The Application Of Standard Deviation Entropy In The Study Of Nonlinear System Complexity

The Shannon entropy is an important measure to study the complexity of a dynam-ical process and can be used to quantify transitions between different dynamical regimes.An alternative intuitive way of quantifying complexity systems is recurrence plots and recurrence quantification analysis.Although several different definitions of entropy based on the recurrence plots have been suggested so far,the influenced by the threshold and the length of the minimum diagonal line,in some cases,These entropy values are inversely correlated with the maximum Lyapunov exponent.Therefore,we proposed a Shannon entropy,which is based on the weighted recurrence plots,to analyze the complexity of the nonlinear systems.And we proved that it is positively correlated with the maximum Lyapunov exponent.Firstly,in this paper,the definition of standard deviation entropy based on the weighted recurrence plots is given.We studied the famous two-dimensional nonlinear system-Henon map,used the standard deviation entropy method to study the mapping of different parameter conditions,and the results were compared with the entropy based on recurrence plots and the entropy based on weighted recurrence plots,then,the correlation between the three entropies and the maximum Lyapunov exponent is given.Secondly,we explore the complexity of a real precipitation data of Gonghai region,the results revealed the evolution law of precipitation data.Finally,we used the standard deviation entropy method to analysis the economic and financial system model.The research showed that the standard deviation entropy can not only detect the bifurcation phenomenon in the system,but also can identify the transition of the equilibrium point.