The Dynamics of Cascaded Monod System Models Through Five Levels

A Monod system model is a set of ordinary differential equations where the terms resemble those which Monod described in his 1949 paper. We focus on the multiple trophic level case in which each trophic level uses only one of the trophic levels for its perpetuation, and no two trophic entities use the same trophic cascaded level. The treatment derives from a primary producer progressively through five trophic levels. Stability types are identified and are related to persistence, and the consequences of some intuitive scaling structures are developed. These considerations are useful to some theoretical questions in ecology and to applications such as bioreactor operation.