Lyapunov指数计算研究及应用

Research on Lyapunov Exponents Algorithm and its Application

Lyapunov指数是判定系统是否处于混沌状态的简捷方法之一,但计算Lyapunov指数的诸多方法普遍存在精度不高、受噪声影响大且计算量大等问题而使应用受到限制。借助计算机代数系统Maple建立基于Wolf算法的Lyapunov指数的机械化算法,可以方便地计算Lyapunov指数,从而可以迅速判定系统的混沌性。

Lyapunov exponents is a simple method of judging whether one system is chaotic or not, but various ways of calculating have been restrained due to the problems of being inaccurate, being affected greatly by noise and abundant calculations. Based on the Wolf algorithm, a new mechanical algorithm for calculating Lyapunov exponents with the help of computer algebra system Maple is established, which can calculate Lyapunov exponents conveniently and judge the system rapidly.