Revival of oscillation from mean-field-induced death: Theory and experiment.

Abstract

The revival of oscillation and maintaining rhythmicity in a network of coupled oscillators offer an open challenge to researchers as the cessation of oscillation often leads to a fatal system degradation and an irrecoverable malfunctioning in many physical, biological, and physiological systems. Recently a general technique of restoration of rhythmicity in diffusively coupled networks of nonlinear oscillators has been proposed in Zou et al. [Nat. Commun. 6, 7709 (2015)], where it is shown that a proper feedback parameter that controls the rate of diffusion can effectively revive oscillation from an oscillation suppressed state. In this paper we show that the mean-field diffusive coupling, which can suppress oscillation even in a network of identical oscillators, can be modified in order to revoke the cessation of oscillation induced by it. Using a rigorous bifurcation analysis we show that, unlike other diffusive coupling schemes, here one has two control parameters, namely the density of the mean-field and the feedback parameter that can be controlled to revive oscillation from a death state. We demonstrate that an appropriate choice of density of the mean field is capable of inducing rhythmicity even in the presence of complete diffusion, which is a unique feature of this mean-field coupling that is not available in other coupling schemes. Finally, we report the experimental observation of revival of oscillation from the mean-field-induced oscillation suppression state that supports our theoretical results.