Complexity Analysis Of Systems Based On Recurrence Plots

Recurrence is the most fundamental characteristic of a dynamic system,which can be used to explore the characteristics of system behavior in phase space.The most powerful tool for visualization and analysis is the recurrence plots.Because the recurrence plots contains the relevant information of all the behaviors of the system,this paper uses the method based on recurrence plots to study the transformation between the complex dynamic system and the correlation between dynamic systems,and apply it to the stock market.In this paper,at first we study the simulation data based on the recurrence plots and the weighted recurrence plots,the shannon entropy is a standard method to evaluate the complexity of the dynamic behaves and can be used to identify the changes between different dynamic behaviors.We study the relationship between the recurrence plots and the time series complexity by combining the method and the simulation data,and the Shannon entropy method of weighted recurrence plots can reflect the complexity of time series,that is,the transition from periodic to chaos or chaos to chaos,and apply the method to the stock market to explore the complexity changes of the stock indexs.Secondly,in order to fully verify the analytical performance of the recurrence plots for time series complexity,we use the recurrence quantitative analysis(RQA)method to further illustrate the recurrence plots study the validity and reliability of dynamic system complexity changes,and the recurrence quantitative analysis can analyze the complexity of the system from a deeper perspective.Again,we study the effect of different thresholds on recurrence quantitative analysis methods,we discover that increasing thresholds can result in the improvement of system complexity and stability.Finally,we use joint recurrence graph(JRP)to study the correlation between dynamic systems.The joint recursive graph can not only reflect the relationship between two sequences but also reflect the degree of mutual influence between them.We combine the three representative indices of Chinese market(SSE,SZSE,CYBZ)to analyze the correlation between them,and conclude that the correlation between SSE and CYBZ is higher than that between the other two.