BIFURCATION AND COMPLEXITY IN A RATIO-DEPENDENT PREDATOR-PREY CHEMOSTAT WITH PULSED INPUT

<正>In this paper,a three dimensional ratio-dependent chemostat model with period- ically pulsed input is considered.By using the discrete dynamical system determined by the stroboscopic map and Floquet theorem,an exact periodic solution with positive concentrations of substrate and predator in the absence of prey is obtained.Whenβis less than some criti- cal value the boundary periodic solution(xs（t）,0,zs（t）)is locally stable,and whenβis larger than the critical value there are periodic oscillations in substrate,prey and predator.Increasing the impulsive period T,the system undergoes a series of period-doubling bifurcation leading to chaos,which implies that the dynamical behaviors of the periodically pulsed ratio-dependent predator-prey ecosystem are very complex.