一类高阶离散系统的全局渐近稳定性

Globally Asymptotically Stability for a Class of Higher Order Discrete Systems

研究了二元高阶离散系统xn=A+yn-q/xn-p,yn=A+xn-p/yn-q的振荡性、有界性及收敛性,由于二元系统的任一正解(xn,yn)∈S={(x,y)｜(x-A)(y-A)=1,x>0,y>0},由此得出了两个一元高阶离散系统:xn=A+A/xn-p+1yn-q(yn-p-A)在平衡点的全局渐xn-p(xn-q-A),yn=A+A/yn-q+1近稳定性.

In this paper, we study oscillatory, bounded, and convergence of the second dimensional discrete system xn=A+yn-q/xn-p,yn=A+xn-p/yn-p with any positive solution (xn,yn)∈S={(x,y)|(x-A)(y-A)=1,x>0,y>0}. As a consequence, we proved that the globally asymptotically stability of unique positive equilibrium of the one dimensional discrete systems xn=A+A/xn-p+1xn-p(xn-q-A),yn=A+A/yn-q+1yn-q(yn-p-A).