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| 求解混沌映射不变分布的符号计算法 | |
| 引用本文： | 陈双平,韩恺,马猛,郑浩然,王煦法.求解混沌映射不变分布的符号计算法[J].数学的实践与认识,2010,40(6). |
| 作者姓名： | 陈双平 韩恺 马猛 郑浩然 王煦法 |
| 作者单位： | 1. 暨南大学珠海学院,广东珠海519070;中国科学技术大学计算机科学与技术系,安徽合肥230027 2. 中国科学技术大学计算机科学与技术系,安徽合肥230027;中原工学院计算机科学系,河南郑州,450007 3. 中国科学技术大学计算机科学与技术系,安徽合肥230027;安徽大学计算机科学与技术学院,安徽合肥230039 4. 中国科学技术大学计算机科学与技术系,安徽合肥,230027 |
| 基金项目： | 国家自然科学基金(60802026); 国家重点基础研究发展计划(2006CB910700); 暨南大学青年基金(51208030) |
| 摘 要： | 根据Frobenius-Perron方程,可以对混沌映射的不变分布从理论上加以分析,从而对混沌映射不变分布作出大致的估计.由此可以利用符号计算的方法求解得到迭代函数系统不变分布的密度近似函数,从而逼近理论解.用几个计算实例和常见数值解法作了比较,试验结果表明符号计算方法具有一定的优势. |
| 关 键 词： | 迭代函数系统 不变分布 数值计算 符号计算 |
Symbolic Computation Solution to Invariant Probability Distribution for Chaotic Mapping |
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| CHEN Shuang-ping,HAN Kai,MA Meng,ZHENG Hao-ran,WANG Xu-fa.Symbolic Computation Solution to Invariant Probability Distribution for Chaotic Mapping[J].Mathematics in Practice and Theory,2010,40(6). | |
| Authors: | CHEN Shuang-ping HAN Kai MA Meng ZHENG Hao-ran WANG Xu-fa |
| Institution: | CHEN Shuang-ping~(1,2),HAN Kai~(2,3),MA Meng~(2,4),ZHENG Hao-ran~2,WANG Xu-fa~2 (1.Zhuhai College of Jinan University,Zhuhai 519070,China) (2.Department of Computer Science & Technology,University of Science , Technology of China,Hefei 230027,China) (3.Department of Computer Science,Zhongyuan University of Technology,Zhenzhou 450007,China) (4.School of Computer Science , Technology,Anhui University,Hefei 230039,China) |
| Abstract: | Based on the analysis of Probenius-Perron equation,the invariant probability distribution of a chaotic mapping can be studied theoretically and it is possible to estimate it. However,by using symbolic computation method,it is easy to get a series of functions that approximate to the theoretical invariant probability distribution.It has been shown that the symbolic computation method has its particular advantage compared with other numerical computation methods by applying them to several examples. |
| Keywords: | iterated-function systems invariant probability distribution numerical computation symbolic computation |
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