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    ON A GENERAL HOMOGENEOUS THREE-DIMENSIONAL SYSTEM OF DIFFERENCE EQUATIONS
    (Amer Inst Mathematical Sciences-Aims, 2021) Touafek, Nouressadat; Tollu, Durhasan Turgut; Akrour, Youssouf
    In this work, we study the behavior of the solutions of following three-dimensional system of difference equations x(n+1) = f(y(n), y(n-1)), y(n+1) = g (z(n), z(n-1)), z(n+1) = h(x(n), x(n-1)) where n is an element of N-0, the initial values x(-1), x(0), y(-1), y(0) z(-1), z(0) are positive real numbers, the functions f, g, h : (0, +infinity)(2) -> (0, +infinity) are continuous and homogeneous of degree zero. By proving some general convergence theorems, we have established conditions for the global stability of the corresponding unique equilibrium point. We give necessary and sufficient conditions on existence of prime period two solutions of the above mentioned system. Also, we prove a result on oscillatory solutions. As applications of the obtained results, some particular systems of difference equations defined by homogeneous functions of degree zero are investigated. Our results generalize some existing ones in the literature.
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    On a System of Difference Equations Defined by the Product of Separable Homogeneous Functions
    (Walter De Gruyter Gmbh, 2023) Boulouh, Mounira; Touafek, Nouressadat; Tollu, Durhasan Turgut
    In this work, we present results on the stability, the existence of periodic and oscillatory solutions of a general second order system of difference equations defined by the product of separable homogeneous functions of degree zero. Concrete systems for the obtained results are provided.
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    On a System of Difference Equations Defined by the Product of Separable Homogeneous Functions
    (Walter De Gruyter Gmbh, 2023) Boulouh, Mounira; Touafek, Nouressadat; Tollu, Durhasan Turgut
    In this work, we present results on the stability, the existence of periodic and oscillatory solutions of a general second order system of difference equations defined by the product of separable homogeneous functions of degree zero. Concrete systems for the obtained results are provided.
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    On the behavior of the solutions of an abstract system of difference equations
    (Springer Heidelberg, 2022) Boulouh, Mounira; Touafek, Nouressadat; Tollu, Durhasan Turgut
    The aim of the present work is to study of the behavior of the solutions of the following abstract system of difference equations defined by x(n+1) = f(1)(x(n), x(n-1)) + f(2)(Y-n, Yn-1), y(n+1) = g(1)(X-n, Xn-1) g(2)(Y-n, Yn-1) where n is an element of No, the initial values x(-1), x(0), y(-1) and y(0) are positive real numbers, and the functions f(1), f(2), g(1), g(2) : (0, + infinity)(2) -> (0, + infinity) are continuous and homogeneous of degree zero.
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    On the solutions of a system of max-type difference equations
    (Tbilisi Centre Math Sci, 2021) Akrour, Youssouf; Mesmouli, Mouataz Billah; Tollu, Durhasan Turgut; Touafek, Nouressadat
    In this paper, we give explicit formulas of the solutions of the system of max-type difference equations x(n+1) = max {x(n-1),x(n)y(n-1)/y(n-2)}, y(n+1) = max {y(n-1), y(n)x(n-1)/x(n-2)}, where n >= 0 and the initial values are positive real numbers.
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    A SOLVABLE SYSTEM OF DIFFERENCE EQUATIONS
    (Korean Mathematical Soc, 2020) Taskara, Necati; Tollu, Durhasan T.; Touafek, Nouressadat; Yazlik, Yasin
    In this paper, we show that the system of difference equations x(n) = ay(n-1)(p) + b(x(n-2)y(n-1))(p-1)/cy(n-1) + dx(n-2)(p-1), y(n) = alpha x(n-1)(p) + beta(y(n-2)x(n-1))(p-1)/gamma x(n-1) + delta y(n-2)(p-1), n is an element of N-0 where the parameters a, b, c, d, alpha, beta, gamma, delta, p and the initial values x(-2) , x(-1), y(-2), y(-1) are real numbers, can be solved. Also, by using obtained formulas, we study the asymptotic behaviour of well-defined solutions of aforementioned system and describe the forbidden set of the initial values. Our obtained results significantly extend and develop some recent results in the literature.