Sales MR, Mugnaine M, Szezech JD, Viana RL, Caldas IL, Marwan N, Kurths J. Stickiness and recurrence plots: An entropy-based approach.
CHAOS (WOODBURY, N.Y.) 2023;
33:033140. [PMID:
37003817 DOI:
10.1063/5.0140613]
[Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/29/2022] [Accepted: 03/03/2023] [Indexed: 06/19/2023]
Abstract
The stickiness effect is a fundamental feature of quasi-integrable Hamiltonian systems. We propose the use of an entropy-based measure of the recurrence plots (RPs), namely, the entropy of the distribution of the recurrence times (estimated from the RP), to characterize the dynamics of a typical quasi-integrable Hamiltonian system with coexisting regular and chaotic regions. We show that the recurrence time entropy (RTE) is positively correlated to the largest Lyapunov exponent, with a high correlation coefficient. We obtain a multi-modal distribution of the finite-time RTE and find that each mode corresponds to the motion around islands of different hierarchical levels.
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