In this paper, we consider a simple chemostat model with inhibitory exponential sub- strate uptake and a time delay. A detailed qualitative analysis about existence and boundedness of its solutions and the local asymp...In this paper, we consider a simple chemostat model with inhibitory exponential sub- strate 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 car- ried out. Using Lyapunov-LaSalle invariance principle, we show that the washout equi- librium is global asymptotic stability for any time delay. Using the fluctuation lemma, the sufficient condition of the global asymptotic stability of the positive equilibrium E＋ is obtained. Numerical simulations are also performed to illustrate the results.展开更多
文摘In this paper, we consider a simple chemostat model with inhibitory exponential sub- strate 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 car- ried out. Using Lyapunov-LaSalle invariance principle, we show that the washout equi- librium is global asymptotic stability for any time delay. Using the fluctuation lemma, the sufficient condition of the global asymptotic stability of the positive equilibrium E＋ is obtained. Numerical simulations are also performed to illustrate the results.
