Investigation about the Lorenz model and logistic equation based on the complexity

The complexity series of the logistic equation and the Lorenz model were respectively calculated using a dynamical nonlinear analysis method for time series— —Lemper-Ziv complexity algorithm, and the physical implication of Lemper-Ziv co mplexity is also discussed. Results show that for the logistic equation, the com plexity is obviously different when the complicated degree of the time series i s variational; and for Lorenz model, i.e. its x-, y-, and z-portions, th eir complexities are all chaotic and are all composed of many cycles whose swings are almost the same and the lengths are different. The result reflects the in ternal quasi-periodicity. Further investigations indicate that when different wi ndow lengths are selected, the characters of the complexity series for a given t ime series are basically the same, and there exists a coherency between the jump s of the complexity series and the jumps of the time series. Thus one can judge the characteristic of a time series by calculating its complexity. This may be u seful to predict the kinetic behavior of a time series.