Lyapunov指数计算算法的设计与实现  

Design and Implementation of Lyapunov Exponents Calculating Algorithm

作　　者：孙克辉[1] 谈国强[1] 盛利元[1] 张泰山[1] 

机构地区：[1]中南大学物理科学与技术学院,长沙410083

出　　处：《计算机工程与应用》2004年第35期12-14,共3页Computer Engineering and Applications

基　　金：湖南省自然科学基金项目(编号:01JJY2110)

摘　　要：为了定量分析混沌系统的动力学特性,论文研究了计算Lyapunov指数的Jacobi矩阵算法,并采用Matlab6.5软件平台设计了基于该算法的Lyapunov指数计算软件,算法程序简洁、可读性强、易于移植,GUI编程技术使人机交换能力增强,制作的Lyapunov指数工具箱能够求解非线性动力学系统的Lyapunov指数谱和分数维。最后,分析了迭代次数、计算步长、解法器和初值等因素对计算精度的影响。In order to analyse the dynamical property of chaos system by fixed quantity,a Jacobi-matrix algorithm to calculate Lyapunov exponent is studied and the Lyapunov exponent calculating software with this algorithm in Matlab platform is designed.The program is concision,easy to read and convent to replant.GUI program technology improves the capability of communication between man and computer.The Lyapunov toolboxes can calculate Lyapunov exponent spectrum and fractal dimension of most nonlinear dynamical systems.At last,some affecting factors to the result such as iteration number,length of the step and solver,etc are discussed.

关 键 词：混沌系统 JACOBI矩阵 LYAPUNOV指数 条件Lyapunov指数 分数维 

分 类 号：O415.5[理学—理论物理]