Study of a chemostat model with Beddington–DeAngelis functional response and pulsed input and washout at different times

In the paper, we considered a food chain chemostat model with a Beddington–DeAngelis functional response of predator, with periodical input and washout occurring at different fixed times. We obtained exact periodic solutions for the model with substrate and prey only. The stability analysis for this periodic solutions yields an invasion threshold for period of pulses of the predator. When the impulsive period is greater than the threshold, there are periodic oscillations in substrate, prey, and predator. If the impulsive period is increased further, the system undergoes the complex dynamic process. By analyzing bifurcation diagrams, we can see that the impulsive system shows two kinds of bifurcations; period-doubling and period-halving.