Controlling Bifurcation and Birhythmicity in a Birhythmic Oscillator

In this paper, the impact of parameters on bifurcation and birhythmicity is studied theoretically and numerically in a fractional-order birhythmic Van der Pol oscillator coupled with delayed feedback and noise. By implementing the multiple-scale expansion approach and stochastic averaging method, deterministic bifurcation and the comprehensive evolution details of stochastic bifurcation are explored respectively. Then, the birhythmicity of the birhythmic oscillator is discussed both under the deterministic and stochastic cases. This investigation may be conducive to understanding the underlying mechanisms which control the biorhythms of the cell cycle in certain biological systems.