On the system of difference equations xn = cny n-3/(an+bnyn-1xn-2y n-3),yn=ynx n-3/(αn+βnxn-1y n-2xn-3)

Abstract

We show that the system of difference equationsxn= cnyn-3an+bnyn-1xn- 2yn-3,yn=γnxn- 3αn+βnxn-1yn- 2xn-3,n∈N0,where the sequences an, bn, cn, αn, βn, γn, n∈N0, and initial values x-i, y-i, i∈{1,2,3} are real numbers, such that cn≠0, γn≠0, n∈N0, can be solved in closed form, and for the case when all the sequences an, bn, cn, αn, βn and γn are constant we describe the asymptotic behavior of well-defined solutions of the system.