Complex dynamics of a predator-prey model with impulsive state feedback control

In the paper, we consider a prey-dependent model with integrated pest management strategies, that is, when the pest population reaches the economic injury level, we use a combination tactics such as biological, cultural, and chemical control tactics such that pests reduce to a tolerable level. The sufficient conditions for the existence and stability of semi-trivial and positive periodic solutions are obtained by using the Poincaré map and the analogue of the Poincaré criterion. The qualitative analysis shows that the positive periodic solution bifurcates from the semi-trivial solution through a fold bifurcation. Finally, we give an example and numerical simulations to explain the mathematical conclusions.