On the dynamics of Tschirhart's predator-prey model

In a series of recent publications Tschirhart constructed a dynamic multi-species model based on a novel general equilibrium model of the ecosystem. With that approach he and Finnoff carried out numerical simulations of rather complex dynamic food webs. While all of their numerical calculations exhibited global stability, the general properties of the underlying dynamic system are not known. This paper explores the analytical dynamics of a predator-prey system derived from Tschirhart's framework of analysis. Although our focus is restricted to a two-species model, the dynamics turn out to be much more complex than suggested by Tschirhart's numerical studies. Although global asymptotic stability of an equilibrium is possible, we also identify areas of local asymptotic stability or instability as well as a stable limit cycle.