Stickiness and recurrence plots: an entropy-based approach
arXiv:2212.12316 · doi:10.1063/5.0140613
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 (RP), 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.
16 pages, 7 figures
References in corpus (11)
- Array Programming with NumPy
- Recurrence Plots for the Analysis of Complex Systems
- Long-Time Correlations in the Stochastic Regime
- Historical Review of Recurrence Plots
- On universality of algebraic decays in Hamiltonian systems
- Recurrence threshold selection for obtaining robust recurrence characteristics in different embedding dimensions
- Characterizing Weak Chaos using Time Series of Lyapunov Exponents
- Stickiness in generic low-dimensional Hamiltonian systems: A recurrence-time statistics approach
- Radius selection using kernel density estimation for the computation of nonlinear measures
- Structure, size, and statistical properties of chaotic components in a mixed-type Hamiltonian system
- Intermittent stickiness synchronization