The fluctuational transition mechanism of non-hyperbolic chaotic invariant sets

Abstract

In order to reveal the general escape mechanism of non-hyperbolic chaotic invariant sets under both weak noise limit and finite noise intensity, the simplest example of Hénon map, which represents the stretching and folding of the phase space, is taken to study the escape mechanism under two kinds of global bifurcation: the fractal boundary crisis and the attractor contact crisis. In this paper, we revealed the general exit mechanism by analyzing the escape paths derived from the shooting method and Monte Carlo simulation. Finally, to further demonstrate universality, an example of high-dimensional differential dynamical system, namely the transient chaos Duffing oscillator, is examined, which underscores the main idea of this paper analyzing specific deterministic structures not only enhances the comprehensibility of the escape process, but also allows for predictions of general escape behavior under weak noise intensity.