Detecting chaotic nature of orbits in global dynamics by permutation entropy of power spectrum

Abstract

This paper presents the permutation entropy of the Power spectrum (PEPS) as a tool to investigate the chaotic nature of dynamics in dynamical systems. The 2D Standard map and Henon–Heiles system, which are well-known test models for both discrete-time and continuous-time systems, are studied. For each system under consideration, the proposed PEPS is compared with the largest Lyapunov exponents (LLE) method, which is the most common method and the Smaller Alignment Index (SALI) methods, which provide fast and effective solutions for chaos detection. The results obtained from the methods used in these models demonstrate that the PEPS method obtained with power spectrum and permutation entropy, which are very efficient tools in chaos research, can accurately describe the chaotic nature of orbits in global dynamics. As the most remarkable feature of this method, we show that it can serve as a fast and useful tool to effectively identify of quasiperiodic orbits as well as regular and chaotic orbits in the global dynamics of dynamical systems.