Volume 24, Issue 3, June 2017, Pages 393 - 404
Proper rational and analytic first integrals for asymmetric 3-dimensional Lotka-Volterra systems
Authors
Jaume Llibre
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain,jllibre@mat.uab.cat
Clàudia Valls
Departamento de Matemática, Instituto Superior Técnico, 1049–001 Lisboa, Portugal,cvalls@math.ist.utl.pt
Received 12 February 2017, Accepted 20 April 2017, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2017.1341701How to use a DOI?
- Keywords
- polynomial integrability; rational integrability; analytic integrability; asymmetric Lotka-Volterra systems
- Abstract
We go beyond in the study of the integrability of the classical model of competition between three species studied by May and Leonard [19], by considering a more realistic asymmetric model. Our results show that there are no global analytic first integrals and we provide all proper rational first integrals of this extended model by classifying its invariant algebraic surfaces.
- Copyright
- © 2017 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 - Jaume Llibre AU - Clàudia Valls PY - 2021 DA - 2021/01/06 TI - Proper rational and analytic first integrals for asymmetric 3-dimensional Lotka-Volterra systems JO - Journal of Nonlinear Mathematical Physics SP - 393 EP - 404 VL - 24 IS - 3 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2017.1341701 DO - 10.1080/14029251.2017.1341701 ID - Llibre2021 ER -