When is sync globally stable in sparse networks of identical Kuramoto oscillators?

Yury Sokolov and G. Bard Ermentrout

Physica A: Statistical Mechanics and its Applications, 2019, vol. 533, issue C

Abstract: Synchronization in systems of coupled Kuramoto oscillators may depend on their natural frequencies, coupling, and underlying networks. In this paper, we reduce the alternatives to only one by considering identical oscillators where the only parameter that is allowed to change is the underlying network. While such a model was analyzed over the past few decades by studying the size of the basin of attraction of the synchronized state on restricted families of graphs, here we address a qualitative question on general graphs. In an analogy to resistive networks with current sources, we describe an algorithm that produces initial conditions that are often outside of the basin of attraction of the synchronized state. In particular, if a graph allows a cyclic graph clustering with a sufficient number of clusters or contains a sufficiently long induced subpath without cut vertices of the graph then there is a non-synchronous stable phase-locked solution. Thus, we provide a partial answer to when the synchronized state is not globally stable.

Keywords: Kuramoto model; Global stability; Graph Laplacian; Synchronization; Phase-locked solutions; Sparse networks (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:533:y:2019:i:c:s037843711931194x

DOI: 10.1016/j.physa.2019.122070

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