On the Existence of Complex Dynamics in Pure and Simple Microbial Competition in Bioreactors

Abstract

This paper examines the conditions necessary for the emergence of complex dynamic behavior in systems of pure and simple microbial competition in the chemostat under time-invariant feed conditions. In particular, we study the effect of variable yield coefficients and the presence of microorganisms in the inflow on the dynamics of such systems. This is accomplished through the study of a mathematical model of two microbial populations competing for a single nutrient in a chemostat. A numerical investigation is carried out for a particular case for which the yield coefficient associated with one species is linearly dependent on the substrate, while the other species exists in the inflow. Both Monod and substrate inhibition growth rates are examined. The numerical investigation showed the existence of complex behavior in the model, characterized by the existence of stable quasi-periodic states resulting from torus bifurcations of limit cycles. Also, limit cycles may undergo period doubling leading to periodic states of increasing period. It seems that the variability of the yield coefficient of one species and the presence of at least one microorganism in the inflow are necessary conditions for complex dynamics to arise in pure and simple competition in the chemostat.