Abstract
A mathematical model for the dynamics of a prey–dependent 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 pest–eradication 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 prey–dependent consumption concerning integrated pest management are very complex, including period–doubling cascades, chaotic bands with periodic windows, crises, symmetry–breaking bifurcations and supertransients.
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