时间序列最大Lyapunov指数的计算

Computing the Largest Lyapunov Exponent from Time Series

从Lyapunov指数的定义出发,研究了一种快速、高效计算时间序列最大Lyapunov指数方法。通过对几种已知模型的数值模拟表明:最大Lyapunov指数与重构相空间的维数和延迟时间在较大的变化范围能很好符合,重构相空间所需的数据较少,维数较低,使计算在结果保持准确的前提下大大简化。

A method to calculate the largest Lyapunov exponent from the observed time series based on its definition is proposed. We have tested it on several known systems, such as the Logistic model, the Henon mapping and the Lorenz system. It is found that the estimated largest Lyapunov exponent from time series has a reasonable good accuracy. More remarkably, the simulation result is independent of the embedding dimension and the delay time to a certain extent. The shorter data and the lower dimension of phase space simplify the computation without significant loss of precision.