Progression through different synchronized and desynchronized regimes in brain networks has been reported to reflect physiological and behavioral states, such as working memory and attention. Moreover, intracranial recordings of epileptic seizures show a progression towards synchronization as brain regions are recruited and the seizures evolve. In this paper, we build on our previous work on noise- induced transitions on networks to explore the interplay between transitions and synchronization. We consider a bistable dynamical system that is initially at a stable equilibrium (quiescent) that coexists with an oscillatory state (active). The addition of noise will typically lead to escape from the quiescent to the active state. If a number of such systems are coupled, these escapes can spread sequentially in the manner of a “domino effect.” We illustrate our findings numerically in an example system with three coupled nodes. We first show that a symmetrically coupled network with amplitude-dependent coupling exhibits new phenomena of accelerating and decelerating domino effects modulated by the strength and sign of the coupling. This is quantified by numerically computing escape times for the system with weak coupling. We then apply phase-amplitude-dependent coupling and explore the interplay between synchronized and desynchronized dynamics in the system. We consider escape phases between nodes where the cascade of noise-induced escapes is associated with various types of partial synchrony along the sequence. We show examples for the three-node system in which there is multistability between in-phase and antiphase solutions where solutions switch between the two as the sequence of escapes progresses.


  1. generalized Hopf normal form
  2. escape phase
  3. escape time
  4. sequential escape
  5. noise-induced transition

MSC codes

  1. 92C42
  2. 34D06
  3. 37H20
  4. 37G05

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Supplementary Material

Index of Supplementary Materials

Title of paper: Sequential Escapes and Synchrony Breaking for Networks of Bistable Oscillatory Nodes

Authors: Jennifer Creaser, Peter Ashwin, and Krasimira Tsaneva-Atanasova

File: M134577_01.pdf

Type: PDF

Contents: Figure SM1 shows the choice of escape threshold lies between the potential barrier and the sink for parameter values considered here. Figures SM2-3 show realizations of a three node network with amplitude coupling; Figure SM4 shows realizations and order parameter values of a three node network with amplitude coupling; Figure SM5 shows an alternative approach to getting changes in synchrony in a three node system by changing the shear of each node. Figure SM6 shows the distributions of the escape times and the order parameters for a three node network at parameter values for which there is a change in synchrony during the sequence of escapes.


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Information & Authors


Published In

cover image SIAM Journal on Applied Dynamical Systems
SIAM Journal on Applied Dynamical Systems
Pages: 2829 - 2846
ISSN (online): 1536-0040


Submitted: 16 June 2020
Accepted: 7 October 2020
Published online: 17 December 2020


  1. generalized Hopf normal form
  2. escape phase
  3. escape time
  4. sequential escape
  5. noise-induced transition

MSC codes

  1. 92C42
  2. 34D06
  3. 37H20
  4. 37G05



Funding Information

Engineering and Physical Sciences Research Council https://doi.org/10.13039/501100000266 : EP/N014391/1

Funding Information

Institute for Advanced Study, Technische Universität München https://doi.org/10.13039/501100015072

Funding Information

Medical Research Council https://doi.org/10.13039/501100000265 : MR/S019499/1

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