| 摘要: |
| 详细研究了一个三阶非线性差分方程的动力学性质.通过使用数学技巧，清晰而又完整地描绘了这一方程的轨道结构规律，发现此方程的任一非平凡解正负半环相继长度周期性地出现，且最小周期为7；在一个周期内这个规律是3+，2-，1+，1-.使用这个规律，证明了这个方程的正平衡点是全局渐近稳定的. |
| 关键词: 非线性差分方程 非平凡解 环长 振动与非振动 全局渐近稳定性 |
| DOI：10.3969/J.ISSN.1000-5137.2020.03.002 |
| 分类号:O175.13 |
| 基金项目:The Natural Science Foundation of China (10771094, 61473340); The Natural Science Foundation of Zhejiang University of Science and Technology (F701108G14); The Distinguished Professor Foundation of Qianjiang Scholar in Zhejiang Province |
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| Trajectory structure rule of a third-order nonlinear difference equation |
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PAN Zhikang, LI Xianyi
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School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, Zhejiang, China
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| Abstract: |
| In this paper the dynamics for a third-order nonlinear difference equation is considered in detail. By utilizing some beautiful mathematical skills, we describe the rule for the trajectory structure of this equation clearly and completely. The successive lengths of positive and negative semicycles of any nontrivial solutions of this equation occur periodically with prime period 7; the rule is 3+, 2-, 1+, 1- in a period. Using the rule, we verify that the positive equilibrium point of the equation is globally asymptotically stable. |
| Key words: nonlinear difference equation nontrivial solution cycle length oscillation and nonoscillation global asymptotic stability |
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