The dynamics of natural mortality for pest control model with impulsive effect

In this paper, a mathematical model is proposed with biologically based impulsive control strategy for pest control. Some sufficient conditions for the existence and globally asymptotical stability of the semi-trivial periodic solution are obtained. Also, the conditions ensuring the permanence of system are given. In addition, we show that there exists a global asymptotically stable semi-trivial periodic solution via bifurcation theory.