【摘要】 考虑差分方程xn -1=exp α1-xn1- βxn,n∈N ,这里α >0 ,β∈ (0 ,1) ,通过构造辅助函数H(x) =x0 +f(x0 ) -x -f(x) ,证明了 .如果α≤ 1- β,则方程的每一个解xn 均满足 0 <xn<1β ,并进一步推证了平衡点 x =1是渐近稳定的 .同时得到了 x =1全局渐近稳定的充分条件更多还原

【Abstract】 Consider the difference equation x n =exp [α(1-x n)/(1-βx n] n ∈N,where α>0,β∈(0,1) and 0<x 0<1β .we show that when α≤1-β ,every solution of the equation suit 0<x n<1β .Furthermore the equilibrium point =1 is asymptotically stable.The result is got that the equilibrium point =1 is the sufficient conditions of glibal attractor更多还原