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.


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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