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A detailed study on a solvable system related to the linear fractional difference equation
(Amer Inst Mathematical Sciences-Aims, 2021) Tollu, Durhasan Turgut; Yalcinkaya, Ibrahim; Ahmad, Hijaz; Yao, Shao-Wen
In this paper, we present a detailed study of the following system of difference equations x(n+1) = a/1+y(n)x(n-1), y(n+1) = b/1+x(n)y(n-1), n is an element of N-0, where the parameters a, b, and the initial values x(-1), x(0), y(-1), Y-0 are arbitrary real numbers such that x(n) and y(n) are defined. We mainly show by using a practical method that the general solution of the above system can be represented by characteristic zeros of the associated third-order linear equation. Also, we characterized the well-defined solutions of the system. Finally, we study long-term behavior of the well-defined solutions by using the obtained representation forms.