一类非线性差分方程平衡解的稳定性和吸引性

The Stability and the Attractivity of Equilibrium Solutions for a Class of Nonlinear Difference Equation

研究了非线性差分方程Xn+1=[xn+xn-1]/[xn·xn-1+β]=,n=1,2,…的正平衡解存在性及渐近稳定性,以及正平衡点X=(β-2)^(1/2)在适当的参数条件下是所有正解的全局吸引子,其中β∈[2,+∞],初值x-1,x0∈(0,∞).

The existence and asymptotic stability of the positive equilibrium solutions to the following nonlinear difference equation,Xn＋1=[xn＋xn-1]/[xn·xn-1＋β],n=1,2,…,were investigated in this paper.The results showed that the positive equilibrium of the equation was a global attractor with a basin that depends on certain conditions posed on the coefficients where β∈（2,＋∞） and the initial values x-1,x0∈（0,∞）.