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Abstract:
The study considers two species competing for one limiting nutrient in an open system like the chemostat. One species produces a secondary metabolite, which has a growth-inhibiting effect on the species, but can also be exploited as a secondary resource. A basic model is introduced which consists of four nonlinear ordinary differential equations and incorporates metabolite production and consumption. As a first variant of this basic model we include interspecific competition. A second variant considers the introduction of a lethal inhibitor, that cannot be eliminated by one of the species and is selective for the stronger competitor.
We find that our basic model either supports the competitive exclusion principle or creates stable coexistence. The eventual outcome depends on the choice of parameter values. The dynamic of the system changes in a fundamental way, if interspecific competition is included; a supercritical as well as a subcritical Hopf bifurcation occur for appropriate parameter values. We discuss our results in relation to data from an experimental model system, which serves as basis for our mathematical assumptions and is motivated by pathogens related to the genetic disease Cystic Fibrosis.
