The Dynamics of a Preydependent Consumption Model Concerning Integrated Pest Management

A mathematical model for the dynamics of a preydependent consumption model concerning integrated pest management is proposed and analyzed. We show that there exists a globally stable pesteradication periodic solution when the impulsive period is less than some critical values. Furthermore, the conditions for the permanence of the system are given. By using bifurcation theory, we show the existence of a nontrival periodic solution if the pesteradication periodic solution loses its stability. When the unique positive periodic solution loses its stability, numerical simulation shows there is a characteristic sequence of bifurcations, leading to a chaotic dynamics, which implies that dynamical behaviors of preydependent consumption concerning integrated pest management are very complex, including perioddoubling cascades, chaotic bands with periodic windows, crises, symmetrybreaking bifurcations and supertransients.