Global Asymptotic Stability of a Family of Nonlinear Difference Equations
In this note, we consider global asymptotic stability of the following nonlinear difference equation xn=(∏i=1v(xn-kiβi+1)+∏i=1v(xn-kiβi-1))/(∏i=1v(xn-kiβi+1)-∏i=1v(xn-kiβi-1)), n=0,1,…, where ki∈ℕ (i=1,2,…,v), v≥2, β1∈[-1,1], β2,β3,…,βv∈(-∞,+∞), x-m,x-m+1,…,x-1∈(0,∞), and m=max1≤i≤v{ki}. Our resu...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2013/750852 |
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| author | Maoxin Liao |
| author_facet | Maoxin Liao |
| author_sort | Maoxin Liao |
| collection | DOAJ |
| description | In this note, we consider global asymptotic stability of the following nonlinear difference equation xn=(∏i=1v(xn-kiβi+1)+∏i=1v(xn-kiβi-1))/(∏i=1v(xn-kiβi+1)-∏i=1v(xn-kiβi-1)), n=0,1,…, where ki∈ℕ (i=1,2,…,v), v≥2, β1∈[-1,1], β2,β3,…,βv∈(-∞,+∞), x-m,x-m+1,…,x-1∈(0,∞), and m=max1≤i≤v{ki}. Our result generalizes the corresponding results in the recent literature and simultaneously conforms to a conjecture in the work by Berenhaut et al. (2007). |
| format | Article |
| id | doaj-art-4baccc8925554e55b7cc75d73119a97b |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-4baccc8925554e55b7cc75d73119a97b2025-02-03T05:58:48ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2013-01-01201310.1155/2013/750852750852Global Asymptotic Stability of a Family of Nonlinear Difference EquationsMaoxin Liao0School of Mathematics and Physics, University of South China, Hengyang, Hunan 421001, ChinaIn this note, we consider global asymptotic stability of the following nonlinear difference equation xn=(∏i=1v(xn-kiβi+1)+∏i=1v(xn-kiβi-1))/(∏i=1v(xn-kiβi+1)-∏i=1v(xn-kiβi-1)), n=0,1,…, where ki∈ℕ (i=1,2,…,v), v≥2, β1∈[-1,1], β2,β3,…,βv∈(-∞,+∞), x-m,x-m+1,…,x-1∈(0,∞), and m=max1≤i≤v{ki}. Our result generalizes the corresponding results in the recent literature and simultaneously conforms to a conjecture in the work by Berenhaut et al. (2007).http://dx.doi.org/10.1155/2013/750852 |
| spellingShingle | Maoxin Liao Global Asymptotic Stability of a Family of Nonlinear Difference Equations Discrete Dynamics in Nature and Society |
| title | Global Asymptotic Stability of a Family of Nonlinear Difference Equations |
| title_full | Global Asymptotic Stability of a Family of Nonlinear Difference Equations |
| title_fullStr | Global Asymptotic Stability of a Family of Nonlinear Difference Equations |
| title_full_unstemmed | Global Asymptotic Stability of a Family of Nonlinear Difference Equations |
| title_short | Global Asymptotic Stability of a Family of Nonlinear Difference Equations |
| title_sort | global asymptotic stability of a family of nonlinear difference equations |
| url | http://dx.doi.org/10.1155/2013/750852 |
| work_keys_str_mv | AT maoxinliao globalasymptoticstabilityofafamilyofnonlineardifferenceequations |