Global attractivity in a rational recursive sequence

摘要

Our aim in this paper is to investigate the periodic character, invariant intervals and the global attractivity of all positive solutions of the nonlinear difference equationxn+1=α+βxnγ−xn−1,n=0,1,…,where α⩾0, β,γ>0. We show that the positive equilibrium of the equation is a global attractor with a basin that depends on certain conditions posed on the coefficients.