Dynamic Analysis of an Impulsively Controlled Predator-Prey Model with General Functional Response and Seasonal Effect

Based on the predator-prey (natural enemy-pest) system with general functional response and seasonal effect, an impulsive differential system to model the processes of periodically releasing natural enemies and spraying pesticides at different fixed times for pest control is considered. The dynamics of the system are analyzed by using the Floquet theory and comparison techniques. Sufficient conditions for the local asymptotic stability and the global asymptotic stability of the prey-eradication periodic solution are established, respectively, the latter corresponding to the success of the integrated pest management strategy from which our predator-prey system arises. Further, it is proven that this system is permanent under some conditions via a comparison method involving multiple Lyapunov functions. Finally, numerical simulations are carried out to substantiate our analytical findings.