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

Leonhard Lücken:

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, which measures the sensitivity of each oscillator’s phase to perturbations. We are able to find parameter regions where multiple stable two-cluster states coexist.