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.
Bibliographical noteThe authors thankfully acknowledge the insightful suggestions by the anonymous referees. DB acknowledges CSIR, New Delhi, India. TB acknowledges Science and
Engineering Research Board (Department of Science and Technology, India) [Grant No. SB/FTP/PS-05/2013]. D.B. acknowledges Haradhan Kundu, Department of
Mathematics, University of Burdwan, for his useful suggestions regarding computations.