摘要
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,∞).
出处
《天水师范学院学报》
2011年第2期26-28,共3页
Journal of Tianshui Normal University
基金
天水师范学院中青年教师科研资助项目"混沌在通信系统中的应用"(TSA0939)阶段性成果
关键词
差分方程
渐近稳定性
正平衡解
difference equation
asymptotic stability
positive equilibrium of equation