Abstract
In this paper, we consider a hibernation plankton-nutrient chemostat model with impulsive switched systems describing. Employing the discrete dynamical system determined by the stroboscopic map, we obtain a plankton-extinction periodic solution. Further, it is globally asymptotically stable. The permanent condition of the system (2.1) is also obtained by the theory on impulsive differential equation. Our results reveal that the impulsive diffusion amount plays an important role on the chemostat system.
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