Complicated dynamics of a three species chemostat food chain

Abstract

<p>We consider a model of the chemostat that involves a three species food chain with no imposed periodicities. The bottom trophic level species depends on a single, essential, growth-limiting nutrient. For a particular choice of prototype response functions, numerical simulations exhibit complicated dynamical behavior for reasonable parameter values. Using bifurcation theory methods we show the possibility of chaotic dynamics in a neighborhood of a particular equilibrium point. Moreover, we examine the role of each of the response functions with respect to the dynamics (i.e. chaos) of the model by systematically changing one response function at a time from linear to a more biologically reasonable Michaelis-Menten response function.</p>