随机脉冲微分方程的p阶矩稳定性和参激白噪声作用下Lorenz系统的脉冲同步

考察了随机脉冲微分系统的p阶矩稳定性问题,在更符合脉冲系统一般假设的情况下,建立了条件更弱的随机脉冲微分系统p阶矩稳定性判定定理.并应用该判定定理,考察了参激白噪声作用下Lorenz系统的脉冲同步问题,证明了同步误差系统的p阶矩稳定性,从而说明在p阶矩的意义下,两个系统是可以用脉冲方法实现同步的.数值模拟验证了随机Lorenz系统脉冲同步的可行性. 关键词： 随机脉冲微分方程 p阶矩稳定性')" href="#">p阶矩稳定性 脉冲 同步     

一种异结构分数阶混沌系统投影同步的新方法

基于Lyapunov稳定性理论和分数阶系统稳定理论以 及分数阶非线性系统性质,提出了一种用来判定分数阶混沌系统是 否稳定的新的判定定理,并把该理论运用于对分数阶混沌系统的控制与 同步,同时给出了数学证明过程,严格保证了该方法的正确性与一般适用性. 运用所提出的稳定性定理,实现了异结构分数阶混沌系统的投影同步. 对分数阶Lorenz混沌系统与分数阶Liu混沌系统实现了投影同步; 针对四维超混沌分数阶系统,也实现了异结构投影同步. 该稳定性定理避 免了求解分数阶平衡点以及Lyapunov指数的问题,从而可以方便地选 择出控制律,并且所得的控制器结构简单、适用范围广. 数值仿真的结果取得了预期的效果,进一步验证了这一稳定性定理的 正确性及普遍适用性.     

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.     

基于Lyapunov方程的分数阶混沌系统同步

对阶次小于1的分数阶系统提出了基于Lyapunov方程的系统稳定性判定理论. 将该理论应用于分数阶混沌系统的同步,实现了未知参数的分数阶Lorenz混沌系统的自适应同步. 仿真结果证实了该理论的正确性. 关键词： 分数阶混沌系统 同步 Lyapunov方程 自适应     

随机粗糙面激光脉冲散射四阶统计特征

依据基尔霍夫近似,推导出一维高斯随机粗糙面四阶统计特性解析式,并获得脉冲波入射下粗糙面双点双频四阶矩互相关函数.数值计算不同入射角,不同高度起伏和相干长度,随机粗糙面双点双频四阶矩互相关函数随相干频谱带宽频差,散射角的变化情况.计算结果表明,高度起伏和相干长度对粗糙面散射四阶统计特的影响很大,粗糙面越光滑,在镜反射方向有最大的四阶矩散射峰值和小的相关带宽.随着粗糙度增加,随机粗糙面脉冲散射的四阶矩的相干分量减弱,展宽现象明显;而相干带宽频差越大,四阶矩衰减越快. 关键词： 四阶矩统计特征 双点双频互相关函数 随机粗糙面 脉冲波散射     

超混沌Lorenz系统的常数脉冲与自适应脉冲的混合控制

研究了超混沌Lorenz系统的控制问题;基于脉冲控制原理和自适应控制策略,提出了常数脉冲和自适应脉冲相结合的混合控制方法,该方法可以扩大将系统控制到稳定周期轨道的控制参数的范围.数值实验证明了这种混合控制的方法的有效性. 关键词： 超混沌Lorenz系统 常数脉冲控制 自适应脉冲控制     

分数阶系统有限时间稳定性理论及分数阶超混沌Lorenz系统有限时间同步

研究了分数阶系统有限时间稳定性理论及分数阶混沌系统的同步问题.根据分数阶微分性质及分数阶系统稳定性理论,建立了分数阶系统有限时间稳定性理论并进行了证明.根据该理论设计控制器实现了分数阶超混沌Lorenz系统有限时间同步并运用数值仿真进行了验证. 关键词： 分数阶 超混沌Lorenz系统 稳定 有限时间同步     

一类参数不确定统一混沌系统的脉冲滞后同步

针对一类具有传输信道时间延迟且参数不确定的统一混沌系统，提出了一种脉冲控制同步方法.该方法将两个非自治混沌系统之间脉冲同步的实用稳定性问题转化为同步误差系统在原点的实用稳定性问题，基于脉冲微分方程的相关理论，给出了同步误差系统在原点的实用稳定判据，仿真结果验证了方法的有效性. 关键词： 统一混沌系统 混沌同步 脉冲控制 实用稳定性     

基于改进脉冲控制方法的超混沌系统同步

针对一类整数阶与分数阶超混沌系统的同步问题, 分别提出了改进的脉冲同步方法. 基于Lyapunov稳定性理论与脉冲微分方程理论, 给出超混沌系统一组新的全局渐近同步判据. 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, 所得充分条件更次保守且更为实用. 通过对超混沌Chen系统同步的数值仿真研究, 验证了所提方法的有效性和可行性.     

非自治混沌系统的脉冲同步

研究两个非自治混沌系统之间的脉冲同步的实用稳定性,将问题转化为同步误差系统的原点的实用稳定性．利用脉冲微分方程的相关理论,给出了同步误差系统原点实用稳定的相关判据,并给出了误差范围的理论表达式．计算机仿真实验的结果验证了理论结果 关键词：     

L p-Equivalence of impulsive equations

By means of a modification of Schauder's theorem, sufficient conditions for theL _p -equivalence of impulsive nonlinear differential equations are found.     

Strong stability of impulsive systems

The strong stability of the zero solution of impulsive systems with impulses at fixed moments of time is investigated. It is proved that the existence of piecewise continuous functions with certain properties is a necessary and sufficient condition for the strong stability of the zero solution of such systems. By using differential inequalities for piecewise continuous functions, sufficient conditions for the strong stability of the zero solution are found.     

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.     

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.     

Topological classification of impulsive differential equations

The present paper is concerned with the topological classification of impulsive differential equations. Under the assumption that the linear part of the right-hand side of the equation considered has an exponential dichotomy and the nonlinear perturbation is small enough, it is proved that for the underlying equations there existN + 1 types topologically different from one another.     

First-order impulsive partial differential inequalities

We deal with the Cauchy problem for nonlinear impulsive partial differential equations of first order. Theorems on impulsive differential inequalities are obtained. Comparison results implying uniqueness criteria are proved.     

Adaptive impulsive synchronization of uncertain chaotic systems

The Letter develops an adaptive impulsive scheme that includes a sole restriction criterion to achieve synchronization of chaotic nonlinear systems with unknown parameters. The system is assumed to satisfy the local Lipschitz condition while a Lipschitz constant and the uncertain system parameters are estimated by augmented adaptation equations. Adaptation of all parameters is proven to converge exponentially. The significance of the related control parameters and their margins in the criterion is also discussed in detail. The Lorenz system has been simulated to illustrate the theoretical analysis.