Synchronization of weakly coupled oscillators: coupling, delay and topology (Q2872150)

This paper consists of several generalisations of known results for networks of identical coupled phase oscillators. Pulse-coupled and phase-coupled phase oscillator networks are first introduced, and then a weak coupling approximation is made, so that both forms are described by the same equation, and delays are replaced by phase shifts. The first result is a sufficient condition for the in-phase state to be almost globally asymptotically stable, in terms of the coupling function. Several following results state that certain types of equilibrium solutions are unstable.NEWLINENEWLINE The final result shows how one finite network with phase lags randomly chosen from some distribution can be approximated by another similar network, since they both have the same continuum limit (as the number of oscillators tends to infinity). Note that nowhere in the paper are actual delays analysed.