Birhythmicity, synchronization, and turbulence in an oscillatory system with nonlocal inertial coupling

We consider a model where a population of diffusively coupled limit-cycle oscillators, described by the complex Ginzburg-Landau equation, interacts nonlocally via an inertial field. For sufficiently high intensity of nonlocal inertial coupling, the system exhibits birhythmicity with two oscillation modes at largely different frequencies. Stability of uniform oscillations in the birhythmic region is analyzed by means of the phase dynamics approximation. Numerical simulations show that, depending on its parameters, the system has irregular intermittent regimes with local bursts of synchronization or desynchronization.