Local stability and Lyapunov functionals for n-dimensional quasipolynomialconservative systems

Citation
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
Citations number
41
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN journal
0022247X → ACNP
Volume
256
Issue
1
Year of publication
2001
Pages
242 - 256
Database
ISI
SICI code
0022-247X(20010401)256:1<242:LSALFF>2.0.ZU;2-J
Abstract
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.