Non-algebraic limit cycles in Holling type III zooplankton-phytoplankton models

Autor:	Homero G. Díaz-Marín, Osvaldo Osuna
Jazyk:	angličtina
Rok vydání:	2021
Předmět:	predator-prey models functional-response puiseux series newton polygon limit cycles invariant algebraic curve Mathematics QA1-939
Zdroj:	Cubo, Vol 23, Iss 3, Pp 343-355 (2021)
Druh dokumentu:	article
ISSN:	0719-0646 0716-7776
DOI:	10.4067/S0719-06462021000300343
Popis:	We prove that for certain polynomial differential equations in the plane arising from predator-prey type III models with generalized rational functional response, any algebraic solution should be a rational function. As a consequence, limit cycles, which are unique for these dynamical systems, are necessarily trascendental ovals. We exemplify these findings by showing a numerical simulation within a system arising from zooplankton-phytoplankton dynamics.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/143d5964f181475c990344e7a2ffadf1 Zobrazit plný text záznamu View record in DOAJ