基于支持向量机回归的Lyapunov指数计算方法研究

Algorithm for computing Lyapunov exponent based on support vector

Lyapunov指数是描述动力学系统混沌性质的重要指标,在小样本条件下准确、快速地计算Lyapunov指数是一个难题.对此,提出一种基于支持向量机回归的Lyapunov指数计算方法,通过量子遗传算法对支持向量机模型的参数进行优化,推导了支持向量机回归应用于计算Lyapunov指数的公式.通过对混沌序列进行仿真实验,仿真结果表明,在小样本数据情况下,此方法可行有效.

Lyapunov exponent（LE） is an important indicator to describe the nature of chaotic dynamical systems.It’s difficult to calculate LE accurately and fast with small sample size.In this paper,an algorithm for computing LE based on support vector regression（SVR） is proposed,the parameters of support vector machine（SVM） model are optimized by using quantum genetic algorithm（QGA）,and the formula of the LE based on SVR is derived.Simulation results show that the proposed algorithm is feasible and effective with much less samples.