Boundedness and Global Attractivity of a Higher-Order Nonlinear Difference Equation
We investigate the local stability, prime period-two solutions, boundedness, invariant intervals, and global attractivity of all positive solutions of the following difference equation: 𝑦𝑛+1=(𝑟+𝑝𝑦𝑛+𝑦𝑛−𝑘)/(𝑞𝑦𝑛+𝑦𝑛−𝑘), 𝑛∈ℕ0, where the parameters 𝑝,𝑞,𝑟∈(0,∞),𝑘∈{1,2,3,…} and the initial conditions 𝑦−𝑘,...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2010/610467 |
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| _version_ | 1832550329845022720 |
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| author | Xiu-Mei Jia Wan-Tong Li |
| author_facet | Xiu-Mei Jia Wan-Tong Li |
| author_sort | Xiu-Mei Jia |
| collection | DOAJ |
| description | We investigate the local stability, prime period-two
solutions, boundedness, invariant intervals, and global attractivity
of all positive solutions of the following difference equation: 𝑦𝑛+1=(𝑟+𝑝𝑦𝑛+𝑦𝑛−𝑘)/(𝑞𝑦𝑛+𝑦𝑛−𝑘), 𝑛∈ℕ0, where the parameters 𝑝,𝑞,𝑟∈(0,∞),𝑘∈{1,2,3,…} and the initial conditions 𝑦−𝑘,…,𝑦0∈(0,∞). We show that the unique positive equilibrium of this equation is a global
attractor under certain conditions. |
| format | Article |
| id | doaj-art-0f78d5d8560841fea171b006e9c3f3dc |
| 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-0f78d5d8560841fea171b006e9c3f3dc2025-02-03T06:06:58ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2010-01-01201010.1155/2010/610467610467Boundedness and Global Attractivity of a Higher-Order Nonlinear Difference EquationXiu-Mei Jia0Wan-Tong Li1Department of Mathematics, Hexi University, Zhangye, Gansu 734000, ChinaSchool of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, ChinaWe investigate the local stability, prime period-two solutions, boundedness, invariant intervals, and global attractivity of all positive solutions of the following difference equation: 𝑦𝑛+1=(𝑟+𝑝𝑦𝑛+𝑦𝑛−𝑘)/(𝑞𝑦𝑛+𝑦𝑛−𝑘), 𝑛∈ℕ0, where the parameters 𝑝,𝑞,𝑟∈(0,∞),𝑘∈{1,2,3,…} and the initial conditions 𝑦−𝑘,…,𝑦0∈(0,∞). We show that the unique positive equilibrium of this equation is a global attractor under certain conditions.http://dx.doi.org/10.1155/2010/610467 |
| spellingShingle | Xiu-Mei Jia Wan-Tong Li Boundedness and Global Attractivity of a Higher-Order Nonlinear Difference Equation Discrete Dynamics in Nature and Society |
| title | Boundedness and Global Attractivity of a Higher-Order Nonlinear Difference Equation |
| title_full | Boundedness and Global Attractivity of a Higher-Order Nonlinear Difference Equation |
| title_fullStr | Boundedness and Global Attractivity of a Higher-Order Nonlinear Difference Equation |
| title_full_unstemmed | Boundedness and Global Attractivity of a Higher-Order Nonlinear Difference Equation |
| title_short | Boundedness and Global Attractivity of a Higher-Order Nonlinear Difference Equation |
| title_sort | boundedness and global attractivity of a higher order nonlinear difference equation |
| url | http://dx.doi.org/10.1155/2010/610467 |
| work_keys_str_mv | AT xiumeijia boundednessandglobalattractivityofahigherordernonlineardifferenceequation AT wantongli boundednessandglobalattractivityofahigherordernonlineardifferenceequation |