay systems using delayed impulse and its application to impulsive master-slave synchronization

This Letter is concerned with impulsive control of a class of nonlinear time-delay systems. Some uniform stability criteria for the closed-loop time-delay system under delayed impulsive control are derived by using piecewise Lyapunov functions. Then the criteria are applied to impulsive master-slave synchronization of some secure communication systems with transmission delays and sample delays under delayed impulsive control. Two numerical examples are given to illustrate the effectiveness of the derived results.     

Stabilizability of discrete chaotic systems via unified impulsive control

This Letter is concerned with the asymptotical stabilization problem of discrete chaotic systems by using a novel unified impulsive control scheme. Sufficient conditions for asymptotical stability of the impulsive controlled discrete systems are obtained by means of the Lyapunov stability theory and algebraic inequality techniques. Finally, numerical simulations on the Hénon and Ushio discrete chaotic systems are presented to illustrate the effectiveness and usefulness of the unified impulsive control scheme.     

Impulsive synchronisation of a class of fractional-order hyperchaotic systems

In this paper,an impulsive synchronisation scheme for a class of fractional-order hyperchaotic systems is proposed.The sufficient conditions of a class of integral-order hyperchaotic systems’ impulsive synchronisation are illustrated.Furthermore,we apply the sufficient conditions to a class of fractional-order hyperchaotic systems and well achieve impulsive synchronisation of these fractional-order hyperchaotic systems,thereby extending the applicable scope of impulsive synchronisation.Numerical simulations further demonstrate the feasibility and effectiveness of the proposed scheme.     

参数不确定时延超混沌系统的脉冲同步方法研究

针对一类参数不确定的异构时延超混沌系统,采用响应系统与驱动系统状态变量误差的线性反馈作为脉冲控制信号,基于Lyapunov稳定性理论实现了超混沌系统的脉冲同步,给出了渐近稳定条件,并构造了一个具有时延的数字保密通信系统.该方案保密性高,鲁棒性强.数值仿真表明系统能快速达到同步,应用混沌密码序列对数字信号进行加密后,信息信号可以在接收端有效地恢复出来. 关键词： 时延 脉冲同步 数字保密通信     

Adaptive impulsive synchronization for a class of fractional-order chaotic and hyperchaotic systems

In this paper, the adaptive impulsive synchronization for a class of fractional-order chaotic and hyperchaotic systems with unknown Lipschitz constant is investigated. Firstly, based on the adaptive control theory and the impulsive differential equations theory, the impulsive controller, the adaptive controller and the parametric update law are designed, respectively. Secondly, by constructing the suitable response system, the original fractional-order error system can be converted into the integral-order one. Finally, the new sufficient criterion is derived to guarantee the asymptotical stability of synchronization error system by the Lyapunov stability theory and the generalized Barbalat's lemma. In addition, numerical simulations demonstrate the effectiveness and feasibility of the proposed adaptive impulsive control method.     

Lipschitz quasistability of impulsive systems of differential equations

A suitable comparison lemma is used to obtain sufficient conditions for uniform Lipschitz quasistability of an arbitrary solution of an impulsive system of differential equations with unfixed moments of impulse effect. The results are applied to finding conditions for uniform Lipschitz quasistability for linear impulsive systems with unfixed moments of impulse effect.