Role of delay for the symmetry in the dynamics of networks

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.

Publication DOI: https://doi.org/10.1103/PhysRevE.83.046223
Divisions: Engineering & Applied Sciences
Additional Information: ©2011 American Physical Society. Role of delay for the symmetry in the dynamics of networks O. D’Huys, I. Fischer, J. Danckaert, and R. Vicente Phys. Rev. E 83, 046223 – Published 26 April 2011
Uncontrolled Keywords: Condensed Matter Physics,Statistical and Nonlinear Physics,Statistics and Probability
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Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
https://journal ... sRevE.83.046223 (Publisher URL)
PURE Output Type: Article
Published Date: 2011-04-26
Authors: D'Huys, Otti ( 0000-0001-7498-6771)
Fischer, I.
Danckaert, J.
Vicente, Raul

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