On a Third-Order System of Difference Equations with Variable Coefficients
We show that the system of three difference equations xn+1=an(1)xn-2/(bn(1)ynzn-1xn-2+cn(1)), yn+1=an(2)yn-2/(bn(2)znxn-1yn-2+cn(2)), and zn+1=an(3)zn-2/(bn(3)xnyn-1zn-2+cn(3)), n∈N0, where all elements of the sequences an(i), bn(i), cn(i), n∈N0, i∈{1,2,3}, and initial values x-j, y-j, z-j, j∈{0,1,2...
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| Main Authors: | , , , |
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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/10.1155/2012/508523 |
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| _version_ | 1832548129411432448 |
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| author | Stevo Stević Josef Diblík Bratislav Iricanin Zdenek Šmarda |
| author_facet | Stevo Stević Josef Diblík Bratislav Iricanin Zdenek Šmarda |
| author_sort | Stevo Stević |
| collection | DOAJ |
| description | We show that the system of three difference equations xn+1=an(1)xn-2/(bn(1)ynzn-1xn-2+cn(1)), yn+1=an(2)yn-2/(bn(2)znxn-1yn-2+cn(2)), and zn+1=an(3)zn-2/(bn(3)xnyn-1zn-2+cn(3)), n∈N0, where all elements of the sequences an(i), bn(i), cn(i), n∈N0, i∈{1,2,3}, and initial values x-j, y-j, z-j, j∈{0,1,2}, are real numbers, can be solved. Explicit formulae for solutions of the system are derived, and some consequences on asymptotic behavior of solutions for the case when coefficients are periodic with period three are deduced. |
| format | Article |
| id | doaj-art-817529fae65f41f58b3a33dee6d01196 |
| 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-817529fae65f41f58b3a33dee6d011962025-02-03T06:42:06ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/508523508523On a Third-Order System of Difference Equations with Variable CoefficientsStevo Stević0Josef Diblík1Bratislav Iricanin2Zdenek Šmarda3Mathematical Institute of the Serbian Academy of Sciences, Knez Mihailova 36/III, 11000 Beograd, SerbiaDepartment of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Brno University of Technology, 60200 Brno, Czech RepublicFaculty of Electrical Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, 11000 Beograd, SerbiaDepartment of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, 61600 Brno, Czech RepublicWe show that the system of three difference equations xn+1=an(1)xn-2/(bn(1)ynzn-1xn-2+cn(1)), yn+1=an(2)yn-2/(bn(2)znxn-1yn-2+cn(2)), and zn+1=an(3)zn-2/(bn(3)xnyn-1zn-2+cn(3)), n∈N0, where all elements of the sequences an(i), bn(i), cn(i), n∈N0, i∈{1,2,3}, and initial values x-j, y-j, z-j, j∈{0,1,2}, are real numbers, can be solved. Explicit formulae for solutions of the system are derived, and some consequences on asymptotic behavior of solutions for the case when coefficients are periodic with period three are deduced.http://dx.doi.org/10.1155/2012/508523 |
| spellingShingle | Stevo Stević Josef Diblík Bratislav Iricanin Zdenek Šmarda On a Third-Order System of Difference Equations with Variable Coefficients Abstract and Applied Analysis |
| title | On a Third-Order System of Difference Equations with Variable Coefficients |
| title_full | On a Third-Order System of Difference Equations with Variable Coefficients |
| title_fullStr | On a Third-Order System of Difference Equations with Variable Coefficients |
| title_full_unstemmed | On a Third-Order System of Difference Equations with Variable Coefficients |
| title_short | On a Third-Order System of Difference Equations with Variable Coefficients |
| title_sort | on a third order system of difference equations with variable coefficients |
| url | http://dx.doi.org/10.1155/2012/508523 |
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