条件Lyapunov指数和时间τ-条件Lyapunov指数的研究  

Study on the Conditional Lyapunov Exponents and Time- Lyapunov Exponents

作　　者：何岱海[1] 徐健学[1] 陈永红[1] 谭宁[1] 

机构地区：[1]西安交通大学非线性动力学研究所,西安710049

出　　处：《电路与系统学报》2000年第2期33-37,共5页Journal of Circuits and Systems

基　　金：国家自然科学基金资助项目!(19702015)。

摘　　要：本文研究条件Lyapunov指数与－条件Lyapunov指数的定义、求解技术及其应用。两种指数从不同角度对系统本质特性进行刻划。条件Lyapunov指数在混沌同步中有重要应用，近来它还被用来进行相空间重构问题的研究。时间－条件Lyapunov指数是一类利用状态变量的离散采样作驱动信号的脉冲方式同步的重要定量指标。本文提出一种简便的求解技术，在Wolf求解Lyapunov指数谱程序的基础上，稍加改动即可使其适用于Lyapunov指数、条件Lyapunov指数和时间－条件Lyapunov指数的计算，对其正确性进行了验证。研究发现对时间－条件Lyapunov指数的计算，可以准确估计脉冲方式同步的最大间隔和最优区间，对于实际工作具有重要意义。The definition, solving method and potential applications of the conditional Lyapunov exponents(CLE) and time- Lyapunov exponents are discussed . These two exponents describe the essential properties of dynamical systems from different points of view. The conditional Lyapunov exponent plays an important part in chaotic synchronization and has been used in the research of phase space reconstruction recently. On the other hand, time- Lyapunov exponents are important quantitative indexes in the impulsive synchronization. The contribution of this paper is to propose handy algorithm to derive these two exponents. Using our method and doing little modification on the basis of Wolf programming, which is used to calculate Lyapunov exponents of differential dynamic systems, these two exponents can be acquired easily. The correctness of the result are also verified. Using this algorithm, the longest time-interval and the best time for impulsive synchronization can also be estimated.

关 键 词：混沌同步 脉冲同步 条件Lyapunov指数 

分 类 号：O24[理学—计算数学] TN711.4[理学—数学]