Slow Switching in Globally Coupled Oscillators: Robustness and Occurrence through Delayed Coupling

Details Slow Switching in Globally Coupled Oscillators: Robustness and Occurrence through Delayed Coupling Slow Switching in Globally Coupled Oscillators: Robustness and Occurrence through Delayed Coupling

2000-12-25

arxiv.org/abs/cond-mat/0012456v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

10 pages, 14 figures, RevTex, twocolumn, to appear in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.63.046214

The phenomenon of slow switching in populations of globally coupled oscillators is discussed. This characteristic collective dynamics, which was first discovered in a particular class of the phase oscillator model, is a result of the formation of a heteroclinic loop connecting a pair of clustered states of the population. We argue that the same behavior can arise in a wider class of oscillator models with the amplitude degree of freedom. We also argue how such heteroclinic loops arise inevitably and persist robustly in a homogeneous population of globally coupled oscillators. Although the heteroclinic loop might seem to arise only exceptionally, we find that it appears rather easily by introducing the time-delay in the population which would otherwise exhibit perfect phase synchrony. We argue that the appearance of the heteroclinic loop induced by the delayed coupling is then characterized by transcritical and saddle-node bifurcations. Slow switching arises when the system with a heteroclinic loop is weakly perturbed. This will be demonstrated with a vector model by applying weak noises. Other types of weak symmetry-breaking perturbations can also cause slow switching.

Affiliated with

Also associated with

No associations

Rating

Slow Switching in Globally Coupled Oscillators: Robustness and Occurrence through Delayed Coupling does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Slow Switching in Globally Coupled Oscillators: Robustness and Occurrence through Delayed Coupling, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Slow Switching in Globally Coupled Oscillators: Robustness and Occurrence through Delayed Coupling will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-223772