Analysis of a model of two parallel food chains (Q841336)

A mathematical model of two parallel food chains in a chemostat is investigated. Each food chain consists of a prey species \(x\) and a predator species \(y\). Two food chains are symmetric in the sense that the prey species are identical and so are the specialized predator species. Both of the prey species in the parallel food chains share the same nutrient \(R\). The authors show that as the input concentration \(R^{(0)}\) of the nutrient varies, there are several possible outcomes: (1) all species go extinct; (2) only the two prey species survive; (3) all species coexist at equilibrium; (4) all species coexist in the form of oscillations. The authors analyze cases (1)-(3) rigorously; for case (4), the authors do extensive numerical studies to present all possible phenomena, which include limit cycles, heteroclinic cycles, and chaos.