Global analysis of competition for perfectly substitutable resources with linear response

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, …