Abstract

DIAZ-MARIN, Homero  and  OSUNA, Osvaldo. On the invariant rational curves of a certain family of polynomial differential equations. Rev.colomb.mat. [online]. 2022, vol.56, n.1, pp.93-111.  Epub Jan 02, 2024. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v56n1.105621.

In this work, we present sufficient conditions to determine if the limit cycles of certain differential systems in the plane are algebraic or not. In particular, we obtain criteria such that the limit cycles of equations derived from predatory prey models with rational functional response are necessarily transcendental ovals.

Keywords : algebraic limit-cycles; Puiseux series; Newton polygon; predator-prey models; functional-response.

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