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...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/93491 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/93491 |
| Access Level: | acceso abierto |
| Palabra clave: | Periodic predator-prey Volterra model Subharmonic coexistence states Global structure Minimal complexity Chaotic dynamics Ecuaciones diferenciales Análisis matemático 1202.19 Ecuaciones Diferenciales Ordinarias 1202 Análisis y Análisis Funcional |
| Sumario: | 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 cooperativeand quasi-cooperative dynamics, as a consequence of the ordering imposed by the maximum principle. |
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