On the applicability of the Poincaré-Birkhoff twist theorem to a class of planar periodic predator-prey models
type: Item
instance of: scholarly article
title: On the applicability of the Poincaré-Birkhoff twist theorem to a class of planar periodic predator-prey models
zbMATH Open document ID: 1441.34060
author: Julián López-Gómez
author: Eduardo Muñoz-Hernández
author: Fabio Zanolin
published in: Discrete and Continuous Dynamical Systems
publication date: 2020-04-16T00:00:00Z
review text: The authors deal with the existence of subharmonics of arbitrary order in a generalized class of non-autonomous predator-prey systems of Volterra type with periodic coefficients. 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. However, in the degenerate models, whether or not the twist theorem can be applied to get subharmonics of a given order might depend on the particular nodal behavior of the several weight function coefficients involved in the setting of the model. Finally, in order to analyze how the subharmonics might be lost as the model degenerates, the exact point-wise behavior of the T-periodic solutions of a non-degenerate model is ascertained as a perturbation parameter makes it degenerate. This is a valuable work in this field.
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 37E40
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 37C60
zbMATH DE Number: 7190113
zbMATH Keywords: periodic predator-prey model of Volterra type
zbMATH Keywords: subharmonic coexistence states
zbMATH Keywords: Poincaré-Birkhoff twist theorem
zbMATH Keywords: degenerate versus non-degenerate models
zbMATH Keywords: point-wise behavior of the low order subharmonics as the model degenerates
reviewed by: Changjin Xu
MaRDI profile type: Publication
full work available at URL: dcds.2020119
OpenAlex ID: W3004174848
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DOI: 10.3934/DCDS.2020119
description: scientific article; zbMATH DE number 7190113