一个差分方程的全局渐近稳定性

Global asymptotic stability of a difference equation

文中研究差分方程xn=BA11nnxxnn--ii11x+n-Ai22nx+nB-i22nx+n-Ain33x+n-Bi33nxxnn--ii44,n=0,1,…,的全局渐近稳定性,其中{A1n}n+=∞0,{A2n}n+=∞0,{An3}n+=∞0,{Bn1}n+=∞0,{Bn2}n+=∞0,{B3n}n+=∞0都是非负实数列,i1,i2,i3,i4∈{1,2,…},α=max{i1,i2,i3,i4},初始值x-1,x-2,…,x-α∈(0,∞),从而得到了该方程唯一正平衡解是全局渐近稳定的一个充分条件。

Global asymptotic stability of the following difference equation Xn=An^1xn-i1＋An^2xn-i2＋An^3xn-i3xn-i4/Bn^1xn-i1xn-i2＋Bn^2xn-i3＋Bn^3xn-i4,n=0,1,…, is studied, where, {An^1}n=0^＋∞,{An^2}n=0^＋∞,{An^3}n=0^＋∞,{Bn^1}n=0^＋∞,{Bn^2}n=0^＋∞,{Bn^3}n=0^＋∞ are sequences of non-negative real numbers,i1,i2,i3,i4∈{1,2,…},α=max{i1,i2,i3,i4}, and the initial conditions x-1,x-2,…,x-α∈（0,∞）,A sufficient condition under which the unique equilibrium of this equation is globally asymptotically stable is obtained.