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 complexity is also discussed. Results show that for the logistic equation, the complexity is obviously different when the complicated degree of the time series is variational; and for Lorenz model, i.e. its x-, y-, and z-portions, their 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 internal quasiperiodicity. Further investigations indicate that when different window lengths are selected, the characters of the complexity series for a given time series are basically the same, and there exists a coherency between the jumps 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 useful to predict the kinetic behavior of a time series.