A Graphical Chaotic Criterion Based on Improved Surrogate Data Method

The surrogate data method is an effective way for nonlinear system analysis, but it cannot directly judge whether the signal is in the chaotic state as it is based on the idea of the exclusion method to improve the confidence level of the chaos identification. A pseudo-periodic surrogate data method for chaotic identification of quasi-periodical signals is introduced, and 3 defects of the method are found in numerical experiments: the ineffectiveness of phase space reconstruction in real signal analysis, the linearization of the surrogate data, and the poor fault tolerance of the test statistics. Methods for improvement are proposed to solve these problems respectively. The improved pseudo-periodic surrogate data method is applied to different kinds of signals, such as periodic signals and chaotic signals generated by the Logistic model and other typical chaotic signals. It is found that the complexity of all chaotic signals under all the noise radii shows a linear growth trend; and for the periodic signal, the Lempel-Ziv(LZ) complexity keeps steady when the noise radius is less than 0.1, and the value of LZ complexity begins to grow monotonously when the noise radius is greater than 0.1. The results of the data experiment are analyzed, which can prove that the linear growth trend of the complexity under all the noise radii is a common feature of the chaotic signal and it can be used as an effective graphical chaotic criterion.