| 一类非线性差分方程平衡解的稳定性和吸引性 |
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| 引用本文： | 党红刚,何万生.一类非线性差分方程平衡解的稳定性和吸引性[J].天水师范学院学报,2011,31(2):26-28. |
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| 作者姓名： | 党红刚 何万生 |
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| 作者单位： | 天水师范学院数学与统计学院,甘肃天水,741001 |
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| 基金项目： | 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” |
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| 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,∞）.
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| 关 键 词： | 差分方程 渐近稳定性 正平衡解 |
The Stability and the Attractivity of Equilibrium Solutions for a Class of Nonlinear Difference Equation |
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| Dang Honggang,He Wansheng.The Stability and the Attractivity of Equilibrium Solutions for a Class of Nonlinear Difference Equation[J].Journal of Tianshui Normal University,2011,31(2):26-28. |
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| Authors: | Dang Honggang He Wansheng |
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| Institution: | (School of Mathematics and Statistics,Tianshui Normal University,Tianshui Gansu 741001,China) |
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| Abstract: | 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,∞). |
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| Keywords: | difference equation asymptotic stability positive equilibrium of equation |
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