Fekih-Salem Radhouane, Lobry Claude, Sari Tewfik
Université de Tunis El Manar, ENIT, LAMSIN, BP 37, Le Belvédère, 1002 Tunis, Tunisie; Université de Monastir, ISIMa, BP 49, Av Habib Bourguiba, 5111 Mahdia, Tunisie.
Université de Nice et MODEMIC, Le Gd Palais Bt6, 2 BD de Cimiez, 06000 Nice, France.
Math Biosci. 2017 Apr;286:104-122. doi: 10.1016/j.mbs.2017.02.007. Epub 2017 Feb 14.
This paper deals with a two-microbial species model in competition for a single-resource in the chemostat including general intra- and interspecific density-dependent growth rates with distinct removal rates for each species. In order to understand the effects of intra- and interspecific interference, this general model is first studied by determining the conditions of existence and local stability of steady states. With the same removal rate, the model can be reduced to a planar system and then the global stability results for each steady state are derived. The bifurcations of steady states according to interspecific interference parameters are analyzed in a particular case of density-dependent growth rates which are usually used in the literature. The operating diagrams show how the model behaves by varying the operating parameters and illustrate the effect of the intra- and interspecific interference on the disappearance of coexistence region and the occurrence of bi-stability region. Concerning the small enough interspecific interference terms, we would shed light on the global convergence towards the coexistence steady state for any positive initial condition. When the interspecific interference pressure is large enough this system exhibits bi-stability where the issue of the competition depends on the initial condition.
本文研究了恒化器中两种微生物在单一资源竞争中的模型，包括一般的种内和种间密度依赖生长速率，且每种微生物具有不同的去除率。为了理解种内和种间干扰的影响，首先通过确定稳态的存在条件和局部稳定性来研究这个一般模型。在去除率相同时，该模型可简化为平面系统，进而得出每个稳态的全局稳定性结果。在文献中常用的密度依赖生长速率的特定情况下，分析了根据种间干扰参数的稳态分岔。操作图展示了模型如何通过改变操作参数来表现，并说明了种内和种间干扰对共存区域消失和双稳态区域出现的影响。对于足够小的种间干扰项，我们将阐明对于任何正初始条件向共存稳态的全局收敛情况。当种间干扰压力足够大时，该系统表现出双稳态，此时竞争问题取决于初始条件。
