Fast and slow domino regimes in transient network dynamics

Peter Ashwin, Jennifer Creaser, and Krasimira Tsaneva-Atanasova
Phys. Rev. E 96, 052309 – Published 8 November 2017

Abstract

It is well known that the addition of noise to a multistable dynamical system can induce random transitions from one stable state to another. For low noise, the times between transitions have an exponential tail and Kramers' formula gives an expression for the mean escape time in the asymptotic limit. If a number of multistable systems are coupled into a network structure, a transition at one site may change the transition properties at other sites. We study the case of escape from a “quiescent” attractor to an “active” attractor in which transitions back can be ignored. There are qualitatively different regimes of transition, depending on coupling strength. For small coupling strengths, the transition rates are simply modified but the transitions remain stochastic. For large coupling strengths, transitions happen approximately in synchrony—we call this a “fast domino” regime. There is also an intermediate coupling regime where some transitions happen inexorably but with a delay that may be arbitrarily long—we call this a “slow domino” regime. We characterize these regimes in the low noise limit in terms of bifurcations of the potential landscape of a coupled system. We demonstrate the effect of the coupling on the distribution of timings and (in general) the sequences of escapes of the system.

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  • Received 24 January 2017

DOI:https://doi.org/10.1103/PhysRevE.96.052309

©2017 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear Dynamics

Authors & Affiliations

Peter Ashwin1,2, Jennifer Creaser1,2, and Krasimira Tsaneva-Atanasova1,2,3

  • 1Department of Mathematics, University of Exeter, Exeter EX4 4QF, United Kingdom
  • 2EPSRC Centre for Predictive Modelling in Healthcare, University of Exeter, Exeter EX4 4QJ, United Kingdom
  • 3Living Systems Institute, University of Exeter, Exeter EX4 4QD, United Kingdom

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Issue

Vol. 96, Iss. 5 — November 2017

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