Large fluctuations and nonlinear dynamics of birhythmicity

Abstract

Birhythmicity, which arises due to the simultaneous existence of two stable limit cycles, has been shown to be an interesting dynamical scenario in chemical reactions and biology. Here we present an extension of the Decroly-Goldbeter model for birhythmicity in glycolysis within a Hamiltonian structure incorporating the stochastic substrate injection rate, the critical controlling factor in glycolytic oscillations. Our analysis reveals several generic features of nonlinear dynamics of birhythmicity in the weak-noise limit, e.g., crossover of birhythmicity to monorhythmic behaviour, period-doubling bifurcations leading to chaos and noise-induced transition between attractors.