On a difference equation with exponentially decreasing nonlinearity
type: Item
instance of: scholarly article
title: On a difference equation with exponentially decreasing nonlinearity
zbMATH Open document ID: 1229.92017
DOI: 10.1155/2011/147926
author: E. Braverman
author: S. H. Saker
published in: Discrete Dynamics in Nature and Society
publication date: 2012-01-23T00:00:00Z
review text: Summary: We establish a necessary and sufficient condition for global stability of a nonlinear discrete red blood cells survival model and demonstrate that local asymptotic stability implies global stability. Oscillation and solution bounds are investigated. We also show that, for different values of the parameters, the solution exhibits some time-varying dynamics, that is, if the system is moved in a direction away from stability (by increasing the parameters), then it undergoes a series of bifurcations that leads to increasingly long periodic cycles and finally to deterministic chaos. We also study the chaotic behavior of the model with a constant positive perturbation and prove that, for large enough values of one of the parameters, the perturbed system is again stable.
Mathematics Subject Classification ID: 92C30
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 37N25
Mathematics Subject Classification ID: 39A30
Mathematics Subject Classification ID: 92C50
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 5999614
Wikidata QID: Q58655417
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/147926
OpenAlex ID: W2022620637
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description: scientific article; zbMATH DE number 5999614