B. Hernandez-bermejo et V. Fairen, Local stability and Lyapunov functionals for n-dimensional quasipolynomialconservative systems, J MATH ANAL, 256(1), 2001, pp. 242-256
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.