On the Global Asymptotic Stability of a Second-Order System of Difference Equations
A sufficient condition is obtained for the global asymptotic stability of the following system of difference equations 𝑧𝑛+1=(𝑡𝑛𝑧𝑛−1+𝑎)/(𝑡𝑛+𝑧𝑛−1),𝑡𝑛+1=(𝑧𝑛𝑡𝑛−1+𝑎)/(𝑧𝑛+𝑡𝑛−1),𝑛=0,1,2,…, where the parameter 𝑎𝜖(0,∞) and the initial values (𝑧𝑘,𝑡𝑘)𝜖(0,∞) (for 𝑘=−1,0)....
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2008/860152 |
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| _version_ | 1832552788151762944 |
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| author | Ibrahim Yalcinkaya |
| author_facet | Ibrahim Yalcinkaya |
| author_sort | Ibrahim Yalcinkaya |
| collection | DOAJ |
| description | A sufficient condition is obtained for the global asymptotic
stability of the following system of difference equations 𝑧𝑛+1=(𝑡𝑛𝑧𝑛−1+𝑎)/(𝑡𝑛+𝑧𝑛−1),𝑡𝑛+1=(𝑧𝑛𝑡𝑛−1+𝑎)/(𝑧𝑛+𝑡𝑛−1),𝑛=0,1,2,…, where the parameter 𝑎𝜖(0,∞) and the initial values (𝑧𝑘,𝑡𝑘)𝜖(0,∞) (for 𝑘=−1,0). |
| format | Article |
| id | doaj-art-8aa919fe20e44ac09da5e284b800abfb |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-8aa919fe20e44ac09da5e284b800abfb2025-02-03T05:57:43ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2008-01-01200810.1155/2008/860152860152On the Global Asymptotic Stability of a Second-Order System of Difference EquationsIbrahim Yalcinkaya0Department of Mathematics, Faculty of Education, University of Selcuk, 42099 Meram Yeni Yol, Konya, TurkeyA sufficient condition is obtained for the global asymptotic stability of the following system of difference equations 𝑧𝑛+1=(𝑡𝑛𝑧𝑛−1+𝑎)/(𝑡𝑛+𝑧𝑛−1),𝑡𝑛+1=(𝑧𝑛𝑡𝑛−1+𝑎)/(𝑧𝑛+𝑡𝑛−1),𝑛=0,1,2,…, where the parameter 𝑎𝜖(0,∞) and the initial values (𝑧𝑘,𝑡𝑘)𝜖(0,∞) (for 𝑘=−1,0).http://dx.doi.org/10.1155/2008/860152 |
| spellingShingle | Ibrahim Yalcinkaya On the Global Asymptotic Stability of a Second-Order System of Difference Equations Discrete Dynamics in Nature and Society |
| title | On the Global Asymptotic Stability of a Second-Order System of Difference Equations |
| title_full | On the Global Asymptotic Stability of a Second-Order System of Difference Equations |
| title_fullStr | On the Global Asymptotic Stability of a Second-Order System of Difference Equations |
| title_full_unstemmed | On the Global Asymptotic Stability of a Second-Order System of Difference Equations |
| title_short | On the Global Asymptotic Stability of a Second-Order System of Difference Equations |
| title_sort | on the global asymptotic stability of a second order system of difference equations |
| url | http://dx.doi.org/10.1155/2008/860152 |
| work_keys_str_mv | AT ibrahimyalcinkaya ontheglobalasymptoticstabilityofasecondordersystemofdifferenceequations |