Calculation of the largest Lyapunov exponent in the discrete dynamical system with wavelet analysis

The largest Lyapunov exponent is an important parameter of detecting and characterizing chaos produced from a dynamical system. Based on simulative calculation, it has been found that the largest Lyapunov exponent of the small-scale wavelet transform modulus of a discrete dynamical system is the same as the system's. At the same time, the calculated results show that calculating the largest Lyapunov exponent with the small-scale wavelet transform modulus can efficiently eliminate the effect of strong large-scale noiss because of the high-pass filtering characteristic of small-scale wavelet transform.