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The European Physical Journal Special Topics

, Volume 227, Issue 10–11, pp 1091–1100 | Cite as

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

  • Peter AshwinEmail author
  • Jennifer Creaser
  • Krasimira Tsaneva-Atanasova
Open Access
Regular Article
Part of the following topical collections:
  1. Advances in Nonlinear Dynamics of Complex Networks: Adaptivity, Stochasticity, Delays

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.

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Copyright information

© The Author(s) 2018

Open Access This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://doi.org/creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  1. 1.Department of Mathematics and EPSRC Centre for Predictive Modelling in HealthcareUniversity of ExeterExeterUK

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