Control of birhythmicity through conjugate self-feedback: Theory and experiment

Debabrata Biswas, Tanmoy Banerjee, Jürgen Kurths

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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.
Original languageEnglish
Article number042226
Pages (from-to)1-7
Number of pages7
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Issue number4
Publication statusPublished - 31 Oct 2016

Bibliographical note

D.B. acknowledges the financial support from CSIR, New Delhi, India, T.B. acknowledges the financial support from SERB, Department of Science and Technol-
ogy (DST), India [Project Grant No.: SB/FTP/PS-005/2013]


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