Two-cluster bifurcations in systems of globally pulse-coupled oscillators

Details Two-cluster bifurcations in systems of globally pulse-coupled oscillators Two-cluster bifurcations in systems of globally pulse-coupled oscillators

2011-03-31

arxiv.org/abs/1103.6154v1

Nonlinear Sciences

Adaptation and Self-Organizing Systems

12 pages. 6 figures

Scientific paper

For a system of globally pulse-coupled phase-oscillators, we derive conditions for stability of the completely synchronous state and all possible two-cluster states and explain how the different states are naturally connected via bifurcations. The coupling is modeled using the phase-response-curve (PRC), which measures the sensitivity of each oscillator's phase to perturbations. For large systems with a PRC, which turns to zero at the spiking threshold, we are able to find the parameter regions where multiple stable two-cluster states coexist and illustrate this by an example. In addition, we explain how a locally unstable one-cluster state may form an attractor together will its homoclinic connections. This leads to the phenomenon of intermittent, asymptotic synchronization with abating beats away from the perfect synchrony.

Affiliated with

Also associated with

No associations

Rating

Two-cluster bifurcations in systems of globally pulse-coupled oscillators 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 Two-cluster bifurcations in systems of globally pulse-coupled oscillators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Two-cluster bifurcations in systems of globally pulse-coupled oscillators will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-245471