On Global Attractivity of a Class of Nonautonomous Difference Equations

We mainly investigate the global behavior to the family of higher-order nonautonomous recursive equations given by yn=(p+ryn-s)/(q+ϕn(yn-1,yn-2,…,yn-m)+yn-s), n∈ℕ0, with p≥0,r,q>0,s,m∈ℕ and positive initial values, and present some sufficient conditions for the parameters and maps ϕn:(ℝ+)m→ℝ+,n∈ℕ...

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Main Authors: Wanping Liu, Xiaofan Yang, Jianqiu Cao
Format: Article
Language:English
Published: Wiley 2010-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2010/364083
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author Wanping Liu
Xiaofan Yang
Jianqiu Cao
author_facet Wanping Liu
Xiaofan Yang
Jianqiu Cao
author_sort Wanping Liu
collection DOAJ
description We mainly investigate the global behavior to the family of higher-order nonautonomous recursive equations given by yn=(p+ryn-s)/(q+ϕn(yn-1,yn-2,…,yn-m)+yn-s), n∈ℕ0, with p≥0,r,q>0,s,m∈ℕ and positive initial values, and present some sufficient conditions for the parameters and maps ϕn:(ℝ+)m→ℝ+,n∈ℕ0, under which every positive solution to the equation converges to zero or a unique positive equilibrium. Our main result in the paper extends some related results from the work of Gibbons et al. (2000), Iričanin (2007), and Stević (vol. 33, no. 12, pages 1767–1774, 2002; vol. 6, no. 3, pages 405–414, 2002; vol. 9, no. 4, pages 583–593, 2005). Besides, several examples and open problems are presented in the end.
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spelling doaj-art-1f65fbab2610425abf6ecdb213b51ca22025-08-20T03:54:42ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2010-01-01201010.1155/2010/364083364083On Global Attractivity of a Class of Nonautonomous Difference EquationsWanping Liu0Xiaofan Yang1Jianqiu Cao2College of Computer Science, Chongqing University, Chongqing 400044, ChinaCollege of Computer Science, Chongqing University, Chongqing 400044, ChinaSchool of Computer and Information, Chongqing Jiaotong University, Chongqing 400074, ChinaWe mainly investigate the global behavior to the family of higher-order nonautonomous recursive equations given by yn=(p+ryn-s)/(q+ϕn(yn-1,yn-2,…,yn-m)+yn-s), n∈ℕ0, with p≥0,r,q>0,s,m∈ℕ and positive initial values, and present some sufficient conditions for the parameters and maps ϕn:(ℝ+)m→ℝ+,n∈ℕ0, under which every positive solution to the equation converges to zero or a unique positive equilibrium. Our main result in the paper extends some related results from the work of Gibbons et al. (2000), Iričanin (2007), and Stević (vol. 33, no. 12, pages 1767–1774, 2002; vol. 6, no. 3, pages 405–414, 2002; vol. 9, no. 4, pages 583–593, 2005). Besides, several examples and open problems are presented in the end.http://dx.doi.org/10.1155/2010/364083
spellingShingle Wanping Liu
Xiaofan Yang
Jianqiu Cao
On Global Attractivity of a Class of Nonautonomous Difference Equations
Discrete Dynamics in Nature and Society
title On Global Attractivity of a Class of Nonautonomous Difference Equations
title_full On Global Attractivity of a Class of Nonautonomous Difference Equations
title_fullStr On Global Attractivity of a Class of Nonautonomous Difference Equations
title_full_unstemmed On Global Attractivity of a Class of Nonautonomous Difference Equations
title_short On Global Attractivity of a Class of Nonautonomous Difference Equations
title_sort on global attractivity of a class of nonautonomous difference equations
url http://dx.doi.org/10.1155/2010/364083
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