Local Stability and Lyapunov Functionals for n-Dimensional Quasipolynomial Conservative Systems
Dynamical Systems
2019-11-04 v1 Mathematical Physics
math.MP
Symplectic Geometry
Exactly Solvable and Integrable Systems
Biological Physics
Abstract
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.
Cite
@article{arxiv.1910.03309,
title = {Local Stability and Lyapunov Functionals for n-Dimensional Quasipolynomial Conservative Systems},
author = {Benito Hernández-Bermejo and Victor Fairén},
journal= {arXiv preprint arXiv:1910.03309},
year = {2019}
}