A delayed chemostat model with impulsive diffusion and input on nutrients.

*(English)*Zbl 1184.92055Summary: A chemostat model with delayed response in growth and impulsive diffusion and input on nutrients is considered. Using the discrete dynamical system determined by the stroboscopic map, we obtain a microorganism-extinction periodic solution. Further, it is globally attractive. The permanence condition of the investigated system is also obtained by the theory of impulsive delay differential equations. Finally, numerical analysis is inserted to illustrate the dynamical behaviors of the chemostat system. Our results reveal that the impulsive input amount of nutrients plays an important role on the outcome of the chemostat. Our results provide strategy basis for biochemical reaction management.

##### MSC:

92D40 | Ecology |

34K45 | Functional-differential equations with impulses |

34K60 | Qualitative investigation and simulation of models involving functional-differential equations |

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\textit{J. Jiao} and \textit{S. Cai}, Adv. Difference Equ. 2009, Article ID 514240, 17 p. (2009; Zbl 1184.92055)

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