Sequential escapes and synchrony breaking for networks of bistable oscillatory nodes

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 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.