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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
104/2013

Spatially structured networks of pulse-coupled phase oscillators on metric spaces

Stilianos Louca and Fatihcan M. Atay

Abstract

The Winfree model describes finite networks of phase oscillators that interact by broadcasting pulses modulating the current frequency of connected oscillators. We study a generalization of the model and its fluid-dynamical limit for networks, where oscillators are distributed on some abstract $\sigma$-finite Borel measure space over a separable metric space. We give existence and uniqueness statements for solutions to the continuity equation for the oscillator phase densities. We further show that synchrony in networks of identical oscillators is locally asymptotically stable for finite, strictly positive measures and under suitable conditions on the oscillator response function and the coupling kernel of the network. The conditions on the latter are a generalization of the strong connectivity of finite graphs to abstract convolution kernels.

Received:
19.11.13
Published:
25.11.13
MSC Codes:
34C15, 70K20, 35A01, 35A02
Keywords:
coupled oscillators, Winfree model, stability, synchrony

Related publications

inJournal
2014 Repository Open Access
Stilianos Louca and Fatihcan M. Atay

Spatially structured networks of pulse-coupled phase oscillators on metric spaces

In: Discrete and continuous dynamical systems / A, 34 (2014) 9, pp. 3703-3745