Global dynamics of the Hastings-Powell system
type: Item
instance of: scholarly article
title: Global dynamics of the Hastings-Powell system
zbMATH Open document ID: 1296.34136
DOI: 10.1155/2013/469072
author: Luis N. Coria
published in: Mathematical Problems in Engineering
publication date: 2014-10-13T00:00:00Z
review text: Summary: This paper studies the problem of bounding a domain that contains all compact invariant sets of the Hastings-Powell system. The results were obtained using the first-order extremum conditions and the iterative theorem to a biologically meaningful model. As a result, we calculate the bounds given by a tetrahedron with excisions, described by several inequalities of the state variables and system parameters. Therefore, a region is identified where all the system dynamics are located, that is, its compact invariant sets: equilibrium points, periodic-homoclinic-heteroclinic orbits, and chaotic attractors. It was also possible to formulate a nonexistence condition of the compact invariant sets. Additionally, numerical simulations provide examples of the calculated boundaries for the chaotic attractors or periodic orbits. The results provide insights regarding the global dynamics of the system.
Mathematics Subject Classification ID: 34D35
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 37N25
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 6354316
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/469072
OpenAlex ID: W2106474849
Wikidata QID: Q59027814
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description: scientific article; zbMATH DE number 6354316