Visual Correlation Analysis of Periodic and Aperiodic Functions Using Recurrence Analysis

Abstract

the study of many types of processes requires in-depth data analysis. To understand the dynamics of a system, it is often necessary to use various methods of analysis to determine the relationships and the nature of the system’s behavior. This study focuses on data analysis using the method of nonlinear dynamics in the form of constructing recurrence diagrams and analyzing their quantitative measures. Based on the analysis of periodic and aperiodic functions, their visual differences are demonstrated. Subsequent studies will allow to determine the dependencies and the nature of the behavior of dynamic systems. It should be noted that the state of complex dynamic systems can change significantly with time, which complicates the study of such systems. In this regard, the considered functions will be modified with different coefficients, which will allow a visual correlation analysis of different functions and the effect of coefficients on them in the form of changes in recurrence diagrams and their quantitative measures. In addition, a similar analysis is possible for data obtained from different sensors or devices. In this case, the data can be presented as an n-dimensional signal, usually of a complex shape, and to simplify the initial analysis, it is proposed to use the construction of recurrence plots for them