ON A SECOND ORDER RATIONAL DIFFERENCE EQUATION

Abstract

In this paper, we investigate the stability of the following differenceequationxn+1 =ax4n + bxnx3n−1 + cx2nx2n−1 + dx3nxn−1 + ex4n−1Ax4n + Bxnx3n−1 + Cx2nx2n−1 + Dx3nxn−1 + Ex4n−1,n = 0, 1, . . . ,where the parameters a, b, c, d, e, A, B, C, D, E are positive realnumbers and the initial values x0, x−1 are arbitrary positive numbers.