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Role of delay for the symmetry in the dynamics of networks

D’Huys, Otti; Fischer, Ingo; Danckaert, Jan; Vicente, Raul
Physical Review E 83, 046223 (1-7) (2011)

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.