一类高阶有理差分方程的全局渐近稳定性

Global asymptotic stability of a class of high-order rational difference equation

运用子序列分析法研究一类高阶有理差分方程xn=xn-mxn-k+axn-m+xn-k的全局渐近稳定性,式中:m,k∈Z+,xs,xs+1,…,x0∈(0,∞),a∈[0,∞),s=min{1-m,1-k}.

A method of subsequence analysis was used to study the global asymptotic stability of a class of higher-order rational difference equations,xn=xn-mxn-k＋a/xn-m＋xn-k where m,k∈Z^＋,xs,xs＋1,……x0∈（0,∞）,a∈[0,∞）,s=min{1-m,1-k}.