Global Asymptotic Stability of a Rational System
The main goal of this paper is to investigate the global asymptotic behavior of the difference equation xn+1=β1xn/A1+yn, yn+1=β2xn+γ2yn/xn+yn, n=0,1,2,… with β1,β2,γ2,A1∈(0,∞) and the initial value (x0,y0)∈[0,∞)×[0,∞) such that x0+y0≠0. The major conclusion shows that, in the case where γ2<β2, if...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/286375 |
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| _version_ | 1832547527420805120 |
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| author | Lin-Xia Hu Xiu-Mei Jia |
| author_facet | Lin-Xia Hu Xiu-Mei Jia |
| author_sort | Lin-Xia Hu |
| collection | DOAJ |
| description | The main goal of this paper is to investigate the global asymptotic behavior of the difference equation xn+1=β1xn/A1+yn, yn+1=β2xn+γ2yn/xn+yn, n=0,1,2,… with β1,β2,γ2,A1∈(0,∞) and the initial value (x0,y0)∈[0,∞)×[0,∞) such that x0+y0≠0. The major conclusion shows that, in the case where γ2<β2, if the unique positive equilibrium (x-,y-) exists, then it is globally asymptotically stable. |
| format | Article |
| id | doaj-art-b3f4f014e7e5408bbc0b079eccbb9b87 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-b3f4f014e7e5408bbc0b079eccbb9b872025-02-03T06:44:34ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/286375286375Global Asymptotic Stability of a Rational SystemLin-Xia Hu0Xiu-Mei Jia1Department of Mathematics, Tianshui Normal University, Tianshui, Gansu 741001, ChinaDepartment of Mathematics, Hexi University, Zhangye, Gansu 734000, ChinaThe main goal of this paper is to investigate the global asymptotic behavior of the difference equation xn+1=β1xn/A1+yn, yn+1=β2xn+γ2yn/xn+yn, n=0,1,2,… with β1,β2,γ2,A1∈(0,∞) and the initial value (x0,y0)∈[0,∞)×[0,∞) such that x0+y0≠0. The major conclusion shows that, in the case where γ2<β2, if the unique positive equilibrium (x-,y-) exists, then it is globally asymptotically stable.http://dx.doi.org/10.1155/2014/286375 |
| spellingShingle | Lin-Xia Hu Xiu-Mei Jia Global Asymptotic Stability of a Rational System Abstract and Applied Analysis |
| title | Global Asymptotic Stability of a Rational System |
| title_full | Global Asymptotic Stability of a Rational System |
| title_fullStr | Global Asymptotic Stability of a Rational System |
| title_full_unstemmed | Global Asymptotic Stability of a Rational System |
| title_short | Global Asymptotic Stability of a Rational System |
| title_sort | global asymptotic stability of a rational system |
| url | http://dx.doi.org/10.1155/2014/286375 |
| work_keys_str_mv | AT linxiahu globalasymptoticstabilityofarationalsystem AT xiumeijia globalasymptoticstabilityofarationalsystem |