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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 is an important index to describe the chaotic properties of dynamical systems. It is a difficult problem to calculate Lyapunov exponents quickly and accurately under small sample conditions. In this paper, a Lyapunov exponent calculation method based on support vector machine regression is proposed. Through quantum genetic algorithm The parameters of SVM model are optimized, and the formulas of SVM regression for calculating Lyapunov exponent are deduced.The simulation results show that this method is feasible and effective in the case of small sample data.