EPI INRIA DISCO, L2S-CNRS-Supélec, 3 rue Joliot Curie, 91192, Gif-sur-Yvette, France.
J Biol Dyn. 2012;6:612-27. doi: 10.1080/17513758.2012.663795.
We study chemostat models in which multiple species compete for two or more limiting nutrients. First, we consider the case where the nutrient flow and species removal rates and input nutrient concentrations are all given as positive constants. In that case, we use Brouwer degree theory to give conditions guaranteeing that the models admit globally asymptotically stable componentwise positive equilibrium points, from all componentwise positive initial states. Then we use the results to develop stabilization theory for a class of controlled chemostats with two or more limiting nutrients. For cases where the dilution rate and input nutrient concentrations can be selected as controls, we prove that many different componentwise positive equilibria can be made globally asymptotically stable. This extends the existing control results for chemostats with one limiting nutrient. We demonstrate our methods in simulations.
我们研究了在两种或多种限制营养物质竞争的恒化器模型中。首先，我们考虑营养物质流量和物种去除率以及输入营养物质浓度均为正常数的情况。在这种情况下，我们使用 Brouwer 度理论给出了保证模型从所有组分正初始状态都存在全局渐近稳定的组分正平衡点的条件。然后，我们使用这些结果为具有两种或多种限制营养物质的一类受控恒化器开发了稳定化理论。对于可以选择稀释率和输入营养物质浓度作为控制的情况，我们证明可以使许多不同的组分正平衡点全局渐近稳定。这扩展了具有一种限制营养物质的恒化器的现有控制结果。我们在模拟中演示了我们的方法。
