Chaotic dynamics of a microbial system of coupled food chains

We analyze a mathematical model of a simple microbial system consisting of two microbial populations competing for a single nutrient and two predator populations, each one feeding upon one competitor, in a chemostat. Monod's model is employed for the specific growth rates of all the microbial popula tions. We use numerical bifurcation techniques to determine the effect of t he operating conditions of the chemostat on the dynamics of the system and construct its operating diagram. We demonstrate that the system exhibits ch aotic behavior and multistability. Two different routes to chaos are observ ed. Chaotic behavior is reached either through a sequence of period doublin gs or through birth and breaking of quasi-periodic states, as the operating conditions are varied. In some cases, transition from periodic to chaotic behavior is accompanied at certain parameter values by limit-point bifurcat ions of periodic states, the effect being multistablity, i.e. coexistence o f stable periodic states with other stable periodic, quasi-periodic or chao tic states. The results demonstrate the importance of the interaction of fo od chains with regard to the dynamics exhibited by systems of microbial spe cies inhabiting a common environment. (C) 2001 Elsevier Science B.V. All ri ghts reserved.