Solvability of a third-order system of nonlinear difference equations via a generalized Fibonacci sequence

Abstract

In this paper, we solve in closed-form the following third-order system of nonlinear difference equations xn+1= ynyn−1xn−1pxn(anyn−2q+bnynyn−1),yn+1= xnxn−1yn−1qyn(cnxn−2p+dnxnxn−1),p,q∈ℕ,n∈ℕ0 x−i,y−i,i=0,1,2(an)n∈ℕ0,(bn)n∈ℕ0,(cn)n∈ℕ0,(dn)n∈ℕ0