Stochastic Web Map: Survival probability and escape frequency
K. B. Hidalgo-Castro, J. A. M\'endez-Berm\'udez, Edson D. Leonel

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 and nonlinearity . By analyzing the survival probability and escape frequency , we show that in the chaotic regime escape dynamics is governed by a single time scale ; here is the size of the escape horizon. Deviations at large and small indicate a breakdown of the quasilinear approximation. Then, upon rescaling the time by , escape statistics becomes universal, independent of . These results demonstrate that escape is controlled by global transport rather than symmetry.
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Taxonomy
TopicsChaos control and synchronization · stochastic dynamics and bifurcation · Quantum chaos and dynamical systems
