一个有理递归序列解的性质

文中分析了方程xn＋1=a＋bxn^2/1＋xn-2^2（其中a，6∈0，∞），a＋b〉0）的解的性质．并得山①当a=0，0〈b〈2时，方程的每一个解最终严格递减到0；②当b=0，0〈a时，方程的每一个非平凡解关于方程的平衡解振动。特别，当b=0、0〈a≤2时，方程的每一个正解收敛到平衡解x^-上.

Property of Solution for a Rational Recursive Sequence

Property of solution for equation xn＋1=a＋bxn^2/1＋xn-2^2（a,6∈0,∞）,a＋b〉0）was analyzed. Ifa = 0,0 〈 b 〈 2, then each nontrivial solution will be ultimately strictly digressive to zero; if b = 0,0 〈 a, then each nontrivial solution will be oscillate respect to balance solution. Specially, if b =0, 0〈a 〈 2, each positive solution will be convergent to balanced solution x^-.