On the system of rational difference equations <it>x</it><sub><it>n</it>+1</sub> = <it>f</it>(<it>y</it><sub><it>n</it>-<it>q</it></sub>, <it>x</it><sub><it>n</it>-<it>s</it></sub>), <it>y</it><sub><it>n</it>+1</sub> = <it>g</it>(<it>x</it><sub><it>n</it>-<it>t</it></sub>, <it>y</it><sub><it>n</it>-<it>p</it></sub>)
<p/> <p>We study the global behavior of positive solutions of the system of rational difference equations <it>x</it><sub><it>n</it>+1</sub> = <it>f</it>(<it>y</it><sub><it>n</it>-<it>q</it></sub&...
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2006-01-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://www.advancesindifferenceequations.com/content/2006/051520 |
| _version_ | 1828258008721784832 |
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| author | Xi Hongjian Sun Taixiang |
| author_facet | Xi Hongjian Sun Taixiang |
| author_sort | Xi Hongjian |
| collection | DOAJ |
| description | <p/> <p>We study the global behavior of positive solutions of the system of rational difference equations <it>x</it><sub><it>n</it>+1</sub> = <it>f</it>(<it>y</it><sub><it>n</it>-<it>q</it></sub>, <it>x</it><sub><it>n</it>-<it>s</it></sub>), <it>y</it><sub><it>n</it>+1</sub> = <it>g</it>(<it>x</it><sub><it>n</it>-<it>t</it></sub>, <it>y</it><sub><it>n</it>-<it>p</it></sub>), <it>n</it> = 0,1,2,..., where <it>p</it>, <it>q</it>, <it>s</it>, <it>t</it> ∈ {0,1,2,...} with <it>s</it> ≥ <it>t</it> and <it>p</it> ≥ <it>q</it>, the initial values <it>x</it><sub>-<it>s</it></sub>, <it>x</it><sub>-<it>s</it>+1</sub>,...,<it>x</it><sub>0</sub>, <it>y</it><sub>-<it>p</it></sub>, <it>y</it><sub>-<it>p</it>+1</sub>,...<it>y</it><sub>0</sub> ∈ (0,+∞). We give sufficient conditions under which every positive solution of this system converges to the unique positive equilibrium.</p> |
| first_indexed | 2024-04-13T02:48:49Z |
| format | Article |
| id | doaj.art-b0e339733e1948819dafe0764e5c6e26 |
| institution | Directory Open Access Journal |
| issn | 1687-1839 1687-1847 |
| language | English |
| last_indexed | 2024-04-13T02:48:49Z |
| publishDate | 2006-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-b0e339733e1948819dafe0764e5c6e262022-12-22T03:05:54ZengSpringerOpenAdvances in Difference Equations1687-18391687-18472006-01-0120061051520On the system of rational difference equations <it>x</it><sub><it>n</it>+1</sub> = <it>f</it>(<it>y</it><sub><it>n</it>-<it>q</it></sub>, <it>x</it><sub><it>n</it>-<it>s</it></sub>), <it>y</it><sub><it>n</it>+1</sub> = <it>g</it>(<it>x</it><sub><it>n</it>-<it>t</it></sub>, <it>y</it><sub><it>n</it>-<it>p</it></sub>)Xi HongjianSun Taixiang<p/> <p>We study the global behavior of positive solutions of the system of rational difference equations <it>x</it><sub><it>n</it>+1</sub> = <it>f</it>(<it>y</it><sub><it>n</it>-<it>q</it></sub>, <it>x</it><sub><it>n</it>-<it>s</it></sub>), <it>y</it><sub><it>n</it>+1</sub> = <it>g</it>(<it>x</it><sub><it>n</it>-<it>t</it></sub>, <it>y</it><sub><it>n</it>-<it>p</it></sub>), <it>n</it> = 0,1,2,..., where <it>p</it>, <it>q</it>, <it>s</it>, <it>t</it> ∈ {0,1,2,...