Qualitative Study of Solutions of Some Difference Equations
We obtain in this paper the solutions of the following recursive sequences 𝑥𝑛+1=𝑥𝑛𝑥𝑛−3/𝑥𝑛−2(±1±𝑥𝑛𝑥𝑛−3), 𝑛=0,1,…, where the initial conditions are arbitrary real numbers and we study the behaviors of the solutions and we obtained the equilibrium points of the considered equations. Some qualitative be...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/248291 |
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| author | Hamdy El-Metwally E. M. Elsayed |
| author_facet | Hamdy El-Metwally E. M. Elsayed |
| author_sort | Hamdy El-Metwally |
| collection | DOAJ |
| description | We obtain in this paper the solutions of the following recursive sequences 𝑥𝑛+1=𝑥𝑛𝑥𝑛−3/𝑥𝑛−2(±1±𝑥𝑛𝑥𝑛−3), 𝑛=0,1,…, where the initial conditions are arbitrary real numbers and we study the
behaviors of the solutions and we obtained the equilibrium points of the
considered equations. Some qualitative behavior of the solutions such as the
boundedness, the global stability, and the periodicity character of the solutions
in each case have been studied.
We presented some numerical examples by giving some numerical values
for the initial values and the coefficients of each case. Some figures have been
given to explain the behavior of the obtained solutions in the case of numerical examples by using the mathematical program Mathematica to confirm the
obtained results. |
| format | Article |
| id | doaj-art-388582dd89794667a166e5e94e73cc2d |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-388582dd89794667a166e5e94e73cc2d2025-08-20T03:55:11ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/248291248291Qualitative Study of Solutions of Some Difference EquationsHamdy El-Metwally0E. M. Elsayed1Department of Mathematics, Rabigh College of Science and Art, King Abdulaziz University, P.O. Box 344, Rabigh 21911, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EgyptWe obtain in this paper the solutions of the following recursive sequences 𝑥𝑛+1=𝑥𝑛𝑥𝑛−3/𝑥𝑛−2(±1±𝑥𝑛𝑥𝑛−3), 𝑛=0,1,…, where the initial conditions are arbitrary real numbers and we study the behaviors of the solutions and we obtained the equilibrium points of the considered equations. Some qualitative behavior of the solutions such as the boundedness, the global stability, and the periodicity character of the solutions in each case have been studied. We presented some numerical examples by giving some numerical values for the initial values and the coefficients of each case. Some figures have been given to explain the behavior of the obtained solutions in the case of numerical examples by using the mathematical program Mathematica to confirm the obtained results.http://dx.doi.org/10.1155/2012/248291 |
| spellingShingle | Hamdy El-Metwally E. M. Elsayed Qualitative Study of Solutions of Some Difference Equations Abstract and Applied Analysis |
| title | Qualitative Study of Solutions of Some Difference Equations |
| title_full | Qualitative Study of Solutions of Some Difference Equations |
| title_fullStr | Qualitative Study of Solutions of Some Difference Equations |
| title_full_unstemmed | Qualitative Study of Solutions of Some Difference Equations |
| title_short | Qualitative Study of Solutions of Some Difference Equations |
| title_sort | qualitative study of solutions of some difference equations |
| url | http://dx.doi.org/10.1155/2012/248291 |
| work_keys_str_mv | AT hamdyelmetwally qualitativestudyofsolutionsofsomedifferenceequations AT emelsayed qualitativestudyofsolutionsofsomedifferenceequations |