title: Control of birhythmicity through conjugate self-feedback: Theory and experiment.
abstract: Birhythmicity arises in several physical, biological, and chemical systems. Although many control schemes have been proposed for various forms of multistability, only a few exist for controlling birhythmicity. In this paper we investigate the control of birhythmic oscillation by introducing a self-feedback mechanism that incorporates the variable to be controlled and its canonical conjugate. Using a detailed analytical treatment, bifurcation analysis, and experimental demonstrations, we establish that the proposed technique is capable of eliminating birhythmicity and generates monorhythmic oscillation. Further, the detailed parameter space study reveals that, apart from monorhythmicity, the system shows a transition between birhythmicity and other dynamical forms of bistability. This study may have practical applications in controlling birhythmic behavior of several systems, in particular in biochemical and mechanical processes.
authors.affiliation: Chaos and Complex Systems Research Laboratory, Department of Physics, University of Burdwan, Burdwan 713 104, West Bengal, India.
authors.forename: Debabrata
authors.initials: D
authors.lastname: Biswas
authors.affiliation: Chaos and Complex Systems Research Laboratory, 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, Russian Academy of Sciences, 603950 Nizhny Novgorod, Russia.
authors.forename: Jürgen
authors.initials: J
authors.lastname: Kurths