非线性差分方程x_(n+1)=f(x_n,x_(n-k))的全局渐近稳定性(英文)

Global asymptotic stability of the nonlinear difference equation x_(n+1)=f(x_n,x_(n-k))

考虑了非线性差分方程xn+1=f(xn,xn-k),n=0,1,…,其中k∈{1,2,…,},f(u,v)关于u递增,关于v递减,初始值x-k,x-k+1,…,x0∈(0,+∞),得到这个方程的唯一正平衡点是全局渐近稳定的一个充分条件.

A nonlinear difference equation xn＋1=f（xn,xn-k）,n=0,1 … ,where x-k,x-k＋1,… ,X0∈ （0,＋∞） is considered. The sufficient conditions are obtained under which the unique positive equilibrium of this equation is globally asymptotically stable.