一类三阶有理差分方程解的全局行为

Global Behavior of a Third Order Rational Difference Equation

主要研究一类有理差分方程在参数取不同值情况下的奇点集和全局行为。通过变换和替换将该方程转化为Riccati方程进行求解,并证明了该方程的解最终将收敛到零或者非零不动点或者是无界的。

In this paper, we mainly studied forbidden sets and global behavior of a third order rational difference equation in the ease of different parameters. We converted the equation into a Riecati equation, and proved that the solutions of the equation eventually converge to zero or non - zero fixed point or unbounded.