title: 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.
authors.affiliation: Department of Physics, University of Burdwan, Burdwan 713 104, West Bengal, India.
authors.forename: Debarati
authors.initials: D
authors.lastname: Ghosh
authors.affiliation: Department of Physics, University of Burdwan, Burdwan 713 104, West Bengal, India.
authors.forename: Tanmoy
authors.initials: T
authors.lastname: Banerjee
authors.affiliation: Potsdam Institute for Climate Impact Research, Telegraphenberg, D-14415 Potsdam, Germany.|Institute of Physics, Humboldt University Berlin, D-12489 Berlin, Germany.|Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3FX, United Kingdom.|Institute of Applied Physics of the Russian Academy of Sciences, 603950 Nizhny Novgorod, Russia.
authors.forename: Jürgen
authors.initials: J
authors.lastname: Kurths