The Dynamics of a Chemostat Model with State Dependent impulsive Effects

We consider the dynamic behaviors of a mathematical chemostat model with state dependent impulsive perturbations. By using the Poincare map and analogue of Poincare's criterion, some conditions for the existence and stability of positive periodic solution are obtained. Moreover, we show that there is no periodic solution with order larger than or equal to three. Numerical simulation are carried out to illustrate the feasibility of our main results, thus implying that the presence of pulses makes the dynamic behavior more complex.

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