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 language | English |
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Article number | 046223 |
Journal | Physical Review E |
Volume | 83 |
Issue number | 4 |
DOIs | |
Publication status | Published - 1 Apr 2011 |
Externally published | Yes |
Keywords
- Synchronization
- coupled oscillators
- Patterns
- Networks and genealogical trees
- Delay and functional equations