Chaotic behavior of a chemostat model with Beddington–DeAngelis functional response and periodically impulsive invasion

In the paper, we considered a predator–prey model with Beddington–DeAngelis functional response in periodic pulsed chemostat. We discussed the boundness of system and the stability of prey and predator-eradication periodic solution of system. Further, using numerical simulation method, we show that this impulsive system with periodically pulsed substrate display a series of complex phenomena, which include (1) period-doubling cascade, (2) period-halfing cascade, (3) chaos and (4) periodic window.