Bifurcation of nontrivial periodic solutions for a biochemical model with impulsive perturbations

In this paper, a biochemical model with the impulsive perturbations is considered. By using the Floquet theorem, we find the boundary-periodic solution is asymptotically stable if the impulsive period is larger than a critical value. On the contrary, it is unstable if the impulsive period is less than the critical value. The problem of finding nontrivial periodic solutions is reduced to showing the existence of the nontrivial fixed points for the associated stroboscopic mapping of time snapshot equal to the common period of input. It is then shown that once a threshold condition is reached, a stable nontrivial periodic solution emerges via a supercritical bifurcation. Furthermore, influences of the impulsive input on the inherent oscillations are studied numerically, which shows the rich dynamics in the positive octant.