RT Journal Article
T1 Subharmonic solutions for a class of predator-prey models with degenerate weights in periodic environments
A1 López Gómez, Julián
A1 Muñoz Hernández, Eduardo
A1 Zanolin, Fabio
AB 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.
PB De Gruyter
SN 2391-5455
YR 2023
FD 2023-06-20
LK https://hdl.handle.net/20.500.14352/93491
UL https://hdl.handle.net/20.500.14352/93491
LA eng
NO López-Gómez, Julián, Eduardo Muñoz-Hernández, y Fabio Zanolin. «Subharmonic Solutions for a Class of Predator-Prey Models with Degenerate Weights in Periodic Environments». Open Mathematics 21, n.o 1 (20 de junio de 2023): 20220593. https://doi.org/10.1515/math-2022-0593.
NO Ministerio de Ciencia, Innovación y Universidades (España)
DS Docta Complutense
RD 5 abr 2025