Stochastic Web Map: Survival probability and escape frequency

TL;DR

This paper investigates escape dynamics in the Stochastic Web Map, revealing a universal scaling law for escape times governed by system parameters and showing that escape behavior is dominated by global transport mechanisms.

Contribution

The study introduces a universal scaling law for escape times in the SWM and demonstrates that escape dynamics are governed by global transport rather than symmetry effects.

Findings

Escape time scales as n_typ ∝ K^{-2}h^{2}.

Escape statistics become universal after rescaling time.

Escape is controlled by global transport mechanisms.

Abstract

We study transport and escape in the Stochastic Web Map (SWM), an area-preserving system with phase-space structure controlled by a symmetry parameter $q$ and nonlinearity $K$. By analyzing the survival probability $P_{\text{S}}(n)$ and escape frequency $P_{\text{E}}(\ln n)$, we show that in the chaotic regime escape dynamics is governed by a single time scale $n_{\text{typ}}\propto K^{-2}h^{2}$; here $h$ is the size of the escape horizon. Deviations at large $K$ and small $h$ indicate a breakdown of the quasilinear approximation. Then, upon rescaling the time by $n_{\text{typ}}$, escape statistics becomes universal, independent of $q$. These results demonstrate that escape is controlled by global transport rather than symmetry.