Authors: Stević, Stevo 
Tollu, Durhasan Turgut
Affiliations: Mathematics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: On a two-dimensional nonlinear system of difference equations close to the bilinear system
Journal: AIMS Mathematics
Volume: 8
Issue: 9
First page: 20561
Last page: 20575
Issue Date: 2023
Rank: ~M21a
ISSN: 2473-6988
DOI: 10.3934/math.20231048
Abstract: 
We consider the two-dimensional nonlinear system of difference equations xn = xn−k ayn−l + byn−(k+l) cyn−l + dyn−(k+l), yn = yn−k αxn−l + βxn−(k+l) γxn−l + δxn−(k+l), for n ∈ N0, where the delays k and l are two natural numbers, and the initial values x−j, y−j, 1 ≤ j ≤ k+l, and the parameters a, b, c, d, α, β, γ, δ are real numbers. We show that the system of difference equations is solvable by presenting a method for finding its general solution in detail. Bearing in mind that the system of equations is a natural generalization of the corresponding one-dimensional difference equation, whose special cases appear in the literature from time to time, our main result presented here also generalizes many results therein.
Keywords: closed-form formula | nonlinear system of difference equations | solvable system
Publisher: AIMS Press

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