Statistical Complexity And Its Application Based On Ordinal Pattern Transition Networks

Complex network approaches have recently been developed as prominent tools for nonlinear time series analysis and already found many interesting applications to observational and experimental data from various fields.In this line of research,several major examples are recurrence networks,visibility graphs,and transition networks.Ordinal pattern transition networks have been generalizing the well-established concepts of ordinal time series analysis,providing new insights for characterizing nonlinear dynamics.This paper mainly uses the Ordinal Pattern Transition Network(OPTN)to describe the time series,and proposes two new OP transition frequency based statistical complexity measures(SCM),there by extending the existing OP frequency based SCM.The main research contents of this paper are as follows:1.The complexity-entropy plane is used to distinguish the deterministic chaotic system from the uncertain stochastic system.We apply SCMs to the complexity-entropy plane of the Logistic map of chaotic system that varies with the parameter r,and combine the results of fractional Brownian motion and fractional Gaussian noise in the complexity-entropy plane,we further find that our two new SCMs methods can better distinguish chaotic system from stochastic system.2.SCMs were used to identify different dynamical transitions.In this paper,we apply the SCMs to the Logistic map and the R(?)ssler system,and identify the different dynamic transitions of the Logistic map and the R(?)ssler system.3.The practicability of the new method is verified by the actual data.We apply the SCMs method to real-world fluid experiment data and human electrocardiogram(ECG)data.The results show that the OP transition frequency based SCMs can describe the complexity of real-world system.