Title: Control of birhythmicity: A self-feedback approach,
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.