Spatially structured networks of pulse-coupled phase oscillators on metric spaces
type: Item
instance of: scholarly article
title: Spatially structured networks of pulse-coupled phase oscillators on metric spaces
zbMATH Open document ID: 1312.34077
author: Stilianos Louca
author: Fatihcan M. Atay
published in: Discrete and Continuous Dynamical Systems
publication date: 2014-12-02T00:00:00Z
review text: This paper develops a very general framework for studying networks of coupled phase oscillators of the Winfree type. Here the oscillators are distributed over an arbitrary separable metric space \(X\), with a \(\sigma\)-finite Borel measure describing the distribution of oscillators in different region of the space, and the interaction between two oscillators depending on their positions in the space \(X\) through a coupling kernel. Two models are considered, one (the field model) in which there is a unique phase at each point of \(X\), and one (the fluid model) in which there is a probability distribution of phases at each point, evolving according to a continuity equation. Relations between the two models are discussed. Existence and uniqueness of solutions for the dynamical equations is proved in a suitable functional-analytic framework. In the case of identical oscillators, conditions for local asymptotic stability of synchronized oscillations are studied, for both the field and the fluid models. These involve the notion of strongly connecting coupling kernel, which generalizes the concept of strong connectivity of finite graphs, as well as conditions on the pulse and response functions of the oscillators.
reviewed by: Guy Katriel
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 34D06
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 92C20
zbMATH DE Number: 6375852
zbMATH Keywords: coupled oscillators
zbMATH Keywords: Winfree model
zbMATH Keywords: stability
zbMATH Keywords: synchrony
zbMATH Keywords: existence-uniqueness of solutions
zbMATH Keywords: phase response
Wikidata QID: Q59941647
MaRDI profile type: Publication
full work available at URL: dcds.2014.34.3703
OpenAlex ID: W1989766417
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DOI: 10.3934/DCDS.2014.34.3703
description: scientific article; zbMATH DE number 6375852