Local stability and Lyapunov functionals for n-dimensional quasipolynomialconservative systems

We present a method for determining the local stability of equilibrium poin ts of conservative generalizations of the Lotka-Volterra equations. These g eneralizations incorporate both an arbitrary number of species-including od d-dimensional systems-and nonlinearities of arbitrarily high order in the i nterspecific interaction terms. The method combines a reformulation of the equations in terms of a Poisson structure and the construction of their Lya punov functionals via the energy-Casimir method. These Lyapunov functionals are a generalization of those traditionally known for Lorka-Volterra syste ms. Examples are given. (C) 2001 Academic Press.