Recurrence density analysis of multi-wing and multi-scroll chaotic systems

Abstract

Search and localization of hidden attractors is an important problem in nonlinear science. Basic methods for investigating chaotic systems such as bifurcation and Lyapunov spectrum analysis are not fully feasible for this purpose. A promising technique to detect hidden attractors is the recurrence analysis. Recurrence plots allow quick dynamics exploration and recognizing different oscillation types. In this paper, we compare two methods of scroll number estimation in chaotic systems with multi-scroll and multi-wing attractors. The first is the distance plot, shortcomings of which we reveal and therefore propose the second, more advanced approach based on the measurement of the recurrence plot density. The results of computer experiments show that proposed method is more reliable in determining the number of scrolls in multi-scroll and multi-wing attractors. The presented algorithm can be used in various fields, including embedded system design for information security, data classification and clusterization, communication, biological rhythms analysis and other applications.