COMPLEX DYNAMIC BEHAVIOR OF AUTONOMOUS MICROBIAL FOOD-CHAINS

The dynamic behaviour of food chains under chemostat conditions is stu died. The microbial food chain consists of substrate (non-growing reso urces), bacteria (prey), ciliates (predator) and carnivore (top predat or). The governing equations are formulated at the population level. Y et these equations are derived from a dynamic energy budget model form ulated at the individual level. The resulting model is an autonomous s ystem of four first-order ordinary differential equations. These food chains resemble those occuring in ecosystems. Then the prey is general ly assumed to grow logistically. Therefore the model of these systems is formed by three first-order ordinary differential equations. As wit h these ecosystems, there is chaotic behaviour of the autonomous micro bial food chain under chemostat conditions with biologically relevant parameter values. It appears that the trajectories on the attractors c onsists of two superimposed oscillatory behaviours, a slow one for pre dator-top predator and a fast one for the prey-predator on one branch at which the top predator increases slowly. In some regions of the par ameter space there are multiple attractors.