一类非线性差分方程平衡解的稳定性及二周期解的存在性

The Stability of Equilibrium Solutions and the Existence of 2-Periodic Solutions for a Class of Nonlinear Difference Equation

研究了非线性差分方程xn+1=(xnxn-1+xn-2+α)/(xn-1+xnxn-2+β),n=1,2,3,…的正平衡解存在性及渐近稳定性,并对其二周期解的存在性进行了探讨,其中α,β∈[0,+∞),初值x-2,x-1,x0∈(0,+∞).

Abstract：In this paper we investigate the existence and the asymptotic stability of the positive equilibrium solutions to the follow-ing nonlinear difference equations xn＋1=（xnxn-1＋xn-2＋α）/（xn-1＋xnxn-2＋β）,n=1,2,3,…and the initial values x-2,x-1,x0∈（0,＋∞）.We also discuss the existence of 2-periodic solutions to the equations.