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oai:docta.ucm.es:20.500.14352/934452025-03-22T00:56:31Zcom_20.500.14352_14col_20.500.14352_15

On the applicability of the poincaré–Birkhoff twist theorem to a class of planar periodic predator-prey models López Gómez, Julián Muñoz Hernández, Eduardo Zanolin, Fabio This paper studies the existence of subharmonics of arbitrary order in a generalized class of non-autonomous predator-prey systems of Volterra type with periodic coefficients. When the model is non-degenerate it is shown that the Poincaré–Birkhoff twist theorem can be applied to get the existence of subharmonics of arbitrary order. However, in the degenerate models, whether or not the twist theorem can be applied to get subharmonics of a given order might depend on the particular nodal behavior of the several weight function-coefficients involved in the setting of the model. Finally, in order to analyze how the subharmonics might be lost as the model degenerates, the exact point-wise behavior of the T-periodic solutions of a non-degenerate model is ascertained as a perturbation parameter makes it degenerate. 2024-01-16T16:38:45Z 2024-01-16T16:38:45Z 2024-01-16T16:38:45Z 2020 journal article https://hdl.handle.net/20.500.14352/93445 1553-5231 10.3934/dcds.2020119 eng info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-097104-B-I00/ES/SISTEMAS DE REACCION DIFUSION/ López-Gómez, J., Muñoz-Hernández, E., & Zanolin, F. (2020). On the applicability of the poincaré–Birkhoff twist theorem to a class of planar periodic predator-prey models. Discrete And Continuous Dynamical Systems, 40(4), 2393-2419. https://doi.org/10.3934/dcds.2020119 restricted access American Institute of Mathematical Sciences