Qualitative behavior of a rational difference equation <inline-formula><graphic file="1687-1847-2011-6-i1.gif"/></inline-formula>
<p>Abstract</p> <p>This article is concerned with the following rational difference equation <it>y</it><sub><it>n</it>+1 </sub>= (<it>y</it><sub><it>n </it></sub>+ <it>y</it><sub><it>n&l...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2011-01-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://www.advancesindifferenceequations.com/content/2011/1/6 |
| _version_ | 1818752950770597888 |
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| author | Qian Xiao Qi-hong Shi |
| author_facet | Qian Xiao Qi-hong Shi |
| author_sort | Qian Xiao |
| collection | DOAJ |
| description | <p>Abstract</p> <p>This article is concerned with the following rational difference equation <it>y</it><sub><it>n</it>+1 </sub>= (<it>y</it><sub><it>n </it></sub>+ <it>y</it><sub><it>n</it>-1</sub>)/(<it>p </it>+ <it>y</it><sub><it>n</it></sub><it>y</it><sub><it>n</it>-1</sub>) with the initial conditions; <it>y</it><sub>-1</sub>, <it>y</it><sub>0 </sub>are arbitrary positive real numbers, and <it>p </it>is positive constant. Locally asymptotical stability and global attractivity of the equilibrium point of the equation are investigated, and non-negative solution with prime period two cannot be found. Moreover, simulation is shown to support the results.</p> |
| first_indexed | 2024-12-18T04:59:37Z |
| format | Article |
| id | doaj.art-3579e3d6ddca41b785def49b9442d8ce |
| institution | Directory Open Access Journal |
| issn | 1687-1839 1687-1847 |
| language | English |
| last_indexed | 2024-12-18T04:59:37Z |
| publishDate | 2011-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-3579e3d6ddca41b785def49b9442d8ce2022-12-21T21:20:10ZengSpringerOpenAdvances in Difference Equations1687-18391687-18472011-01-01201116Qualitative behavior of a rational difference equation <inline-formula><graphic file="1687-1847-2011-6-i1.gif"/></inline-formula>Qian XiaoQi-hong Shi<p>Abstract</p> <p>This article is concerned with the following rational difference equation <it>y</it><sub><it>n</it>+1 </sub>= (<it>y</it><sub><it>n </it></sub>+ <it>y</it><sub><it>n</it>-1</sub>)/(<it>p </it>+ <it>y</it><sub><it>n</it></sub><it>y</it><sub><it>n</it>-1</sub>) with the initial conditions; <it>y</it><sub>-1</sub>, <it>y</it><sub>0 </sub>are arbitrary positive real numbers, and <it>p </it>is positive constant. Locally asymptotical stability and global attractivity of the equilibrium point of the equation are investigated, and non-negative solution with prime period two cannot be found. Moreover, simulation is shown to support the results.</p>http://www.advancesindifferenceequations.com/content/2011/1/6Global stabilityattractivitysolution with prime period twonumerical simulation |
| spellingShingle | Qian Xiao Qi-hong Shi Qualitative behavior of a rational difference equation <inline-formula><graphic file="1687-1847-2011-6-i1.gif"/></inline-formula> Advances in Difference Equations Global stability attractivity solution with prime period two numerical simulation |
| title | Qualitative behavior of a rational difference equation <inline-formula><graphic file="1687-1847-2011-6-i1.gif"/></inline-formula> |
| title_full | Qualitative behavior of a rational difference equation <inline-formula><graphic file="1687-1847-2011-6-i1.gif"/></inline-formula> |
| title_fullStr | Qualitative behavior of a rational difference equation <inline-formula><graphic file="1687-1847-2011-6-i1.gif"/></inline-formula> |
| title_full_unstemmed | Qualitative behavior of a rational difference equation <inline-formula><graphic file="1687-1847-2011-6-i1.gif"/></inline-formula> |
| title_short | Qualitative behavior of a rational difference equation <inline-formula><graphic file="1687-1847-2011-6-i1.gif"/></inline-formula> |
| title_sort | qualitative behavior of a rational difference equation inline formula graphic file 1687 1847 2011 6 i1 gif inline formula |
| topic | Global stability attractivity solution with prime period two numerical simulation |
| url | http://www.advancesindifferenceequations.com/content/2011/1/6 |
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