Chaos in a food chain chemostat with pulsed input and washout

A food-chain chemostat with periodically pulsed input and washout is presented and analyzed. We prove that when the period of pulses is equal to some critical value, there exists a transcritical bifurcation. When the period is more than the critical value, the zooplankton-free periodic solution loses stability, and nutrient, phytoplankton and zooplankton coexist on a periodic solution of period T. If the period is further increase, the system undergoes a series of period-doubling bifurcations leading to chaos. Moreover, the system is also characterized by non-unique dynamic. Finally, we give a brief discussion and find that periodically pulsed input and washout destroys the equilibria of the unforced continuous system and initiates chaos