Reliable computation of equilibrium states and bifurcations in ecological systems analysis

A problem of frequent interest in analyzing nonlinear ODE models of ecological systems is the location of equilibrium states and bifurcations. Interval-Newton techniques are explored for identifying, with certainty, all equilibrium states and all codimension-1 and codimension-2 bifurcations of interest within specified model parameter intervals. The methodology is applied to a tritrophic food chain in a chemostat (Canale’s model), and a modification of thereof. This modification aids in elucidating the nonlinear effects of introducing a hypothetical contaminant into a food chain.