On the Solutions of Three-Dimensional Rational Difference Equation Systems
In this paper, we are interested in a technique for solving some nonlinear rational systems of difference equations of third order, in three-dimensional case as a special case of the following system:xn+1=ynzn−1/yn±xn−2,yn+1=znxn−1/zn±yn−2, and zn+1=xnyn−1/xn±zn−2 with initial conditions x−2,x−1,x0,...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/2480294 |
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doaj-399ec1e665c84c06a104ba76b3c58ce92021-04-26T00:03:55ZengHindawi LimitedJournal of Mathematics2314-47852021-01-01202110.1155/2021/2480294On the Solutions of Three-Dimensional Rational Difference Equation SystemsH. S. Alayachi0A. Q. Khan1M. S. M. Noorani2School of Mathematical SciencesDepartment of MathematicsSchool of Mathematical SciencesIn this paper, we are interested in a technique for solving some nonlinear rational systems of difference equations of third order, in three-dimensional case as a special case of the following system:xn+1=ynzn−1/yn±xn−2,yn+1=znxn−1/zn±yn−2, and zn+1=xnyn−1/xn±zn−2 with initial conditions x−2,x−1,x0,y−2, y−1,y0,z−2,z−1, and z0 are nonzero real numbers. Moreover, we study some behavior of the systems such as the boundedness of solutions for such systems. Finally, we present some numerical examples by giving some numerical values for the initial values 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 MATLAB to confirm the obtained results.http://dx.doi.org/10.1155/2021/2480294 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
H. S. Alayachi A. Q. Khan M. S. M. Noorani |
| spellingShingle |
H. S. Alayachi A. Q. Khan M. S. M. Noorani On the Solutions of Three-Dimensional Rational Difference Equation Systems Journal of Mathematics |
| author_facet |
H. S. Alayachi A. Q. Khan M. S. M. Noorani |
| author_sort |
H. S. Alayachi |
| title |
On the Solutions of Three-Dimensional Rational Difference Equation Systems |
| title_short |
On the Solutions of Three-Dimensional Rational Difference Equation Systems |
| title_full |
On the Solutions of Three-Dimensional Rational Difference Equation Systems |
| title_fullStr |
On the Solutions of Three-Dimensional Rational Difference Equation Systems |
| title_full_unstemmed |
On the Solutions of Three-Dimensional Rational Difference Equation Systems |
| title_sort |
on the solutions of three-dimensional rational difference equation systems |
| publisher |
Hindawi Limited |
| series |
Journal of Mathematics |
| issn |
2314-4785 |
| publishDate |
2021-01-01 |
| description |
In this paper, we are interested in a technique for solving some nonlinear rational systems of difference equations of third order, in three-dimensional case as a special case of the following system:xn+1=ynzn−1/yn±xn−2,yn+1=znxn−1/zn±yn−2, and zn+1=xnyn−1/xn±zn−2 with initial conditions x−2,x−1,x0,y−2, y−1,y0,z−2,z−1, and z0 are nonzero real numbers. Moreover, we study some behavior of the systems such as the boundedness of solutions for such systems. Finally, we present some numerical examples by giving some numerical values for the initial values 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 MATLAB to confirm the obtained results. |
| url |
http://dx.doi.org/10.1155/2021/2480294 |
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AT hsalayachi onthesolutionsofthreedimensionalrationaldifferenceequationsystems AT aqkhan onthesolutionsofthreedimensionalrationaldifferenceequationsystems AT msmnoorani onthesolutionsofthreedimensionalrationaldifferenceequationsystems |
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1714657647757623296 |