Abstract
In this paper we investigate the global attractivity of the recursive sequence
chi(n+1) = (alpha - beta chi(n))F(chi(n-1),...,chi(n-k)), n = 0, 1, . . .
where alpha, beta >= 0. We show that the unique positive equilibrium point of the equation is a global attractor with some basin. We apply this result to the rational recursive sequence
chi(n+1) = alpha - beta chi(n)/gamma+(k)Sigma(i=1) a(i)chi(n-i) + (k)Sigma(i=1) b(i)chi(2)(n-i), n = 0, 1, . . .
where alpha, beta, a(i), b(i) >= 0 and gamma > 0, and prove that the positive equilibrium point of the equation is a global attractor with a basin that depends on certain conditions posed on the coefficients. (C) 2008 Elsevier Ltd. All rights reserved.