On a System of Two High-Order Nonlinear Difference Equations

This paper is concerned with dynamics of the solution to the system of two high-order nonlinear difference equations x(n+1) = x(n-k)/(q + Pi(k)(i=0) y(n-i) = y(n-k)/(p + Pi(k)(i=0) x(n-i)), k is an element of N+, n = 0, 1, ..., where p,q is an element of (0, infinity) and i - 0, 1, ....,k. Moreover the rate of convergence of a solution that converges to the equilibrium (0, 0) of the system is discussed. Finally, some numerical examples are considered to show the results obtained.