Lagrange stability and ecological systems

This paper considers the ecological and mathematical relationships among various stability concepts. It is shown that diagonally dominant nonlinear systems have positive solutions for positive initial conditions. The boundedness of such positive solutions leads to a total systems concept of stability: Lagrange stability. This concept is discussed as a compatible method for determining the stability of ecosystems and their mathematical models. Stability in the sense of Lagrange is a total systems concept which does not directly address the problem of the stability of equilibria. A topological presentation is used to describe the Lagrange stability of nonlinear ecosystem compartment models. Finally, the concept of practical stability is developed and discussed with respect to maintaining the desired state of ecosystems in the presence of perturbations.