The dynamical complexity of an impulsive Watt-type prey-predator system

Based on the classical two-prey and one-predator system with Watt-type functional response, an impulsive differential equations to model the process of periodic perturbations on the predator at different fixed time is proposed and investigated. It proves that there exists a locally asymptotically stable prey-eradication periodic solution when the impulse period is less than some critical value, and otherwise, the system can be permanent. Numerical results show that the system considered has more complicated dynamics. It will be useful for studying the dynamic complexity of ecosystems.