BEHAVIOUR OF SOLUTIONS FOR A SYSTEM OF TWO HIGHER-ORDER DIFFERENCE EQUATIONS

In this paper, we investigate the global behavior of the positive solutions of the system of difference equations u(n+1) = au(n-k)/b + c Pi(k)(i=0) v(n-i)(r), v(n+1) = dv(n-k)/e + f Pi(k)(i=0) u(n-i)(r), n is an element of N-0, where the initial conditions u(-i), v(-i), (i = 0,...,k), and the parameters a, b, c, d, e, f, r are positive real numbers, by extending some recent results in the literature. Also, we estimate the rate of convergence of a solution that converges to the zero equilibrium point of the above mentioned system.