Sequential escapes: onset of slow domino regime via a saddle connection

TL;DR

This paper investigates how coupled bistable systems exhibit different escape behaviors under stochastic influences, identifying a saddle connection bifurcation as key to the transition into a slow domino regime.

Contribution

It introduces a localized non-diffusive coupling model and demonstrates a saddle connection bifurcation causes the slow domino transition without equilibrium bifurcations.

Findings

Transition to slow domino regime not linked to equilibrium bifurcations.

Escape time variability increases after the bifurcation.

Identifies saddle connection bifurcation as the mechanism for slow domino regime.

Abstract

We explore sequential escape behaviour of coupled bistable systems under the influence of stochastic perturbations. We consider transient escapes from a marginally stable "quiescent" equilibrium to a more stable "active" equilibrium. The presence of coupling introduces dependence between the escape processes: for diffusive coupling there is a strongly coupled limit (fast domino regime) where the escapes are strongly synchronised while for intermediate coupling (slow domino regime) without partially escaped stable states, there is still a delayed effect. These regimes can be associated with bifurcations of equilibria in the low-noise limit. In this paper we consider a localized form of non-diffusive (i.e pulse-like) coupling and find similar changes in the distribution of escape times with coupling strength. However we find transition to a slow domino regime that is not associated with any bifurcations of equilibria. We show that this transition can be understood as a codimension-one saddle connection bifurcation for the low-noise limit. At transition, the most likely escape path from one attractor hits the escape saddle from the basin of another partially escaped attractor. After this bifurcation we find increasing coefficient of variation of the subsequent escape times.