Two-dimensional product-type systems of difference equations of delay-type (2,2,1,2)
We prove that the following class of systems of difference equations is solvable in closed form: $$ z_{n+1}=\alpha z_{n-1}^aw_n^b,\quad w_{n+1}=\beta w_{n-1}^cz_{n-1}^d,\quad n\in\mathbb{N}_0, $$ where $a, b, c, d\in\mathbb{Z}$, $\alpha, \beta, z_{-1}, z_0, w_{-1}, w_0\in\mathbb{C}\setminus\...
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2017-06-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2017/153/abstr.html |
| _version_ | 1811331628191973376 |
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| author | Stevo Stevic |
| author_facet | Stevo Stevic |
| author_sort | Stevo Stevic |
| collection | DOAJ |
| description | We prove that the following class of systems of difference equations
is solvable in closed form:
$$
z_{n+1}=\alpha z_{n-1}^aw_n^b,\quad
w_{n+1}=\beta w_{n-1}^cz_{n-1}^d,\quad n\in\mathbb{N}_0,
$$
where
$a, b, c, d\in\mathbb{Z}$, $\alpha, \beta, z_{-1}, z_0, w_{-1},
w_0\in\mathbb{C}\setminus\{0\}$.
We present formulas for its solutions in all the cases. The most complex
formulas are presented in terms of the zeros of three different associated
polynomials to the systems corresponding to the cases a=0, c=0 and
$abcd\ne 0$, respectively, which on the other hand depend on some of
parameters a, b, c, d. |
| first_indexed | 2024-04-13T16:23:32Z |
| format | Article |
| id | doaj.art-031d5f92d218414baf8e733ff8da5973 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-13T16:23:32Z |
| publishDate | 2017-06-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-031d5f92d218414baf8e733ff8da59732022-12-22T02:39:48ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912017-06-012017153,121Two-dimensional product-type systems of difference equations of delay-type (2,2,1,2)Stevo Stevic0 Serbian Academy of Sciences, Beograd, Serbia We prove that the following class of systems of difference equations is solvable in closed form: $$ z_{n+1}=\alpha z_{n-1}^aw_n^b,\quad w_{n+1}=\beta w_{n-1}^cz_{n-1}^d,\quad n\in\mathbb{N}_0, $$ where $a, b, c, d\in\mathbb{Z}$, $\alpha, \beta, z_{-1}, z_0, w_{-1}, w_0\in\mathbb{C}\setminus\{0\}$. We present formulas for its solutions in all the cases. The most complex formulas are presented in terms of the zeros of three different associated polynomials to the systems corresponding to the cases a=0, c=0 and $abcd\ne 0$, respectively, which on the other hand depend on some of parameters a, b, c, d.http://ejde.math.txstate.edu/Volumes/2017/153/abstr.htmlSystem of difference equationsproduct-type systemsolvable in closed form |
| spellingShingle | Stevo Stevic Two-dimensional product-type systems of difference equations of delay-type (2,2,1,2) Electronic Journal of Differential Equations System of difference equations product-type system solvable in closed form |
| title | Two-dimensional product-type systems of difference equations of delay-type (2,2,1,2) |
| title_full | Two-dimensional product-type systems of difference equations of delay-type (2,2,1,2) |
| title_fullStr | Two-dimensional product-type systems of difference equations of delay-type (2,2,1,2) |
| title_full_unstemmed | Two-dimensional product-type systems of difference equations of delay-type (2,2,1,2) |
| title_short | Two-dimensional product-type systems of difference equations of delay-type (2,2,1,2) |
| title_sort | two dimensional product type systems of difference equations of delay type 2 2 1 2 |
| topic | System of difference equations product-type system solvable in closed form |
| url | http://ejde.math.txstate.edu/Volumes/2017/153/abstr.html |
| work_keys_str_mv | AT stevostevic twodimensionalproducttypesystemsofdifferenceequationsofdelaytype2212 |