Exploring conservative islands using correlated and uncorrelated noise

TL;DR

This paper investigates how different types of noise influence the penetration of regular islands in conservative dynamical systems, revealing key factors like noise distribution and correlation that affect system behavior.

Contribution

It introduces a comprehensive analysis of noise effects on island penetration using various noise distributions and correlations, providing new insights into dynamical system behavior.

Findings

Standard deviations of noise distributions are crucial for island penetration.

Power-law decay in RTS indicates enhanced trapping due to noise.

Power-law correlated noise causes algebraic RTS decay without sticky motion.

Abstract

In this work, noise is used to analyze the penetration of regular islands in conservative dynamical systems. For this purpose we use the standard map choosing nonlinearity parameters for which a mixed phase space is present. The random variable which simulates noise assumes three distributions, namely equally distributed, normal or Gaussian, and power-law (obtained from the same standard map but for other parameters). To investigate the penetration process and explore distinct dynamical behaviors which may occur, we use recurrence time statistics (RTS), Lyapunov exponents (LEs) and the occupation rate of the phase space. Our main findings are as follows: (i) the standard deviations of the distributions are the most relevant quantity to induce the penetration; (ii) the penetration of islands induce power-law decays in the RTS as a consequence of enhanced trapping; (iii) for the power-law correlated noise an algebraic decay of the RTS is observed, even though sticky motion is absent; and (iv) although strong noise intensities induce an ergodic-like behavior with exponential decays of RTS, the largest Lyapunov exponent is reminiscent of the regular islands.