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

摘要:

本文给出方程x_(n+1)=(x_n x_(n-k))/(αx_n+βx_(n-(k+1)) )的奇点集,解的表达式,并讨论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).

Abstract:

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_n x_(n-k))/(αx_n+βx_(n-(k+1)) ), where inter k∈N, inter n∈N∪{0},α,β are real numbers, the initial conditions (x_(-(k+1) ),x_(-k),⋯,x_0 )∈R^(k+2).