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arXiv · 1403.0102

Synchronization in populations of sparsely connected pulse-coupled oscillators

Alexander Rothkegel·Klaus Lehnertz
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Abstract

We propose a population model for $δ$-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.

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Alexander Rothkegel, Klaus Lehnertz. 2014-03-01. Synchronization in populations of sparsely connected pulse-coupled oscillators. https://doi.org/10.1209/0295-5075%2F105%2F30003

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