On the Dynamics of a Higher-Order Difference Equation
This paper deals with the investigation of the following more general rational difference equation: 𝑦𝑛+1=𝛼𝑦𝑛∑/(𝛽+𝛾𝑘𝑖=0𝑦𝑝𝑛−(2𝑖+1)∏𝑘𝑖=0𝑦𝑛−(2𝑖+1)), 𝑛=0,1,2,…, where 𝛼,𝛽,𝛾,𝑝∈(0,∞) with the initial conditions 𝑥0,𝑥−1,…,𝑥−2𝑘,𝑥−2𝑘−1∈(0,∞). We investigate the existence of the equilibrium points of the consid...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/263053 |
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| author | H. El-Metwally |
| author_facet | H. El-Metwally |
| author_sort | H. El-Metwally |
| collection | DOAJ |
| description | This paper deals with the investigation of the following more general rational difference equation: 𝑦𝑛+1=𝛼𝑦𝑛∑/(𝛽+𝛾𝑘𝑖=0𝑦𝑝𝑛−(2𝑖+1)∏𝑘𝑖=0𝑦𝑛−(2𝑖+1)), 𝑛=0,1,2,…, where 𝛼,𝛽,𝛾,𝑝∈(0,∞) with the initial conditions 𝑥0,𝑥−1,…,𝑥−2𝑘,𝑥−2𝑘−1∈(0,∞). We investigate the existence of the equilibrium points of the considered equation and then study their local and global stability. Also, some results related to the oscillation and the permanence of the considered equation have been presented. |
| format | Article |
| id | doaj-art-bc483809ed284525a433df7268770fe3 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-bc483809ed284525a433df7268770fe32025-02-03T06:42:25ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/263053263053On the Dynamics of a Higher-Order Difference EquationH. El-Metwally0Department of Mathematics, Rabigh College of Science and Art, King Abdulaziz University, P.O. Box 344, Rabigh 21911, Saudi ArabiaThis paper deals with the investigation of the following more general rational difference equation: 𝑦𝑛+1=𝛼𝑦𝑛∑/(𝛽+𝛾𝑘𝑖=0𝑦𝑝𝑛−(2𝑖+1)∏𝑘𝑖=0𝑦𝑛−(2𝑖+1)), 𝑛=0,1,2,…, where 𝛼,𝛽,𝛾,𝑝∈(0,∞) with the initial conditions 𝑥0,𝑥−1,…,𝑥−2𝑘,𝑥−2𝑘−1∈(0,∞). We investigate the existence of the equilibrium points of the considered equation and then study their local and global stability. Also, some results related to the oscillation and the permanence of the considered equation have been presented.http://dx.doi.org/10.1155/2012/263053 |
| spellingShingle | H. El-Metwally On the Dynamics of a Higher-Order Difference Equation Discrete Dynamics in Nature and Society |
| title | On the Dynamics of a Higher-Order Difference Equation |
| title_full | On the Dynamics of a Higher-Order Difference Equation |
| title_fullStr | On the Dynamics of a Higher-Order Difference Equation |
| title_full_unstemmed | On the Dynamics of a Higher-Order Difference Equation |
| title_short | On the Dynamics of a Higher-Order Difference Equation |
| title_sort | on the dynamics of a higher order difference equation |
| url | http://dx.doi.org/10.1155/2012/263053 |
| work_keys_str_mv | AT helmetwally onthedynamicsofahigherorderdifferenceequation |