On the recursive sequence xn+1 = α +xn−1/xn

In this paper we study the global stability, the permanence, and the oscillation character of the recursive sequence xn+1 = α + xn−1 xn , n= 0, 1, . . . , where α is a negative number and the initial conditions x−1 and x0 are negative numbers. © 2005 Elsevier Inc. All rights reserved.