| 许宏飞,李群宏,宁敏,商梦媛.一类分段非线性映射的混沌边界分析[J].海南师范大学学报自科版,2016,29(4):363-368 |
| 一类分段非线性映射的混沌边界分析 |
| Analysis of the Chaotic Boundary in a Class of Piecewise Nonlinear Mapping |
| 投稿时间：2016-09-17 |
| DOI：10.12051/j.issn.1674-4942.2016.04.002 |
| 中文关键词: 分岔 禁区边界 混沌边界 分段非线性不连续映射 Lyapunov 指数 |
| 英文关键词: bifurcation forbidden boundary chaotic boundary piecewise nonlinear mapping Lyapunov exponent |
| 基金项目:广西自然科学基金（2013GXNSFAA019017，2014GXNSFBA118024） |
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| 中文摘要: |
| 文章研究了一类具有非线性分支的分段映射的动力学行为. 该模型可能应用到物理科
学、工程和医学方面，也有助于一些经济模型的研究. 以μ为分岔参数得到系统的分岔图，发现在系
统的不变吸引区间内，周期轨道的每个周期点都有一定的存在范围，这造成分岔结构中出现迭代禁
区现象. 通过理论推导确定了周期轨道周期点的存在范围和禁区边界，进一步通过禁区边界得到了
混沌区域与周期n轨道区域的边界的表达式，应用Lyapunov 指数对分析结果进行了验证. |
| 英文摘要: |
| In this paper the dynamical behaviors of a class of discontinuous one-dimensional mappings with a nonlinear
branch are studied. This kind of models can be used in physical science, engineering, and medical science, and is also helpful to the study of economics models. Taking μ as a bifurcation parameter to draw the bifurcation diagram of the system, we
find that in the invariant attracting region of the system there is an existence range for each point of the periodic orbit, and it
leads to iteration forbidden region appearing in the bifurcation structure. By theoretical derivation, the article determines the
existence ranges of the periodic orbits and the boundary of the forbidden region, obtains the boundary expression of the chaotic region and the period-n orbits region by the boundary of the forbidden region, and finally verifies the analytic results by
the Lyapunov exponents. |
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