Ballyk Mary M, McCluskey C Connell, Wolkowicz Gail S K
Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003, USA.
J Math Biol. 2005 Oct;51(4):458-90. doi: 10.1007/s00285-005-0333-7. Epub 2005 Jul 13.
We study a model of the chemostat with two species competing for two perfectly substitutable resources in the case of linear functional response. Lyapunov methods are used to provide sufficient conditions for the global asymptotic stability of the coexistence equilibrium. Then, using compound matrix techniques, we provide a global analysis in a subset of parameter space. In particular, we show that each solution converges to an equilibrium, even in the case that the coexistence equilibrium is a saddle. Finally, we provide a bifurcation analysis based on the dilution rate. In this context, we are able to provide a geometric interpretation that gives insight into the role of the other parameters in the bifurcation sequence.
我们研究了一个恒化器模型，其中两种物种在线性功能反应的情况下竞争两种完全可替代的资源。利用李雅普诺夫方法给出了共存平衡点全局渐近稳定性的充分条件。然后，使用复合矩阵技术，我们在参数空间的一个子集中进行了全局分析。特别地，我们表明即使共存平衡点是鞍点，每个解也会收敛到一个平衡点。最后，我们基于稀释率进行了分岔分析。在此背景下，我们能够提供一种几何解释，深入了解其他参数在分岔序列中的作用。
