Impact of noise and spatial constraints in Kuramoto oscillators

Abstract

The Kuramoto model is one of the simplest models used to study collective synchronization. We consider the stochastic Kuramoto model with two sources of noise, quenching and asymmetrical inducing, in both a spatial independent (Erd˝os–R´enyi) and a spatial dependent (random geometric graph) networks. We study how them affect to the order parameter and the critical coupling in the steady state. We observed that quenched noise mainly lowers the order parameter after synchronization, while the asymmetrical inducing noise causes an increase of critical coupling for synchronization to be achieved. Finally, we observed that both noise sources overall decreases synchronization capacity when a spatial dependence is introduced in the network