Role of delay for the symmetry in the dynamics of networks

Otti D'Huys*, I. Fischer, J. Danckaert, Raul Vicente

*Corresponding author for this work

Research output: Contribution to journalArticle

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.

Original languageEnglish
Article number046223
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume83
Issue number4
DOIs
Publication statusPublished - 26 Apr 2011

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Symmetry
symmetry
Spatio-temporal Patterns
Bifurcation Point
Steady-state Solution
Symmetry Breaking
Instantaneous
broken symmetry
Bifurcation
oscillators
Predict
Demonstrate
Class

Bibliographical note

©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

Cite this

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Role of delay for the symmetry in the dynamics of networks. / D'Huys, Otti; Fischer, I.; Danckaert, J.; Vicente, Raul.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 83, No. 4, 046223, 26.04.2011.

Research output: Contribution to journalArticle

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