On a solvable system of difference equations of fourth order

Abstract

The system of difference equationsxn=cnxn- 4an+bnyn-1xn-2yn- 3xn-4,yn=γnyn- 4αn+βnxn-1yn- 2xn-3yn-4,n∈N0, where the sequences an,bn,cn,αn, βn,γn,n∈N0, and initial values x-i,y-i,i∈{1,2,3,4} are real numbers, such that cn≠0,γn≠0,n∈N0, is solved in closed form, and based on the obtained formulae is studied the asymptotic behaviour of well-defined solutions of the system.