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

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.