Non-algebraic limit cycles in Holling type III zooplankton-phytoplankton models
Author
Díaz-Marín, Homero G.
Osuna, Osvaldo
Full text
https://revistas.ufro.cl/ojs/index.php/cubo/article/view/284710.4067/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.