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

Homero G. Díaz-Marín; Osvaldo Osuna

doi:10.4067/S0719-06462021000300343

DOI:

https://doi.org/10.4067/S0719-06462021000300343

Abstract

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.

Keywords

Predator-prey models , functional-response , Puiseux series , Newton polygon , limit cycles , invariant algebraic curve

Homero G. Díaz-Marín Facultad de Ciencias Físico-Matemáticas, Universidad Michoacana, Edif. Alfa, Ciudad Universitaria, C.P. 58040, Morelia, Michoacán, México.
Osvaldo Osuna Instituto de Física y Matemáticas, Universidad Michoacana, Edif. C-3, Ciudad Universitaria, C.P. 58040, Morelia, Michoacán, México.

Pages: 343–355
Date Published: 2021-12-01
Vol. 23 No. 3 (2021)

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