Global analysis of solutions of xn+1 = βxn+δxn−2 A+Bxn+Cxn−1

We study the global character of solutions of the third order rational difference equation xn+1 = βxn +δxn−2 A+ Bxn +Cxn−1 , n= 0, 1, . . . , where the parameters β, δ, A are nonnegative, β+δ >0, B,C >0, the initial conditions x−2, x−1, x0 are nonnegative real numbers and the denominator is always positive.  2005 Elsevier Inc. All rights reserved