Stochastic Web Map: Survival probability and escape frequency

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.