离散系统x_(n+1)=Ax_n+B/Cx_(n-1)+D的周期解

Periodic Solutions for Discrete Systems x_(n+1)=Ax_n+B/Cx_(n-1)+D

在这篇文章里,我们利用射影几何中常用的齐次坐标记法把y_n+1=(y_n+α)/(y_(n-1)+β)线性化表示,从而得到了方程有最小正周期m周期解的一个充要条件,作为应用和例子,我们给出了最小正周期m=1,2,3,5的一般表达式,并证明了系统不存在最小正周期m=4的周期解。

We use the homogeneous coordinates of the projective geometry to establish the linearzed equation of x_(n+1)=Ax_n+B/Cx_(n-1)+D, present a sufficient and nessary conditions for y_(n+1)=y_n+α/y_(n-1)+β, having periodic solutions. As application,we establish the generality equations having periodic solutions with period one, two, three and five,further more, proof there are not periodic solution with four.