基于Delaunay三角剖分的最大Lyapunov指数算法研究

Method for the Calculation of Largest Lyapunov Exponent Based on Delaunay Triangulation

针对时间序列最大Lyapunov指数计算速度慢的缺陷,研究了小数据量算法,提出了基于Delaunay三角剖分的最大Lyapunov指数的计算方法。利用Delaunay三角剖分方法解决了邻点搜索速度慢的问题。详细地介绍了算法步骤,分析了算法的运算量,并应用于几种离散映射。仿真试验表明:该方法较稳定、可靠,同时对相空间重构中的嵌入维数不敏感。

In order to solve the problem of slow speed of calculating the largest Lyapunov exponent of time series, a new method is used on Delaunay triangulation for calculating largest Lyapunov exponent. The problem of searching for the neighboring points is solved by Delaunay triangulation. The algorithm steps and time complexity are narrated in detail. The algorithm is used to calculate Lyapunov exponent of several discrete maps. Simulation results show that this algorithm is stable and is not sensitive to the embedding dimension while reconstructing phasespace.