Dynamical behavior of a pest management model with impulsive effect and nonlinear incidence rate

in this paper, we consider the pest management model with spraying microbial pesticide and releasing the infected pests, and the infected pests have the function similar to the microbial pesticide and can infect the healthy pests, further weaken or disable their prey function till death. by using the floquet theory for impulsive differential equations, we show that there exists a globally asymptotically stable pest eradication periodic solution when the impulsive period τ < τmax, we further prove that the system is uniformly permanent if the impulsive period τ > τmax. finally, by means of numerical simulation, we showthatwith the increaseof impulsive period, the system displays complicated behaviors.