Dynamic complexities of a predator–prey model with generalized Holling type III functional response and impulsive effects

Based on the predator–prey (natural enemy–pest) system with generalized Holling type III functional response, an impulsive differential system to model the processes of periodically releasing natural enemies and spraying pesticides at different fixed times for pest control is proposed and investigated. It is shown that if the impulsive period is less than a threshold then the pest-eradication periodic solution is globally asymptotically stable; otherwise the system is permanent. When the system is permanent, further influences of the impulsive perturbations are studied by numerical simulation. Numerical simulation indicates that the system may have complex dynamics.