一类差分方程性质的研究

数学季刊 ›› 2013, Vol. 28 ›› Issue (1): 93-98.

一类差分方程性质的研究

Department of Basic Sciences, Hebei Finance University

收稿日期:2011-07-13 出版日期:2013-03-30 发布日期:2023-03-09
作者简介:XIAO Qian(1984-), female, native of Baoding, Hebei, a lecturer of Hebei Finance University, M.S.D., engages in difference equation.
基金资助:
Supported by the NSF for Colleges and Universities of Hebei Province(Z2011162,Z2011111)

On the Qualitative Behavior of a Difference Equation

Department of Basic Sciences, Hebei Finance University

Received:2011-07-13 Online:2013-03-30 Published:2023-03-09
About author:XIAO Qian(1984-), female, native of Baoding, Hebei, a lecturer of Hebei Finance University, M.S.D., engages in difference equation.
Supported by:
Supported by the NSF for Colleges and Universities of Hebei Province(Z2011162,Z2011111)

摘要/Abstract

摘要： This paper is concerned with the following rational difference equation x_n+1=ax_n-bx_n-1+ex²_n/(cX_n+dx_n-1), with the initial conditions x_-1, x₀∈ (0, +∞) and a, b, c, d, e ∈ R⁺. Locally asymptotically stability, global attractively and boundedness character of the equilibrium point of the equation are investigated. Moreover, simulation is shown to support the results.

关键词: global stability, attractively, boundedness, numerical simulation

Abstract: This paper is concerned with the following rational difference equation xn+1=ax_n-bx_n-1+ex²_n/(cX_n+dx_n-1), with the initial conditions x_-1, x₀∈ (0, +∞) and a, b, c, d, e ∈ R⁺. Locally asymptotically stability, global attractively and boundedness character of the equilibrium point of the equation are investigated. Moreover, simulation is shown to support the results.

Key words: global stability, attractively, boundedness, numerical simulation

中图分类号:

O175.7

肖倩, 石启宏. 一类差分方程性质的研究[J]. 数学季刊, 2013, 28(1): 93-98.

XIAO Qian, SHI Qi-hong. On the Qualitative Behavior of a Difference Equation[J]. Chinese Quarterly Journal of Mathematics, 2013, 28(1): 93-98.

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