| 猫映射周期性与Fibonacci模数列周期性的内在联系 |
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| 引用本文： | 李用江,张辰光,李昌利,葛建华.猫映射周期性与Fibonacci模数列周期性的内在联系[J].计算机应用,2010,30(4):1026-1029. |
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| 作者姓名： | 李用江 张辰光 李昌利 葛建华 |
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| 作者单位： | 1. 西安电子科技大学;广东海洋大学2. 3. 广东海洋大学信息学院 |
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| 基金项目： | 国家863计划项目(B50306290182);;国家自然科学基金资助项目(J60104010107) |
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| 摘 要： | 介绍了Fibonacci数列的模数列周期性定理，并推广至Fibonacci_Q变换矩阵的模周期。通过探讨Fibonacci_Q矩阵的周期与猫映射的周期的关系，揭示了猫映射的模周期与Fibonacci数列的模周期的内在联系；定义了矩阵变换的最佳周期概念，给出了猫映射的最佳周期性定理。通过图像置乱的仿真实验，验证了相关理论的正确性，从而为图像置乱提供了数学理论依据。
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| 关 键 词： | Fibonacci模数列 Fibonacci矩阵 猫映射 最佳周期 图像置乱 |
| 收稿时间： | 2009-10-30 |
| 修稿时间： | 2009-11-16 |
Inherent relationship between the mode periodicities of cat map and Fibonacci series |
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| LI Yong-jiang,ZHANG Chen-guang,LI Chang-li,GE Jian-hua.Inherent relationship between the mode periodicities of cat map and Fibonacci series[J].journal of Computer Applications,2010,30(4):1026-1029. |
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| Authors: | LI Yong-jiang ZHANG Chen-guang LI Chang-li GE Jian-hua |
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| Affiliation: | 1.State Key Laboratory of Integrated Service Networks/a>;Xidian University/a>;Xi'an Shaanxi 710071/a>;China/a>;2.College of Information/a>;Guangdong Ocean University/a>;Zhanjiang Guangdong 524088/a>;3.College of Earth Sciences/a>;Guilin University of Technology/a>;Guilin Guangxi 541004/a>;China |
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| Abstract: | The periodicity theorems of modular series of Fibonacci series were firstly presented,and then the periodicity property of Fibonacci _Q transform matrix was generalized.The relationship between the period of the Fibonacci _Q matrix and that of cat map was discussed,and the inherent relationship between the period of cat map and that of series generated from Fibonacci series was disclosed.The best transform period was secondly defined,and the best periodicity theorem for cat map was given.Finally,the relevan... |
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| Keywords: | Fibonacci mode series Fibonacci matrix cat map best period image scrambling |
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