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In this paper, we deal with the form of the solutions and the periodicity character of the following systems of nonlinear difference equations of order two Zn+1 = Zntn-1/±tn ± tn-1, tn+1 = tnZn-1/±Zn ± Zn-1, where the initial conditions Z-1, Z0, t-1 and t0 are nonzero real numbers. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to investigate the dynamics of a system of fourth-order rational difference equations... where the parameter A is arbitrary positive real number and the initial conditions x-3,x-2,x-1,x0,y-3,y-2,y-1,y0 are arbitrary nonnegative real numbers. By using new iteration method for the more general nonlinear difference equations and inequality skills, we establish some sufficient conditions which guarantee the existence, unstability and global asymptotic stability of the equilibriums for this nonlinear system. Numerical examples to the difference system are given to verify our theoretical results. [ABSTRACT FROM AUTHOR]

In this article we study the existence of solutions and some of their qualitative behavior of the following rational nonlinear difference equation xn+1 = axn-(2k+1)/ b + cxn-kxn-(2k+1) , n = 0, 1, ..., where a, b and c are real numbers, k is a non-negative integer number and the initial conditions x-2k-1, x-2k , ..., x-1, x0 are arbitrary non-negative real numbers. Also, the solutions of some special cases of the equation under consideration will be obtained. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the form of the solutions and the periodicity character of the following systems of nonlinear difference equations of order two zn+1=zn+tn-l/±tn±tn-1,tn+1=tnzn-l/±zn±zn-l where the initial conditions z-1, z0, t-1 and t0 are nonzero real numbers. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to investigate the global stability of the solutions, the boundedness and the periodic character of the nonlinear difference equationxn+1 = βxn+βxn-l+γxn-k + axnxn-k/bxn + cxn-l + dxn-k, n = 0, 1, ..., where the parameters α, β, γ, a, b, c and d are positive real numbers and the initial conditions x-s, x-s+1, ..., x-1, x0 are positive real numbers where s = max{l, k}. Some numerical examples will be given to explicate our results. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to investigate the dynamics of a system of fourth-order rational difference equations xn+1=xn-3-yn-1/A+xn-3yn-1,yn+1=yn-3-xn-1/A+yn-3xn-1, n=0,1,..., where the parameter A is arbitrary positive real number and the initial conditions x-3,x-2,x-1,x0,y-3,y-2,y-1,y0 are arbitrary nonnegative real numbers. By using new iteration method for the more general nonlinear difference equations and inequality skills, we establish some sufficient conditions which guarantee the existence, unstability and global asymptotic stability of the equilibriums for this nonlinear system. Numerical examples to the difference system are given to verify our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we will investigate the local stability of the equilibrium points, global attractor, boundedness and the form of the solutions for the following equations xn+1 = Axnxn-3/Bxn + Cxn-2 and xn+1 =Axnxn-3/ Bxn - Cxn-2 , where the coefficients A, B and C are real positive numbers, and the initial conditions x-3,x-2, x-1, x0 are arbitrary non zero real numbers. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to study the periodic character and the global stability of the positive solutions of the difference equation xn+1 = axn + bxn-k + cxn-l - dxn-s/exn-s - αxn-t, n = 0, 1, ..., where the parameters a, b, c, d, e and α are positive real numbers and the initial conditions x-σ, x-σ+1, ..., x-1, x0 are positive real numbers where σ = max{s, t, k,}. Some numerical examples were given to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we study the behavior of the solutions of the following rational difference equation with big order xn+1 = axn-l + bxn-k + cxn-s + dxn-t/exn-s + fxn-t where the parameters a; b; c; d; e and f are positive real numbers and the initial conditions x-r, x-r+1, x-1 and x0 are positive real numbers where r = max(l, k, s, t). [ABSTRACT FROM AUTHOR]