Taming Explosive Growth through Dynamic Random Links

Abstract

We study the dynamics of a collection of nonlinearly coupled limit cycle oscillators, relevant to systems ranging from neuronal populations to electrical circuits, under coupling topologies varying from a regular ring to a random network. We find that the trajectories of this system escape to infinity under regular coupling, for sufficiently strong coupling strengths. However, when some fraction of the regular connections are dynamically randomized, the unbounded growth is suppressed and the system always remains bounded. Further we determine the critical fraction of random links necessary for successful prevention of explosive behaviour, for different network rewiring time-scales. These results suggest a mechanism by which blow-ups may be controlled in extended oscillator systems.

References in corpus (2)

• Enhancement of spatiotemporal regularity in an optimal window of random coupling
• Epidemics and chaotic synchronization in recombining monogamous populations

Cited by in corpus (4)

• The synchronized dynamics of time-varying networks
• Aging transition under discrete time-dependent coupling: Restoring rhythmicity from aging
• Dangerous Aging Transition in a Network of Coupled Oscillators
• Enhancement of Extreme Events through the Allee effect and its Mitigation through Noise in a Three Species System