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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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| 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. |
| format | Article |
| id | doaj-art-1f65fbab2610425abf6ecdb213b51ca2 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| 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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