【摘要】 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。更多还原

【Abstract】 Global asymptotic stability of the following difference equationxn=A1nxn-i1+A2nxn-i2+A3nxn-i3xn-i4B1nxn-i1xn-i2+B2nxn-i3+B3nxn-i4,n=0,1,…,is studied,where,{A1n}+∞n=0,{A2n}+∞n=0,{A3n}+∞n=0,{B1n}+∞n=0,{B2n}+∞n=0,{B3n}+∞n=0 are sequences of nonnegative 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.更多还原