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Dynamical analysis of a five-dimensioned chemostat model with impulsive diffusion and pulse input environmental toxicant. (English) Zbl 1216.92062
Summary: We consider a five-dimensioned chemostat model with impulsive diffusion and pulse input environmental toxicant. Using the discrete dynamical system determined by the stroboscopic map, we obtain a microorganism-extinction periodic solution. Further, it is globally asymptotically stable. The permanence condition of the investigated system is also analyzed by the theory of impulsive differential equations. Our results reveal that the chemostat environmental changes play an important role on the outcome of the chemostat.
37N25Dynamical systems in biology
39A12Discrete version of topics in analysis
34A37Differential equations with impulses
34C25Periodic solutions of ODE
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