  We present a method for determining the local stability of equilibrium points
of conservative generalizations of the Lotka-Volterra equations. These
generalizations incorporate both an arbitrary number of species -including
odd-dimensional systems- and nonlinearities of arbitrarily high order in the
interspecific interaction terms. The method combines a reformulation of the
equations in terms of a Poisson structure and the construction of their
Lyapunov functionals via the energy-Casimir method. These Lyapunov functionals
are a generalization of those traditionally known for Lotka-Volterra systems.
Examples are given.
