Local Integrability and Linearizability of Three-dimensional Lotka-Volterra Systems
Dynamical Systems
2011-11-14 v1
Abstract
We investigate the local integrability and linearizability of three dimensional Lotka-Volterra equations at the origin. Necessary and sufficient conditions for both integrability and linearizability are obtained for (1,-1,1), (2,-1,1) and (1,-2,1)-resonance. To prove sufficiency, we mainly use the method of Darboux with extensions for inverse Jacobi multipliers, and the linearizability of a node in two variables with power-series arguments in the third variable.
Keywords
Cite
@article{arxiv.1111.2773,
title = {Local Integrability and Linearizability of Three-dimensional Lotka-Volterra Systems},
author = {Waleed Aziz and Colin Christopher},
journal= {arXiv preprint arXiv:1111.2773},
year = {2011}
}