title: 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.
authors: Applied Physics Research Group (APHY), Vrije Universiteit Brussel, 1050 Brussel, Belgium.
authors: O
authors: O
authors: D'Huys
authors: I
authors: I
authors: Fischer
authors: J
authors: J
authors: Danckaert
authors: R
authors: R
authors: Vicente