Sequential escapes and synchrony breaking for networks of bistable oscillatory nodes
Creaser, J; Ashwin, P; Tsaneva-Atanasova, K
Date: 17 December 2020
Journal
SIAM Journal on Applied Dynamical Systems
Publisher
Society for Industrial and Applied Mathematics
Publisher DOI
Abstract
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 ...
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 co-exists with an oscillatory state (active). 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
effect 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 amplitude-phase 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 multi-stability between
in-phase and anti-phase solutions where solutions switch between the two as the sequence of escapes progresses.
Mathematics and Statistics
Faculty of Environment, Science and Economy
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