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American Physical Society, Physical review E: Statistical, nonlinear, and soft matter physics, 4(83)

DOI: 10.1103/physreve.83.046223

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Role of delay for the symmetry in the dynamics of networks

Journal article published in 2011 by Ottilde D'Huys, O. D’Huys, I. Fischer, Jan Danckaert ORCID, R. Vicente
This paper is available in a repository.
This paper is available in a repository.

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Abstract

The symmetry in a network of oscillators determines the spatiotemporal patterns of activity that can emerge. We study how a delay in the coupling affects symmetry-breaking and -restoring bifurcations. We are able to draw general conclusions in the limit of long delays. For one class of networks we derive a criterion that predicts that delays have a symmetrizing effect. Moreover, we demonstrate that for any network admitting a steady-state solution, a long delay can solely advance the first bifurcation point as compared to the instantaneous-coupling regime.