Bifurcation in dynamic problems with seasonal succession

We investigate the bifurcation structure of equilibria in a class of non-autonomous ordinary differential equations governed by a season length parameter, $\tau$, which determines the alternation between growth and decline dynamics. This structure models biological systems exhibiting seasonal variat...

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Autores: Galiano Casas, Gonzalo|||0000-0001-7381-7060, Velasco Valdés, Julián
Tipo de recurso: artículo
Fecha de publicación:2026
País:España
Institución:Universidad de Oviedo (UNIOVI)
Repositorio:RUO. Repositorio Institucional de la Universidad de Oviedo
Idioma:inglés
OAI Identifier:oai:dnet:ruo_________::f7e0e83dd7c76ac9f3864dccab5657a0
Acceso en línea:https://hdl.handle.net/10651/83350
https://dx.doi.org/10.1016/j.nonrwa.2026.104648
Access Level:acceso abierto
Palabra clave:Seasonal succession
Periodic solutions
Bifurcation
Coexistence
Lotka-Volterra
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spelling Bifurcation in dynamic problems with seasonal successionGaliano Casas, Gonzalo|||0000-0001-7381-7060Velasco Valdés, JuliánSeasonal successionPeriodic solutionsBifurcationCoexistenceLotka-VolterraWe investigate the bifurcation structure of equilibria in a class of non-autonomous ordinary differential equations governed by a season length parameter, $\tau$, which determines the alternation between growth and decline dynamics. This structure models biological systems exhibiting seasonal variation, such as insect population dynamics or infectious disease transmission. Using the Crandall–Rabinowitz bifurcation theorem, we establish the existence of a critical threshold $\tau^*$ at which a bifurcation from the extinction equilibrium occurs. We also explore the emergence of secondary bifurcations from, in general, explicitly unknown non-trivial equilibria which can only be treated numerically. Our results are illustrated with a two-species competitive Lotka–Volterra model for the growth season and a Malthusian model for the decline season for which primary and secondary bifurcations may be computed analytically, allowing the validation of numerical approximations. Our analysis shows how seasonality drives transitions between extinction of both populations, of only one, and coexistence of both populations.Supported by the Spanish MCI Project MCI-21-PID2020-116287GB-I00.20262026-01-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articlehttps://hdl.handle.net/10651/83350https://dx.doi.org/10.1016/j.nonrwa.2026.104648reponame:RUO. Repositorio Institucional de la Universidad de Oviedoinstname:Universidad de Oviedo (UNIOVI)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial 4.0 Internationalhttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccessoai:dnet:ruo_________::f7e0e83dd7c76ac9f3864dccab5657a02026-06-07T06:38:51Z
dc.title.none.fl_str_mv Bifurcation in dynamic problems with seasonal succession
title Bifurcation in dynamic problems with seasonal succession
spellingShingle Bifurcation in dynamic problems with seasonal succession
Galiano Casas, Gonzalo|||0000-0001-7381-7060
Seasonal succession
Periodic solutions
Bifurcation
Coexistence
Lotka-Volterra
title_short Bifurcation in dynamic problems with seasonal succession
title_full Bifurcation in dynamic problems with seasonal succession
title_fullStr Bifurcation in dynamic problems with seasonal succession
title_full_unstemmed Bifurcation in dynamic problems with seasonal succession
title_sort Bifurcation in dynamic problems with seasonal succession
dc.creator.none.fl_str_mv Galiano Casas, Gonzalo|||0000-0001-7381-7060
Velasco Valdés, Julián
author Galiano Casas, Gonzalo|||0000-0001-7381-7060
author_facet Galiano Casas, Gonzalo|||0000-0001-7381-7060
Velasco Valdés, Julián
author_role author
author2 Velasco Valdés, Julián
author2_role author
dc.subject.none.fl_str_mv Seasonal succession
Periodic solutions
Bifurcation
Coexistence
Lotka-Volterra
topic Seasonal succession
Periodic solutions
Bifurcation
Coexistence
Lotka-Volterra
description We investigate the bifurcation structure of equilibria in a class of non-autonomous ordinary differential equations governed by a season length parameter, $\tau$, which determines the alternation between growth and decline dynamics. This structure models biological systems exhibiting seasonal variation, such as insect population dynamics or infectious disease transmission. Using the Crandall–Rabinowitz bifurcation theorem, we establish the existence of a critical threshold $\tau^*$ at which a bifurcation from the extinction equilibrium occurs. We also explore the emergence of secondary bifurcations from, in general, explicitly unknown non-trivial equilibria which can only be treated numerically. Our results are illustrated with a two-species competitive Lotka–Volterra model for the growth season and a Malthusian model for the decline season for which primary and secondary bifurcations may be computed analytically, allowing the validation of numerical approximations. Our analysis shows how seasonality drives transitions between extinction of both populations, of only one, and coexistence of both populations.
publishDate 2026
dc.date.none.fl_str_mv 2026
2026-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10651/83350
https://dx.doi.org/10.1016/j.nonrwa.2026.104648
url https://hdl.handle.net/10651/83350
https://dx.doi.org/10.1016/j.nonrwa.2026.104648
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial 4.0 International
http://creativecommons.org/licenses/by-nc/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial 4.0 International
http://creativecommons.org/licenses/by-nc/4.0/
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv reponame:RUO. Repositorio Institucional de la Universidad de Oviedo
instname:Universidad de Oviedo (UNIOVI)
instname_str Universidad de Oviedo (UNIOVI)
reponame_str RUO. Repositorio Institucional de la Universidad de Oviedo
collection RUO. Repositorio Institucional de la Universidad de Oviedo
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