Bifurcation of a three molecular saturated reaction with impulsive input

Although impulsive differential equations have become a widely concerned subject and a lot of models with impulsive effect have been studied in recent years, biochemical reaction models with impulsive input are rarely studied. In this paper, we consider an irreversible three molecular reaction model with impulsive input. By using the Floquet theorem and the method for the small parameter of impulsive differential equations, we obtain sufficient conditions for asymptotical stability and global stability of the given system. The existence of a positive periodic solution is also studied by the bifurcation theory. Further, we also show that our given conditions are right by numerical simulations.