Global Asymptotic Stability in a Class of Difference Equations
We study the difference equation xn=[(f×g1+g2+h)/(g1+f×g2+h)](xn−1,…,xn−r), n=1,2,…, x1−r,…,x0>0, where f,g1,g2:(R+)r→R+ and h:(R+)r→[0,+∞) are all continuous functions, and min1≤i≤r{ui,1/ui}≤f(u1,…,ur)≤max1≤iâ‰Â...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2008-01-01
|
| Series: | Advances in Difference Equations |
| Online Access: | http://dx.doi.org/10.1155/2007/16249 |
| _version_ | 1819163686536740864 |
|---|---|
| author | Jianqiu Cao Yuan Yan Tang Limin Cui Xiaofan Yang |
| author_facet | Jianqiu Cao Yuan Yan Tang Limin Cui Xiaofan Yang |
| author_sort | Jianqiu Cao |
| collection | DOAJ |
| description | We study the difference equation xn=[(f×g1+g2+h)/(g1+f×g2+h)](xn−1,…,xn−r), n=1,2,…, x1−r,…,x0>0, where f,g1,g2:(R+)r→R+ and h:(R+)r→[0,+∞) are all continuous functions, and min1≤i≤r{ui,1/ui}≤f(u1,…,ur)≤max1≤i≤r{ui,1/ui},(u1,…,ur)T∈(R+)r. We prove that this difference equation admits c=1 as the globally asymptotically stable equilibrium. This result extends and generalizes some previously known results. |
| first_indexed | 2024-12-22T17:48:05Z |
| format | Article |
| id | doaj.art-541d0248a7004c8bac1ade32c2b85d40 |
| institution | Directory Open Access Journal |
| issn | 1687-1839 1687-1847 |
| language | English |
| last_indexed | 2024-12-22T17:48:05Z |
| publishDate | 2008-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-541d0248a7004c8bac1ade32c2b85d402022-12-21T18:18:15ZengSpringerOpenAdvances in Difference Equations1687-18391687-18472008-01-01200710.1155/2007/16249Global Asymptotic Stability in a Class of Difference EquationsJianqiu CaoYuan Yan TangLimin CuiXiaofan YangWe study the difference equation xn=[(f×g1+g2+h)/(g1+f×g2+h)](xn−1,…,xn−r), n=1,2,…, x1−r,…,x0>0, where f,g1,g2:(R+)r→R+ and h:(R+)r→[0,+∞) are all continuous functions, and min1≤i≤r{ui,1/ui}≤f(u1,…,ur)≤max1≤i≤r{ui,1/ui},(u1,…,ur)T∈(R+)r. We prove that this difference equation admits c=1 as the globally asymptotically stable equilibrium. This result extends and generalizes some previously known results.http://dx.doi.org/10.1155/2007/16249 |
| spellingShingle | Jianqiu Cao Yuan Yan Tang Limin Cui Xiaofan Yang Global Asymptotic Stability in a Class of Difference Equations Advances in Difference Equations |
| title | Global Asymptotic Stability in a Class of Difference Equations |
| title_full | Global Asymptotic Stability in a Class of Difference Equations |
| title_fullStr | Global Asymptotic Stability in a Class of Difference Equations |
| title_full_unstemmed | Global Asymptotic Stability in a Class of Difference Equations |
| title_short | Global Asymptotic Stability in a Class of Difference Equations |
| title_sort | global asymptotic stability in a class of difference equations |
| url | http://dx.doi.org/10.1155/2007/16249 |
| work_keys_str_mv | AT jianqiucao globalasymptoticstabilityinaclassofdifferenceequations AT yuanyantang globalasymptoticstabilityinaclassofdifferenceequations AT limincui globalasymptoticstabilityinaclassofdifferenceequations AT xiaofanyang globalasymptoticstabilityinaclassofdifferenceequations |