Dynamics of Coupled Oscillator Systems - Abstract

Zaks, Michael

Is synchronization compatible with homoclinicity?

In many applications of coupled oscillators the desired dynamics is synchronized: instantaneous states of all ensemble elements coincide. For globally coupled identical units, synchronous behavior in such cases is governed by the low-dimensional system that may depend on external parameters and exhibit bifurcations when those parameters are varied. To be physically observable, synchronous states should be robust: stable with respect to perturbations that split the ensemble and provoke the departure of separate units from the synchronous cluster. We demonstrate that the situations when the low-dimensional system possesses a saddle equilibrium and undergoes a homoclinic bifurcation, feature a generic mode of instability that leads to the destruction of the cluster state and breakdown of synchrony. We briefly discuss the possibilities for reversal of this effect with the help of the specially tailored non-generic schemes of coupling to the global field.