| 一类四阶有理差分方程的振动规律和全局稳定性 |
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| 引用本文： | 陈云新.一类四阶有理差分方程的振动规律和全局稳定性[J].湖南师范大学自然科学学报,2009,32(4). |
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| 作者姓名： | 陈云新 |
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| 作者单位： | 南华大学数理学院,中国衡阳,421001 |
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| 基金项目： | 国家自然科学基金资助项目，湖南省教育厅科研重点资助项目 |
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| 摘 要： | 主要讨论了一类四阶有理差分方程x_(n+1)=x_(n-2)x_(n-3)/x_(n-2)+x_(n-3)+1,n=0,1,2,…,初始值x_(-3),x_(-2),x_(-1),X_0 ∈(0,∞)的振动规律和全局稳定性,即描述了其解的振动周期为15,且正、负半环长的规律为:4~+,3~-,1~+,2~-,2~+,1~-,1~+,1~-;又指出了解之间存在x_(n+k)△(C(x_(n+k))x_n(C(x_(n+k)C(x_n))(n≥-3)的大小关系;并得到了方程的平衡点是全局渐近稳定的.
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| 关 键 词： | 有理差分方程 振动规律 全局渐近稳定 |
Rules of Oscillation and Global Asymptotic Stability for a Fourth-Order Rational Difference Equation |
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| CHEN Yun-xin.Rules of Oscillation and Global Asymptotic Stability for a Fourth-Order Rational Difference Equation[J].Journal of Natural Science of Hunan Normal University,2009,32(4). |
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| Authors: | CHEN Yun-xin |
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| Abstract: | A fourth-order rational difference equation iS considered.The rules of oscillation and global asymptotic stability is described clearly.Mainly,the lengths of positive and negative semi-cycles of its nontrivial solutions are found to occur periodically with prime period 15.The rule is 4~+,3~-,1~+,2~-,2~+,1~-,1~+,1~-in a period.The relation between solution and solution is x_(n+k)△(C(x_(n+k))x_n(C(x_(n+k)C(x_n))(n≥-3).By utilizing this rule and relation,its negative equilibrium point is verified to be globally asymptotically stable. |
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| Keywords: | rational difference equation osciUatory rule global asymptotic stability |
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