Dynamic behavior of a recursive sequence

摘要

In this paper, the global asymptotic stability, the global attractivity, the boundedness character, the periodic nature and chaotic behavior of solutions of the difference equationxn+1=α−xn−1xn,n=0,1,…,are investigated, where α∈R is a real number, and the initial conditions x−1, x0 are arbitrary real numbers. As might be expected, the six cases α<−1, α=−1, −1<α⩽1, 1<α⩽2, 2<α<3 and α>3 give rise to substantially different dynamic behavior.