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Chaotic behavior of a chemostat model with Beddington-DeAngelis functional response and periodically impulsive invasion. (English) Zbl 1121.92070

Summary: We consider a predator-prey model with Beddington-DeAngelis functional response in a periodic pulsed chemostat. We discuss the boundness of the system and the stability of prey and predator-eradication periodic solutions of the system. Further, using numerical simulations, we show that this impulsive system with periodically pulsed substrate displays a series of complex phenomena, which include (1) period-doubling cascades, (2) period-halfing cascades, (3) chaos and (4) periodic windows.

MSC:

92D40 Ecology
34A37 Ordinary differential equations with impulses
34D05 Asymptotic properties of solutions to ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
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