On Periodic Oscillation and Its Period of a Circadian Rhythm Model

Abstract

We theoretically study periodic oscillation and its period of a circadian rhythm model of Neurospora and provide the conditions for the existence of such a periodic oscillation by the theory of competitive dynamical systems. To present the exact expression of the unique equilibrium in terms of parameters of system, we divide them into eleven classes for the Hill coefficient $n=1$ or $n=2$, among seven classes of which nontrivial periodic oscillations exist. Numerical simulations are made among the seven classes and the models with the Hill coefficient $n=3$ or $n=4$ to reveal the influence of parameter variation on periodic oscillations and their periods. The results show that their periods of the periodic oscillations are approximately 21.5 h, which coincides with the known experiment result observed in constant darkness.

Funding

National Natural Science Foundation of China(11771295)