Electron. J. Differential Equations, Vol. 2017 (2017), No. 153, pp. 1-21.

Two-dimensional product-type systems of difference equations of delay-type (2,2,1,2)

Stevo Stevic

Abstract:
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.

Submitted April 21, 2017. Published June 27, 2017.
Math Subject Classifications: 39A20, 39A45.
Key Words: System of difference equations; product-type system; solvable in closed form.

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Stevo Stevic
Mathematical Institute of the Serbian Academy of Sciences
Knez Mihailova 36/III
11000 Beograd, Serbia
email: sstevic@ptt.rs

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