Control of birhythmicity: A self-feedback approach

Debabrata Biswas, Tanmoy Banerjee, Juergen Kurths

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Abstract

Birhythmicity occurs in many natural and artificial systems. In this paper we propose a self-feedback scheme to control birhythmicity. To establish the efficacy and generality of the proposed control scheme, we apply it on three birhythmic oscillators from diverse fields of natural science, namely, an energy harvesting system, the p53-Mdm2 network for protein genesis (the OAK model) and a glycolysis model (modified Decroly-Goldbeter model). Using the harmonic decomposition technique and energy balance method we derive the analytical conditions for the control of birhythmicity. A detailed numerical bifurcation analysis in the parameter space establishes that the control scheme is capable of eliminating birhythmicity and it can also induce transitions between different forms of bistability. As the proposed control scheme is quite general, it can be applied for control of several real systems, particularly in biochemical and engineering systems.
Original languageEnglish
Article number063110
Pages (from-to)1-11
Number of pages11
JournalChaos
Volume27
Issue number6
Early online date16 Jun 2017
DOIs
Publication statusPublished - Jun 2017

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Biswas, D., Banerjee, T., & Kurths, J. (2017). Control of birhythmicity: A self-feedback approach. Chaos, 27(6), 1-11. [063110]. https://doi.org/10.1063/1.4985561