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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]

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]