(1) Physics Department, Environmental Sciences and Resources Program, Portland State University, 97207 Portland, Oregon, USA;(2) Present address: Museum of Comparative Zoology, Harvard University, 02138 Cambridge, Massachusetts, USA
Abstract:
Summary Several geometrical interpretations of Liapunov functions for non-linear ecological models are examined and their limitations pointed out. In particular the geometrical nonuniqueness of Liapunov functions is illustrated by displaying explicitly and comparing four different Liapunov functions for the symmetric competition model for two species. The main point is that considerable care must be taken in using the geometrical properties of an arbitrary Liapunov function as a guide to stability under perturbations.