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    Öğe
    Global behavior of two-dimensional difference equations system with two period coefficients
    (Tbilisi Center for Mathematical Sciences, 2020) Kara, Merve; Tollu, Durhasan Turgut; Yazlık, Yasin
    In this paper, we investigate the following system of difference equations x(n+1) = alpha(n)/1 + y(n)x(n-1), y(n+1) = beta(n)/1 + x(n)y(n-1), n is an element of N-0, where the sequences (alpha(n))(n is an element of N0), (beta(n))(n is an element of N0) are positive, real and periodic with period two and the initial values x(-1), x(0), y(-1), y(0) are non-negative real numbers. We show that every positive solution of the system is bounded and examine their global behaviors. In addition, we give closed forms of the general solutions of the system by using the change of variables. Finally, we present a numerical example to support our results.
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    Öğe
    Solvability of a system of higher order nonlinear difference equations
    (Hacettepe University, 2020) Kara, Merve; Yazlık, Yasin; Tollu, Durhasan Turgut
    In this paper we show that the system of difference equations xn = ayn-k + dyn-kxn-(k+l)/bxn-(k+l) + cyn-l, yn = ?xn-k + ?xn-kyn-(k+l)/?yn-(k+l) + ?xn-l, where n ? ?0, k and l are positive integers, the parameters a, b, c, d, ?, ?, ?, ? are real numbers and the initial values x-j, y-j, j = 1, k + l, are real numbers, can be solved in the closed form. We also determine the asymptotic behavior of solutions for the case l = 1 and describe the forbidden set of the initial values using the obtained formulas. Our obtained results significantly extend and develop some recent results in the literature.