Synchronization in populations of sparsely connected pulse-coupled oscillators

Abstract

We propose a population model for $\delta$-pulse-coupled oscillators with sparse connectivity. The model is given as an evolution equation for the phase density which take the form of a partial differential equation with a non-local term. We discuss the existence and stability of stationary solutions and exemplify our approach for integrate-and-fire-like oscillators. While for strong couplings, the firing rate of stationary solutions diverges and solutions disappear, small couplings allow for partially synchronous states which emerge at a supercritical Andronov-Hopf bifurcation.

6 pages, 2 figures

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Cited by in corpus (2)

• FitzHugh-Nagumo oscillators on complex networks mimic epileptic-seizure-related synchronization phenomena
• Convergence Results on Pulse Coupled Oscillator Protocols in Locally Connected Networks