Volume 16, Issue 3, September 2009, Pages 339 - 354
Darboux Polynomials for Lotka–Volterra Systems in Three Dimensions
Received 2 January 2009, Accepted 19 February 2009, Available Online 7 January 2021.
- DOI
- 10.1142/S1402925109000261How to use a DOI?
- Keywords
- Lotka–Volterra model; integrability; Darboux polynomials
- Abstract
We consider Lotka–Volterra systems in three dimensions depending on three real parameters. By using elementary algebraic methods we classify the Darboux polynomials (also known as second integrals) for such systems for various values of the parameters, and give the explicit form of the corresponding cofactors. More precisely, we show that a Darboux polynomial of degree greater than one is reducible. In fact, it is a product of linear Darboux polynomials and first integrals.
- Copyright
- © 2009 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Yiannis T. Christodoulides AU - Pantelis A. Damianou PY - 2021 DA - 2021/01/07 TI - Darboux Polynomials for Lotka–Volterra Systems in Three Dimensions JO - Journal of Nonlinear Mathematical Physics SP - 339 EP - 354 VL - 16 IS - 3 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925109000261 DO - 10.1142/S1402925109000261 ID - Christodoulides2021 ER -