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. Monodʹs model is employed for the specific growth rates of all the microbial 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. We demonstrate that the system exhibits chaotic behavior and multistability. Two different routes to chaos are observed. Chaotic behavior is reached either through a sequence of period doublings 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 bifurcations of periodic states, the effect being multistablity, i.e. coexistence of stable periodic states with other stable periodic, quasi-periodic or chaotic states. The results demonstrate the importance of the interaction of food chains with regard to the dynamics exhibited by systems of microbial species inhabiting a common environment.