Abstract
In this paper, we study the global dynamics of a chemostat model with a single nutrient and several competing species. Growth rates are not required to be proportional to food uptakes. Our approach is based on the construction of Lyapunov functions. The Lyapunov functions extend those used by Hsu (SIAM J. Appl. Math. 34:760–763, 1978) and by Wolkowicz and Lu (SIAM J. Appl. Math. 57:1019–1043, 1997) in the case when growth rates are proportional to food uptakes. Our result generalizes a large variety of previous results obtained by Lyapunov techniques.
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