The largest Lyapunov exponent of chaotic dynamical system in scale space and its application

摘要

Within what is called nonlinear time series analysis, it is of great interest to measure the largest Lyapunov exponent, which, if positive, by definition is the most important evidence for chaos.Nowadays wavelet analysis has become an effective tool in signal process. In this paper, we find that the largest Lyapunov exponent of the small-scale wavelet transform modulus of a dynamical system is the same as the system's largest Lyapunov exponent, based on theoretical analysis and numerical experiments. This property is very useful for time series with noise.