Qualitatively distinct mechanisms of noise-induced escape in diffusively coupled bistable elements

TL;DR

This paper identifies three distinct noise-induced escape mechanisms in coupled bistable systems, derived through model reduction, depending on coupling strength, highlighting the interplay of nonlinearity, noise, and coupling.

Contribution

The paper introduces a model-reduction framework that reveals three qualitatively different escape mechanisms based on coupling strength in diffusively coupled bistable elements.

Findings

Three escape mechanisms depending on coupling strength

Validation of reduced models with numerical simulations

Identification of dominant factors driving collective escape

Abstract

The analysis of noise-induced escape in populations of bistable elements is challenging, because nonlinearity, coupling, and noise all play essential roles. We show that the interplay of these three factors yields three qualitatively distinct escape mechanisms depending on coupling strength in populations of diffusively coupled bistable elements. To clarify dominant driving factors of escape dynamics, we develop a model-reduction approach, deriving three effective one-dimensional dynamics: nonlinear mean-field Fokker-Planck equation in the weak-coupling regime, stochastic mean-field dynamics in the strong-coupling regime, and deterministic mean-field dynamics in the intermediate regime. We validate these reduced descriptions by comparing predicted mean escape times with numerical simulations. We identify a distinct dominant driving factor of collective escape in each regime. Notably, the three mechanisms emerge through the interplay of nonlinearity, diffusive coupling, and dynamical noise -- rather than bifurcations of the noise-free system. Our approach serves as a framework applicable to other stochastic nonlinear systems with diffusive coupling, motivating a further search for similar synergistic phenomena.