【摘要】 研究了递推方程yn=1+α1yn-1y+α2yn-3/yn-2,n=0,1,…的正解的性质,其中初始值y-3,y-2,y-1∈(0,+∞)并且α1,α2∈(0,1),α1+α2=1.利用分析法结合变换技巧,证明了其唯一的平衡点是一个全局吸引子并且其解序列按指数收敛于平衡点2.更多还原

【Abstract】 We study the behavior of positive solutions of the recursive equation yn=1+α1yn-1y+α2yn-3/yn-2,n=0,1,… with y-3,y-2y-1∈(0,+∞) and α1,α2∈(0,1),α1+α2=1.Using analysis method coupled with transform technique,we prove that the unique positive equilibrium 2 is global attractor and yn tends to 2,exponentially.更多还原