Fast and slow domino regimes in transient network dynamics
Physical Review E
American Physical Society
©2017 American Physical Society
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.
The authors gratefully acknowledge the financial support of the EPSRC via Grant No. EP/N014391/1. We thank the anonymous referees for their comments, criticisms, and suggestions. P.A. gratefully acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie SkłodowskaCurie Grant Agreement No. 643073 for providing opportunities to discuss this work with members of the CRITICS network
This is the final version of the article. Available from American Physical Society via the DOI in this record.
The accepted version is in ORE at http://hdl.handle.net/10871/30277
Vol. 96, article 052309
- Mathematics