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- Title
Qualitative analysis of a chemostat model with inhibitory exponential substrate uptake and a time delay.
- Authors
Dong, Qinglai; Ma, Wanbiao
- Abstract
In this paper, we consider a simple chemostat model with inhibitory exponential substrate uptake and a time delay. A detailed qualitative analysis about existence and boundedness of its solutions and the local asymptotic stability of its equilibria are carried out. Using Lyapunov-LaSalle invariance principle, we show that the washout equilibrium is global asymptotic stability for any time delay. Using the fluctuation lemma, the sufficient condition of the global asymptotic stability of the positive equilibrium is obtained. Numerical simulations are also performed to illustrate the results.
- Subjects
CHEMOSTAT; TIME delay systems; STABILITY theory; LYAPUNOV functions; PRINCIPLE of relativity (Physics)
- Publication
International Journal of Biomathematics, 2014, Vol 7, Issue 4, p-1
- ISSN
1793-5245
- Publication type
Article
- DOI
10.1142/S1793524514500454