| Markov迭代函数系统分形的动力学特性分析 |
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| 引用本文： | 章立亮. Markov迭代函数系统分形的动力学特性分析[J]. 工程图学学报, 2009, 30(6) |
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| 作者姓名： | 章立亮 |
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| 作者单位： | 宁德师范高等专科学校数学系,福建,宁德,352100 |
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| 基金项目： | 福建省自然科学基金资助项目 |
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| 摘 要： | 研究Markov迭代函数系统(MIFS)的转移概率矩阵与MIFS吸引子分形结构之间的关系.首先提出了分支Markov迭代函数系统的概念并将MIFS系统分解成若干分支系统,给出和证明了几个相关定理.然后讨论转移概率矩阵的零元素对吸引子结构的影响,分析吸引子的局部结构特征,发现MIFS系统吸引子包含自相似结构,基于计算机数学实验分析了吸引子分形形成的动力学特性并给予具体的定性描述.
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| 关 键 词： | 计算机应用 迭代函数系统 Markov链 分形 |
Analysis of the Dynamical Characteristics of Markov Iterated Function Systems |
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| ZHANG Li-liang. Analysis of the Dynamical Characteristics of Markov Iterated Function Systems[J]. Journal of Engineering Graphics, 2009, 30(6) |
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| Authors: | ZHANG Li-liang |
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| Affiliation: | ZHANG Li-liang(Department of Mathematics,Ningde Teachers College,Ningde Fujian 352100,China) |
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| Abstract: | The relationship between transition probability matrix of Markov iterated function systems and the fractal attractor structure of MIFS is researched.Firstly,the filiation Markov iterated function systems is defined,and a MIFS system is broken down into several filiation systems.Secondly,the effect of zero elements in transition probability matrix is discussed.At last,dynamical characteristics of generating fractal image based on computer mathematical experiment is analyzed. |
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| Keywords: | computer application iterated function systems markov chain fractal |
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