Complex dynamics of a chemostat with variable yield and periodically impulsive perturbation on the substrate

In this paper, we consider the dynamic behaviors of a mathematical chemostat model with variable yield and periodically impulsive perturbation on the substrate. The microbial growth rate is the Monod function $${\frac{\mu S}{a+S}}$$ and the variable yield coefficient δ(S) is quadratic (1 + cS2). Using Floquet theory and small amplitude perturbation method, we establish the condition under which the boundary periodic solution is globally asymptotically stable. Moreover, the permanence of the system is discussed in detail. Finally, by means of numerical simulation, we demonstrate that with the increasing of the pulsed substrate in the feed the system exhibits the complex dynamics.