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

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


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.


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How to Cite
H. G. Díaz-Marín and O. Osuna, “Non-algebraic limit cycles in Holling type III zooplankton-phytoplankton models”, CUBO, vol. 23, no. 3, pp. 343–355, Dec. 2021.