(Special Issue) Global behavior of solutions of a two-dimensional system of difference equations

In this paper, we mainly investigate the qualitative and quantitative behavior of the solutions of a discrete system of difference equations xₙ₊₁=xₙ₋₁yₙ₋₁, yₙ₊₁=xₙ₋₁ axₙ₋₁+byₙ₋₁, n=0,1,…, where a, b and the initial values x₋₁,x₀,y₋₁,y₀ are non-zero real numbers. For a∈ R₊-\1\, we show any admissible solution \(xₙ,yₙ)\ₙ₌₋₁^∞ is either entirely located in a certain quadrant of the plane or there exists a natural number $N>0$ (we calculate its value) such that \(xₙ,yₙ)=N^∞ is located. Besides, some numerical simulations with graphs are given to emphasize the efficiency of our theoretical results in the article.