Stability analysis of predator-prey models via Liapunov method

Abstract

As it is well known from the classical applications in the elec trical and mechanical sciences, energy is a suitable Liapunov function: thus, by analogy, all energy functions proposed in ecology are potential Liapunov functions. In this paper, a generalized Lotka-Vol terra model is considered and the stability properties of its non-tri vial equilibrium are studied by means of an energy function, first proposed by Volterra in the context of conservative ecosystems. The advantage of this Liapunov function with respect to the one that can be induced through linearization is also illustrated.