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.
|Journal||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|Publication status||Published - 26 Apr 2011|
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