Desynchronization waves and localized instabilities in oscillator arrays

Abstract

We consider a ring of identical or near identical coupled periodic oscillators in which the connections have randomly heterogeneous strength. We use the master stability function method to determine the possible patterns at the desynchronization transition that occurs as the coupling strengths are increased. We demonstrate Anderson localization of the modes of instability, and show that such localized instability generates waves of desynchronization that spread to the whole array. Similar results should apply to other networks with regular topology and heterogeneous connection strengths.

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Cited by in corpus (5)

• Mathematical frameworks for oscillatory network dynamics in neuroscience
• Synchronization of nearly-identical dynamical systems. I Size instability
• Desynchronized wave patterns in synchronized chaotic regions of coupled map lattices
• The dynamical impact of a shortcut in unidirectionally coupled rings of oscillators
• Scaling and synchronization in a ring of diffusively coupled nonlinear oscillators