Tollu, Durhasan TurgutYalcinkaya, IbrahimAhmad, HijazYao, Shao-Wen2024-02-232024-02-2320211547-10631551-0018https://doi.org/10.3934/mbe.2021273https://hdl.handle.net/20.500.12452/16144In 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.eninfo:eu-repo/semantics/openAccessBehavior Of SolutionsCharacteristic EquationGeneral SolutionSystem Of Difference EquationsPeriodic SolutionArticle18553925408345174932-s2.0-85108283601Q2WOS:000688409900014Q310.3934/mbe.2021273