DYNAMICS OF A LARGE SYSTEM OF COUPLED NONLINEAR OSCILLATORS

We consider the interaction of a large number of limit-cycle oscillators with linear, all-to-all coupling and a distribution of natural frequencies. The system exhibits extremely rich dynamics as the coupling strength and the width of the frequency distribution are varied. We find a variety of steady behaviors that can be described by a stationary distribution in phase space: frequency locking, amplitude death, incoherence and partial locking. An unexpected result is that the system can also exhibit unsteady behavior, in which the phase space distribution evolves periodically, quasiperiodically or even chaotically. The simple form of the model allows us to derive several analytical results. The stability boundaries of amplitude death and incoherence are found explicitly. Rigorous results on the existence and stability of frequency locking are also obtained.