Abstract
A kind of one-prey two-predator system with Ivlev's and Beddington–DeAngelis' functional response and impulsive release at fixed moments is presented. It is shown that the system has a prey-free periodic solution. By using the Floquet theory and small amplitude perturbation skills, it is proved that the prey-free periodic solution of the system is locally asymptotically stable when the period of impulsive release is less than a critical value. Furthermore, permanence of the system is investigated and the condition of permanence is obtained. Finally, numerical simulations show that the system has complex properties which include periodic solution, period-doubling bifurcation, chaos, chaotic windows, half-period bifurcation. A brief discussion on our results and their relation between the continuous system and the impulsive system are given. The results obtained in this paper are confirmed by numerical simulations.
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