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

Abstract

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.

Individual and collective behavior of vibrating motors interacting through a resonant plate

“…A system that can take one of two frequencies depending on the history of the system is sometimes called birhythmic, and the study of birhythmic phenomena in diffusively coupled oscillators has received a surge of interest in recent years [16]. Although many of our results are similar to those found in the study of diffusively coupled oscillators, our system differs from those studied elsewhere in that the interaction strength shows a strong dependence on the interaction frequency and no appreciable dependence on position.…”

Chimera Ising walls in forced nonlocally coupled oscillators

“…Recently, a nonlocally coupled CGLE without a forcing has been studied intensively [13,14,15,16,17,18,19], and a locally coupled CGLE with a forcing has also been investigated widely [20,21,22,23,24,25,26]. To our knowledge, Battogtokh considered the nonlocally coupled CGLE with the forcing for the first time, and demonstrated various interesting phenomena, e.g., nonequilibrium Ising-Bloch transitions [6].…”

Dynamics of the chain of forced oscillators with long-range interaction: From synchronization to chaos

“…The complex Ginzburg-Landau (CGL) equation is typically considered for pattern formation in different media [1,2,3]. CGL equation appears in numerous physical models (see for example [4,5,6,7]). Long-range interaction with finite radius of interaction was considered for complex media in [8,9] and for the α-interaction in [10,11,12,13,14].…”