Dynamic Behavior of a Multiple Species Prey-Predator System with Impulsive Chemical and Biological Control

In an ecosystem multiple predator species often forages on a common prey and the interactions between the predators are neutral. In view of these facts and based on a one-prey-multiple-predators system with Holling IV functional response, an impulsive differential equation to model the process of periodically releasing natural enemies and spraying pesticides at different fixed times for pest control is proposed and investigated.It is proved that there exists a locally asymptotically stable pest-eradication periodic solution when some condition is satisfied(or the impulsive period is less than some critical value). Numerical results show that the system we considered has more complex dynamics including period-doubling cascade, period halfing cascade, quasi-periodic oscillation, chaos, intermittency and crises.