Hamra Mohamed Amine, Yadi Karim
Laboratoire Systèmes Dynamiques et Applications, Tlemcen University, BP 119, 13000, Tlemcen, Algeria.
Acta Biotheor. 2017 Sep;65(3):233-252. doi: 10.1007/s10441-017-9309-4. Epub 2017 May 4.
In this work, we study a several species aerobic chemostat model with constant recycle sludge concentration in continuous culture. We reduce the number of parameters by considering a dimensionless model. First, the existence of a global positive uniform attractor for the model with different removal rates is proved using the theory of dissipative dynamical systems. Hence, we investigate the asymptotic behavior of the model under small perturbations using methods of singular perturbation theory and we prove that, in the case of two species in competition, the unique equilibrium which is positive is globally asymptotically stable. Finally, we establish the link between the open problem of the chemostat with different removal rates and monotone functional responses, and our model when two species compete on the same nutrient. We give some numerical simulations to illustrate the results.
在这项工作中，我们研究了连续培养中具有恒定循环污泥浓度的多物种好氧恒化器模型。我们通过考虑一个无量纲模型来减少参数数量。首先，利用耗散动力系统理论证明了具有不同去除率的模型存在全局正一致吸引子。因此，我们使用奇异摄动理论方法研究了该模型在小扰动下的渐近行为，并证明了在两种物种竞争的情况下，唯一的正平衡点是全局渐近稳定的。最后，我们建立了具有不同去除率和单调功能反应的恒化器开放问题与我们的模型（当两种物种在相同营养物质上竞争时）之间的联系。我们给出了一些数值模拟来说明结果。
