| 一类NMIFS吸引子 |
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| 引用本文： | 王兴元,刘波.一类NMIFS吸引子[J].数学研究及应用,2007,27(2):241-252. |
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| 作者姓名： | 王兴元 刘波 |
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| 作者单位： | 大连理工大学电子与信息工程学院,辽宁,大连,116024 |
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| 摘 要： | 本文给出了NMIFS(Nonlinear Markov Iterated Function System)理论与构造NMIFS吸引子的方法,讨论了一类NMIFS吸引子的平衡向量测度和“矩”的递归计算,分析了NMIFS吸引子的结构特征．研究结果表明:对于MIFS,可以通过递归方法来计算矩M(i)(i=1,2...);而对于NMIFS,因M(i)的计算依赖于M(j)(j≥i),故不能直接计算M(i),而只能计算其近似值．
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| 关 键 词： | NMIFS吸引子 平衡向量测度 矩 |
| 文章编号： | 1000-341X(2007)02-0241-12 |
| 收稿时间： | 2005/5/16 0:00:00 |
| 修稿时间： | 7/1/2005 12:00:00 AM |
A Class of Nonlinear Markov Iterated Function System Attractors |
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| WANG Xing-yuan and LIU Bo.A Class of Nonlinear Markov Iterated Function System Attractors[J].Journal of Mathematical Research with Applications,2007,27(2):241-252. |
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| Authors: | WANG Xing-yuan and LIU Bo |
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| Institution: | School of Electronic and Information Engineering, Dalian University of Technology, Liaoning 116024, China;School of Electronic and Information Engineering, Dalian University of Technology, Liaoning 116024, China |
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| Abstract: | In this article the theory of NMIFS (Nonlinear Markov Iterated Function System) and the construction method of an NMIFS are presented. The balanced vector measure and the recursive calculation of the ``moment' of a class of NMIFS attractors are discussed, and the structure characteristics are analyzed. The result shows that we can calculate the moments $\hat {M}^{(i)}~(i = 1,2, \ldots )$ for MIFS, but for NMIFS, we cannot calculate $\hat {M}^{(i)}$ directly because the calculation of $\hat {M}^{(i)}$depends on the value of $\hat {M}^{(j)}(j \ge i)$. So only the approximated value of $\hat {M}^{(i)}$ could be obtained. |
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| Keywords: | NMIFS attractor balanced vector measure moment |
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