Nonlinear analysis of a microbial pesticide model with impulsive state feedback control

Abstract

In this paper, a new mathematical model for the entomopathogenic nematode attacking pests with impulsive state feedback control is considered. By using the Poincare map, we obtain that the system with impulsive state feedback control has a periodic solution of order one. Sufficient conditions for existence and stability of the order one periodic solution are given. Specifically, the system has a singular order one periodic solution. In some cases, it is possible that the system may also have an order two periodic solution. Our results show that the control measure is effective and reliable.