Dynamical behaviors of a delayed chemostat model with impulsive diffusion on nutrients. (English) Zbl 1216.34083

Jiao, Jianjun; Cai, Shaohong; Chen, Lansun

J. Appl. Math. Comput. 35, No. 1-2, 443-457 (2011).

Summary: A chemostat model with delayed response in growth and impulsive diffusion of nutrients is considered. Using the discrete dynamical system determined by the stroboscopic map, we obtain a microorganism-extinction periodic solution, which is globally attractive. The permanent condition of the investigated system is also obtained by the theory of impulsive delay differential equation. Finally, a numerical analysis illustrates the results.

MSC:

34K60	Qualitative investigation and simulation of models involving functional-differential equations
34K25	Asymptotic theory of functional-differential equations
92D25	Population dynamics (general)
34K45	Functional-differential equations with impulses
34K13	Periodic solutions to functional-differential equations

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