Stability of a generalized Putnam equation
type: Item
instance of: scholarly article
title: Stability of a generalized Putnam equation
zbMATH Open document ID: 1171.39003
author: Xiaofan Yang
author: Xingchang Liu
author: Lidan Wang
published in: Applied Mathematics Letters
publication date: 2009-06-09T00:00:00Z
review text: The authors prove that the equilibrium solution \(\bar{x}=1\) of the difference equation, \[ x_{n+1}=\frac{x_n+x_{n-1}+Ax_{n-2}x_{n-3}}{Ax_n x_{n-1} + x_{n-2} +x_{n-3}},\quad n=0,~1,~2,\dots \] with positive initial conditions is globally asymptotically stable if \(1\leq A<2\). They also conjecture that the equilibrium solution \(\bar{x}=1\) is globally asymptotically stable if \(A<\alpha\) where \(\alpha\approx 3.424.\)
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A20
zbMATH DE Number: 5563167
zbMATH Keywords: rational difference equation
zbMATH Keywords: equilibrium solution
zbMATH Keywords: global asymptotic stability
zbMATH Keywords: Putnam equation
reviewed by: Raghib Abu-Saris
MaRDI profile type: Publication
full work available at URL: j.aml.2008.06.031
OpenAlex ID: W2029754258
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DOI: 10.1016/J.AML.2008.06.031
description: scientific article; zbMATH DE number 5563167