一类非线性差分方程平衡解的稳定性

Stability of Equilibrium Solutions for a Class of Nonlinear Difference Equation

研究了非线性差分方程xn+1=xxnnx+n-x1n-+1xxnn--22++αβ,n=1,2,3,…的正平衡解存在性及渐进稳定性。其中α,β∈[0,+∞],初值x-2,x-1,x0∈(0,∞)。

This paper investigate the existence and the asymptotic stability of the positive equilibrium solutions to the following nonlinear difference equations：xn＋1=xn＋xn-1xn-2＋α/xnxn-1＋xn-2＋β,n=1,2,3… where α,β∈[0,＋∞] and the initial valuesx-2,x-1,x0∈（0,∞）.