Self-organisation of random oscillators

Paper in proceeding, 2015

A model for the stochastic passive advection - diffusion of a scalar with external forcing is further developed by introducing a non-linear phase coupling dynamic between the phases of the stochastic flow and the forcing. The model for the phase coupling dynamic follows the well known Kuramoto model of the limit cycle oscillators with an additional linear coupling term between the phases the two stochastic fields. The aim is to study the impact of a collective phase synchronization or self-organisation on the fluctuation level of the scalar through a simple stochastic passive advection - diffusion relation. The results shown here, present a significant impact of the collective phase synchronization on the correlation time of the fluctuations, and on the suppression of the fluctuation amplitudes. The model predicts that in the presence of an additional linear coupling between the phases of the two stochastic fields, the phase synchronizations leads to a localisation as well as strong suppression of the fluctuation amplitudes. While, in the a-synchronized state we observe a predator-prey behavior between the correlations of the two fields and time auto-correlation of the fluctuations decay with an oscillatory trend.