Subharmonic solutions for a class of predator-prey models with degenerate weights in periodic environments
This article deals with the existence, multiplicity, minimal complexity, and global structure of the subharmonic solutions to a class of planar Hamiltonian systems with periodic coefficients, being the classical predator-prey model of V. Volterra its most paradigmatic example. By means of a topologi...
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| Format: | Article |
| Language: | English |
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De Gruyter
2023-06-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2022-0593 |
| _version_ | 1797795045240209408 |
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| author | López-Gómez Julián Muñoz-Hernández Eduardo Zanolin Fabio |
| author_facet | López-Gómez Julián Muñoz-Hernández Eduardo Zanolin Fabio |
| author_sort | López-Gómez Julián |
| collection | DOAJ |
| description | This article deals with the existence, multiplicity, minimal complexity, and global structure of the subharmonic solutions to a class of planar Hamiltonian systems with periodic coefficients, being the classical predator-prey model of V. Volterra its most paradigmatic example. By means of a topological approach based on techniques from global bifurcation theory, the first part of the paper ascertains their nature, multiplicity and minimal complexity, as well as their global minimal structure, in terms of the configuration of the function coefficients in the setting of the model. The second part of the paper introduces a dynamical system approach based on the theory of topological horseshoes that permits to detect, besides subharmonic solutions, “chaotic-type” solutions. As a byproduct of our analysis, the simplest predator-prey prototype models in periodic environments can provoke chaotic dynamics. This cannot occur in cooperative and quasi-cooperative dynamics, as a consequence of the ordering imposed by the maximum principle. |
| first_indexed | 2024-03-13T03:11:56Z |
| format | Article |
| id | doaj.art-8272b84d924d46f39fc0fb3991e3dbe2 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-03-13T03:11:56Z |
| publishDate | 2023-06-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-8272b84d924d46f39fc0fb3991e3dbe22023-06-26T10:46:45ZengDe GruyterOpen Mathematics2391-54552023-06-0121160963310.1515/math-2022-0593Subharmonic solutions for a class of predator-prey models with degenerate weights in periodic environmentsLópez-Gómez Julián0Muñoz-Hernández Eduardo1Zanolin Fabio2Departamento de Análisis Matemático y Matemática Aplicada, Universidad Complutense de Madrid, Instituto de Matemática Interdisciplinar (IMI), Plaza de las Ciencias 3, 28040 Madrid, SpainDepartamento de Análisis Matemático y Matemática Aplicada, Universidad Complutense de Madrid, Instituto de Matemática Interdisciplinar (IMI), Plaza de las Ciencias 3, 28040 Madrid, SpainDipartimento di Scienze Matematiche, Informatiche e Fisiche, Università degli Studi di Udine, Via delle Scienze 2016, 33100 Udine, ItalyThis article deals with the existence, multiplicity, minimal complexity, and global structure of the subharmonic solutions to a class of planar Hamiltonian systems with periodic coefficients, being the classical predator-prey model of V. Volterra its most paradigmatic example. By means of a topological approach based on techniques from global bifurcation theory, the first part of the paper ascertains their nature, multiplicity and minimal complexity, as well as their global minimal structure, in terms of the configuration of the function coefficients in the setting of the model. The second part of the paper introduces a dynamical system approach based on the theory of topological horseshoes that permits to detect, besides subharmonic solutions, “chaotic-type” solutions. As a byproduct of our analysis, the simplest predator-prey prototype models in periodic environments can provoke chaotic dynamics. This cannot occur in cooperative and quasi-cooperative dynamics, as a consequence of the ordering imposed by the maximum principle.https://doi.org/10.1515/math-2022-0593periodic predator-prey volterra modelsubharmonic coexistence statesglobal structureminimal complexitychaotic dynamics34c2537b5537e4037j12 |
| spellingShingle | López-Gómez Julián Muñoz-Hernández Eduardo Zanolin Fabio Subharmonic solutions for a class of predator-prey models with degenerate weights in periodic environments Open Mathematics periodic predator-prey volterra model subharmonic coexistence states global structure minimal complexity chaotic dynamics 34c25 37b55 37e40 37j12 |
| title | Subharmonic solutions for a class of predator-prey models with degenerate weights in periodic environments |
| title_full | Subharmonic solutions for a class of predator-prey models with degenerate weights in periodic environments |
| title_fullStr | Subharmonic solutions for a class of predator-prey models with degenerate weights in periodic environments |
| title_full_unstemmed | Subharmonic solutions for a class of predator-prey models with degenerate weights in periodic environments |
| title_short | Subharmonic solutions for a class of predator-prey models with degenerate weights in periodic environments |
| title_sort | subharmonic solutions for a class of predator prey models with degenerate weights in periodic environments |
| topic | periodic predator-prey volterra model subharmonic coexistence states global structure minimal complexity chaotic dynamics 34c25 37b55 37e40 37j12 |
| url | https://doi.org/10.1515/math-2022-0593 |
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