Eur. Phys. J. Special Topics 227, 1091–1100 (2018)
https://doi.org/10.1140/epjst/e2018-800038-5

Regular Article

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

Department of Mathematics and EPSRC Centre for Predictive Modelling in Healthcare, University of Exeter, Exeter, EX4 4QJ, UK

^a e-mail: p.ashwin@exeter.ac.uk

Received: 2 April 2018
Received in final form: 13 June 2018
Published online: 12 December 2018

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.