Chaotic dynamics of a food web in a chemostat

We analyze a mathematical model of a simple food web consisting of one predator and two prey populations in a chemostat. Monod’s model is employed for the dependence of the specific growth rates of the two prey populations on the concentration of the rate-limiting substrate and a generalization of Monod’s model for the dependence of the specific growth rate of the predator on the concentrations of the prey populations. We use numerical bifurcation techniques to determine the effect of the operating conditions of the chemostat on the dynamics of the system and construct its operating diagram. Chaotic behavior resulting from successive period doublings is observed. Multistability phenomena of coexistence of steady and periodic states at the same operating conditions are also found.