Comparison of the bifurcation curves of a two-variable and a three-variable circadian rhythm model (Q1031579)

The author compare two dynamical systems in two variables modeling the circadian fluctuations of the proteins PER and TIM in cells by presenting a detailed study of the possible bifurcation. 24 hours periodic solutions of the differential equations have been numerically obtained. For a more realistic model with three variables the possible phase portraits and bifurcations including saddle-node and Hopf bifurcation curves have been investigated together with the relationship with the Takens-Bogdanov bifurcation points. Based on the above curves, the stationary points have been determined and the bifurcation curves of the three and two variables models have been compared.