} with <it>s</it> ≥ <it>t</it> and <it>p</it> ≥ <it>q</it>, the initial values <it>x</it><sub>-<it>s</it></sub>, <it>x</it><sub>-<it>s</it>+1</sub>,...,<it>x</it><sub>0</sub>, <it>y</it><sub>-<it>p</it></sub>, <it>y</it><sub>-<it>p</it>+1</sub>,...<it>y</it><sub>0</sub> ∈ (0,+∞). We give sufficient conditions under which every positive solution of this system converges to the unique positive equilibrium.</p>http://www.advancesindifferenceequations.com/content/2006/051520 |
| spellingShingle | Xi Hongjian Sun Taixiang On the system of rational difference equations <it>x</it><sub><it>n</it>+1</sub> = <it>f</it>(<it>y</it><sub><it>n</it>-<it>q</it></sub>, <it>x</it><sub><it>n</it>-<it>s</it></sub>), <it>y</it><sub><it>n</it>+1</sub> = <it>g</it>(<it>x</it><sub><it>n</it>-<it>t</it></sub>, <it>y</it><sub><it>n</it>-<it>p</it></sub>) Advances in Difference Equations |
| title | On the system of rational difference equations <it>x</it><sub><it>n</it>+1</sub> = <it>f</it>(<it>y</it><sub><it>n</it>-<it>q</it></sub>, <it>x</it><sub><it>n</it>-<it>s</it></sub>), <it>y</it><sub><it>n</it>+1</sub> = <it>g</it>(<it>x</it><sub><it>n</it>-<it>t</it></sub>, <it>y</it><sub><it>n</it>-<it>p</it></sub>) |
| title_full | On the system of rational difference equations <it>x</it><sub><it>n</it>+1</sub> = <it>f</it>(<it>y</it><sub><it>n</it>-<it>q</it></sub>, <it>x</it><sub><it>n</it>-<it>s</it></sub>), <it>y</it><sub><it>n</it>+1</sub> = <it>g</it>(<it>x</it><sub><it>n</it>-<it>t</it></sub>, <it>y</it><sub><it>n</it>-<it>p</it></sub>) |
| title_fullStr | On the system of rational difference equations <it>x</it><sub><it>n</it>+1</sub> = <it>f</it>(<it>y</it><sub><it>n</it>-<it>q</it></sub>, <it>x</it><sub><it>n</it>-<it>s</it></sub>), <it>y</it><sub><it>n</it>+1</sub> = <it>g</it>(<it>x</it><sub><it>n</it>-<it>t</it></sub>, <it>y</it><sub><it>n</it>-<it>p</it></sub>) |
| title_full_unstemmed | On the system of rational difference equations <it>x</it><sub><it>n</it>+1</sub> = <it>f</it>(<it>y</it><sub><it>n</it>-<it>q</it></sub>, <it>x</it><sub><it>n</it>-<it>s</it></sub>), <it>y</it><sub><it>n</it>+1</sub> = <it>g</it>(<it>x</it><sub><it>n</it>-<it>t</it></sub>, <it>y</it><sub><it>n</it>-<it>p</it></sub>) |
| title_short | On the system of rational difference equations <it>x</it><sub><it>n</it>+1</sub> = <it>f</it>(<it>y</it><sub><it>n</it>-<it>q</it></sub>, <it>x</it><sub><it>n</it>-<it>s</it></sub>), <it>y</it><sub><it>n</it>+1</sub> = <it>g</it>(<it>x</it><sub><it>n</it>-<it>t</it></sub>, <it>y</it><sub><it>n</it>-<it>p</it></sub>) |
| title_sort | on the system of rational difference equations it x it sub it n it 1 sub it f it it y it sub it n it it q it sub it x it sub it n it it s it sub it y it sub it n it 1 sub it g it it x it sub it n it it t it sub it y it sub it n it it p it sub |
| url | http://www.advancesindifferenceequations.com/content/2006/051520 |
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