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利用已有理论给出了一个二次多项式混沌系统, 证明了该系统与Tent映射拓扑共轭, 给出了该混沌系统的概率密度函数; 并根据此概率密度函数, 得到了轨道均匀分布的反三角函数映射; 对均匀化前后的混沌系统在不同参数下产生序列的信息熵、Kolmogorov熵、离散熵的特性进行了分析, 结果显示均匀化后产生的混沌序列混沌程度不改变且具有更好的均匀性.
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关键词:
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In this paper, firstly we construct a quadratic chaotic system and prove that it is a topological conjugate system of Tent map. Secondly, having analyzed the probability density function of the system, we propose an anti-trigonometric function map. Additionally, the performances of the quadratic chaotic system such as information entropy, Kolmogorov entropy and discrete entropy are tested for both the original systems and the homogenized systems with different parameters. Numerical simulations show that the information entropy of the uniformly distributed sequence is close to the theoretical limit and the discrete entropy remains unchanged. This result shows that the homogenization method is effective. In conclusion, the chaotic sequence after homogenization not only inherits the diverse properties of the original sequence, but also exhibits better uniformity.-
Keywords:
- Chaos system
[1] Li T Y, York J A 1975 Am. Math. Mon. 82 481
[2] Yu W P, Zhao B 2014 Acta Phys. Sin. 63 120502 (in Chinese) [于万波, 赵斌 2014 物理学报 63 120502]
[3] Yu W P 2014 Acta Phys. Sin. 63 120501 (in Chinese) [于万波 2014 物理学报 63 120501]
[4] Hao B L 2013 Starting with Parabola: An Introduction to Chaotic Dynamics (No.2) (Beijing: Peking University Press) pp114-118 (in Chinese) [郝柏林 2013 从抛物线谈起: 混沌动力学引论(北京: 北京大学出版社)第114-118页]
[5] He Z Y, Li K, Yang L X 1999 J. Electron. Inf. Technol. 5 646 (in Chinese) [何振亚, 李克, 杨绿溪 1999 电子与信息学报 5 646]
[6] Cao G H, Hu K, Tong W 2011 Acta Phys. Sin. 60 110508 (in Chinese) [曹光辉, 胡凯, 佟维 2011 物理学报 60 110508]
[7] Li P Y, Shi J X, Guo J L, Chen X, Yang H J 2015 Acta Electr. Sin. 43 753 (in Chinese) [李佩玥, 石俊霞, 郭嘉亮, 陈雪, 杨怀江 2015 电子学报 43 753]
[8] Zhou H L, Song E B 2009 J. Sichuan Univ. 46 561 (in Chinese) [周海玲, 宋恩彬 2009 四川大学学报 46 561]
[9] Kocarev L, Szczepanski J, Amigo J M, Tomovski I 2006 IEEE Trans. Circuits Syst. I: Regular Papers 53 1300
[10] 10 Amigo J M, Kocarev L, Szczepanski J 2007 Phys. Lett. A 366 211
[11] Amigo J M, Kocarev L, Tomovski I 2007 Physica D 228 77
[12] Liao X F, Xiao D, Chen Y, Xiang T 2009 The Theory and Application of Chaos Cryptography (Beijing: Science Press) pp9-10 (in Chinese) [廖晓峰, 肖迪, 陈勇, 向涛 2009 混沌密码学原理及其应用 (北京: 科学出版社) 第9-10页]
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[1] Li T Y, York J A 1975 Am. Math. Mon. 82 481
[2] Yu W P, Zhao B 2014 Acta Phys. Sin. 63 120502 (in Chinese) [于万波, 赵斌 2014 物理学报 63 120502]
[3] Yu W P 2014 Acta Phys. Sin. 63 120501 (in Chinese) [于万波 2014 物理学报 63 120501]
[4] Hao B L 2013 Starting with Parabola: An Introduction to Chaotic Dynamics (No.2) (Beijing: Peking University Press) pp114-118 (in Chinese) [郝柏林 2013 从抛物线谈起: 混沌动力学引论(北京: 北京大学出版社)第114-118页]
[5] He Z Y, Li K, Yang L X 1999 J. Electron. Inf. Technol. 5 646 (in Chinese) [何振亚, 李克, 杨绿溪 1999 电子与信息学报 5 646]
[6] Cao G H, Hu K, Tong W 2011 Acta Phys. Sin. 60 110508 (in Chinese) [曹光辉, 胡凯, 佟维 2011 物理学报 60 110508]
[7] Li P Y, Shi J X, Guo J L, Chen X, Yang H J 2015 Acta Electr. Sin. 43 753 (in Chinese) [李佩玥, 石俊霞, 郭嘉亮, 陈雪, 杨怀江 2015 电子学报 43 753]
[8] Zhou H L, Song E B 2009 J. Sichuan Univ. 46 561 (in Chinese) [周海玲, 宋恩彬 2009 四川大学学报 46 561]
[9] Kocarev L, Szczepanski J, Amigo J M, Tomovski I 2006 IEEE Trans. Circuits Syst. I: Regular Papers 53 1300
[10] 10 Amigo J M, Kocarev L, Szczepanski J 2007 Phys. Lett. A 366 211
[11] Amigo J M, Kocarev L, Tomovski I 2007 Physica D 228 77
[12] Liao X F, Xiao D, Chen Y, Xiang T 2009 The Theory and Application of Chaos Cryptography (Beijing: Science Press) pp9-10 (in Chinese) [廖晓峰, 肖迪, 陈勇, 向涛 2009 混沌密码学原理及其应用 (北京: 科学出版社) 第9-10页]
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