一类含有二次项的高阶有理差分方程的全局行为

Global behavior of a rational difference equation

本文给出方程x_(n+1)=x_nx_(n-k)αx_n+βx_(n-(k+1))的奇点集及解的表达式,并讨论了该方程解的全局行为,其中k∈N,n∈N∪{0},α,β都是实数,初始值(x_(-(k+1)),x_(-k),…,x_0)∈R^(k+2).

In this paper, we determine the forbidden set, introduce an explicit formula for the solutions and discuss the global behavior of a rational difference equation x_（n＋1）=（x_nx_（n-k））/（αx_n＋βx_（n-（k＋1））） ,where inter k E N, n E N U {0} ,a,flare real numbers, the initial conditions （x_（-（k＋1））,x_（-k）,…,x_0）∈R^（k＋2）.