Université de Haute Alsace, Mulhouse, France.
Math Biosci Eng. 2011 Jul;8(3):827-40. doi: 10.3934/mbe.2011.8.827.
In this paper, we consider a competition model between n species in a chemostat including both monotone and non-monotone growth functions, distinct removal rates and variable yields. We show that only the species with the lowest break-even concentration survives, provided that additional technical conditions on the growth functions and yields are satisfied. We construct a Lyapunov function which reduces to the Lyapunov function used by S. B. Hsu [SIAM J. Appl. Math., 34 (1978), pp. 760-763] in the Monod case when the growth functions are of Michaelis-Menten type and the yields are constant. Various applications are given including linear, quadratic and cubic yields.
在本文中，我们考虑了恒化器中 n 个物种之间的竞争模型，其中包括单调和非单调的生长函数、不同的去除率和可变的产率。我们证明，只要生长函数和产率满足额外的技术条件，只有具有最低盈亏平衡点浓度的物种才能存活。我们构造了一个李雅普诺夫函数，当生长函数为米氏型且产率恒定时，它简化为 S. B. Hsu [SIAM J. Appl. Math., 34 (1978), pp. 760-763] 在单一种群情况下使用的李雅普诺夫函数。给出了各种应用，包括线性、二次和三次产率。
