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.
|Number of pages||1|
|Journal||Phys. Rev. E|
|Publication status||Published - 26 Apr 2011|
- SEMICONDUCTOR-LASERS; OPTICAL FEEDBACK
- HOPF-BIFURCATION; TIME-DELAY; BREAKING;
- CHAOS; SYNCHRONIZATION; STABILIZATION;
- OSCILLATORS; SYSTEMS