On a System of Two High-Order Nonlinear Difference Equations

Abstract EN

This paper is concerned with dynamics of the solution to the system of two high-order nonlinear difference equations xn+1=xn-k/(q+∏i=0kyn-i), yn+1=yn-k/(p+∏i=0kxn-i), k∈N+, n=0,1,…, where p,q∈(0,∞), x-i∈(0,∞), y-i∈(0,∞) 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.