On the recursive sequence \(x_{n+1}=\alpha-(x_n/x_{n-1})\)
type: Item
instance of: scholarly article
title: On the recursive sequence \(x_{n+1}=\alpha-(x_n/x_{n-1})\)
zbMATH Open document ID: 1068.39030
DOI: 10.1007/BF02936054
author: Xing-Xue Yan
author: Zhu Zhao
author: Wan-Tong Li
published in: Journal of Applied Mathematics and Computing
publication date: 2005-03-10T00:00:00Z
review text: It is shown that for arbitrary real \(\alpha\) the equation in the title has a monotone solution converging to the equilibrium \(\alpha-1\). Under additional assumptions, the equilibrium is globally asymptotically stable and a global attractor. The authors also give conditions such that all solutions are bounded, all solutions are chaotic, resp. such that there exists a 2-periodic solution.
reviewed by: Lothar Berg
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A20
Mathematics Subject Classification ID: 37C70
zbMATH DE Number: 2143261
zbMATH Keywords: rational difference equation
zbMATH Keywords: global asymptotic stability
zbMATH Keywords: global attractor
zbMATH Keywords: bounded solution
zbMATH Keywords: chaotic solution
zbMATH Keywords: periodic solutions
zbMATH Keywords: convergence
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02936054
OpenAlex ID: W2331126027
description: scientific article; zbMATH DE number 2143261