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

Debarati Ghosh, Tanmoy Banerjee, Jürgen Kurths

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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. Nature 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 {\it two control parameters}, namely the {\it density of the mean-field} and the {\it 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 an unique feature of this mean-field coupling that is not available in other coupling schemes. Finally, we report the {\it first} experimental observation of revival of oscillation from the mean-field--induced oscillation suppression state that supports our theoretical results.
Original languageEnglish
Article number052908
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Issue number5
Early online date1 Sep 2015
Publication statusPublished - 12 Nov 2015


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