2026-06-29T16:49:37Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/1346092026-04-11T00:01:02Zcom_20.500.14352_14col_20.500.14352_15

Minimal complexity of subharmonics in a class of planar periodic predator-prey models López Gómez, Julián Muñoz Hernández, Eduardo Rafael Gallego, Mariano Mateos This contribution analyzes the existence of $nT$-periodic coexistence states, for $n\geq1$, in two classes of non-autonomous predator-prey Volterra systems with periodic coefficients. In the first place, 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. In the second place, it will be analyzed a degenerate predator-prey model introduced in [9] and [5] and, then, deeply studied in [7]. By analyzing the iterates of the Poincaré map of the system, it is shown that it admits nontrivial $nT$-periodic coexistence states for every $n\geq2$. 2026-04-10T10:23:05Z 2026-04-10T10:23:05Z 2026-04-10T10:23:05Z 2021 conference paper https://hdl.handle.net/20.500.14352/134609 XXXX-XXXX 10651/59093 eng PGC2018-097104-B-I00 López Gómez, J.; Muñoz Hernández, E. y Zanolin, F. (2021) Minimal complexity of subharmonics in a class of planar periodic predator-prey models. En Gallego, R. y Mateos, M.(editores) Proceedings of the XXVI Congreso de Ecuaciones Diferenciales y Aplicaciones. XVI Congreso de Matemática Aplicada (pp. 258-264). Oviedo : Universidad de Oviedo, Servicio de Publicaciones http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 International