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研究了logistic混沌映射的相关性质,指出当系统参数取值改变时,产生的混沌序列在相空间不具有遍历性.基于以上分析,构造了一种分段logistic混沌映射,对logistic映射和定义的分段logistic映射的分岔图和Lyapunov指数进行了研究,同时通过实验对这二种映射生成序列的随机性、相关系数、功率谱等性能进行了比较分析.在此基础上,定义了一种新的混沌系统性能评价指标——分岔迭代次数.结果表明,定义的分段logistic映射不仅具有良好的遍历性,而且对应的混沌系统相关评价指标的性能良好.
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关键词:
- 混沌系统 /
- 相关系数 /
- Lyapunov指数 /
- 功率谱
Properties of logistic chaotic map is studied, and it is pointed out that phase space is not ergodic when parameters of the chaotic system change. Based on these analysis, a piecewise logistic chaotic map is constructed. The bifurcation diagram and Lyapunov exponent of logistic and piecewise logistic map are studied, and the properties of randomicity, correlation coefficient and power spectrum etc. of the sequences generated by these two maps are analyzed experimentally. A new performance evaluation index for chaotic system, the bifurcation iteration time, is defined. Simulation results show that the defined piecewise logistic map is not only ergodic in phase space, and its corresponding chaotic performance evaluation indices are also better.-
Keywords:
- chaotic system /
- correlation coefficient /
- Lyapunov exponent /
- power spectrum
[1] ［1］Matthews R A J 1989 Cryptologia 13 29
[2] ［2］Pareek N K, Patidar V, Sud K K 2006 Image Vision Comput. 24 926
[3] ［3］Rhouma R, Belghith S 2008 Phys. Lett. A 372 5973
[4] ［4］Behnia S, Akhshani A, Mahmodi H, Akhavan A 2008 Chaos Soliton. Fract. 35 408
[5] ［5］Narendra S, Aloka S 2009 Opt. Commun. 282 1104
[6] ［6］Ausloos M, Dirickx M 2006 he logistic Map and the Route to Chaos (Berlin: Springer-Verlag) p36
[7] ［7］Yu Z B, Feng J C 2008 Acta Phys. Sin. 57 1409 (in Chinese) ［余振标、冯久超 2008 57 1409］
[8] ［8］Habutsu T, Nishio Y, Sasase I 1991 Advances in Cryptology Eurcrypt91 (Berlin: Springer-Verlag) p127
[9] ［9］Liu P, Yan C, Huang G X 2007 J. Commun. 28 134 (in Chinese) ［柳平、闫川、黄高显 2007 通信学报 28 134］
[10] ］Zhang Y W, Wang Y M, Shen X B 2007 Sci. Chin. Ser. E 37 183 (in Chinese) ［张翌维、王育民、沈绪榜 2007 中国科学E辑 (信息科学) 37 183］
[11] ］Zhu X J, Chen Y C, Shao Y, Wang J 2008 J. Commun. 29 122 (in Chinese) ［朱晓锦、陈艳春、邵勇、王健 2008 通信学报 29 122］
[12] ］Yang Y X, Liu D, Xin J 2008 J. Electron. Inf. Tech. 30 529 (in Chinese) ［杨延西、刘丁、辛菁 2008 电子与信息学报 30 529］
[13] ］Wang J Z, Chen Z Q, Yuan Z Z 2006 Acta Phys. Sin. 55 3956 (in Chinese) ［王杰智、陈增强、袁著祉 2006 55 3956］
[14] ］Wang X Y, Wang M J 2008 Acta Phys. Sin. 57 731 (in Chinese) ［王兴元、王明军 2008 57 731］
[15] ］Zhang Q C, Tian R L, Wang W 2008 Acta Phys. Sin. 57 2799 (in Chinese) ［张琪昌、田瑞兰、王炜 2008 57 2799］
[16] ］Wang K, Pei W J, Xia H S, Cheung Y M 2008 Phys. Lett. A 372 4388
[17] ］Yang R, Zhang B 2006 Acta Phys. Sin. 55 5667 (in Chinese) ［杨汝、张波 2006 55 5667］
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[1] ［1］Matthews R A J 1989 Cryptologia 13 29
[2] ［2］Pareek N K, Patidar V, Sud K K 2006 Image Vision Comput. 24 926
[3] ［3］Rhouma R, Belghith S 2008 Phys. Lett. A 372 5973
[4] ［4］Behnia S, Akhshani A, Mahmodi H, Akhavan A 2008 Chaos Soliton. Fract. 35 408
[5] ［5］Narendra S, Aloka S 2009 Opt. Commun. 282 1104
[6] ［6］Ausloos M, Dirickx M 2006 he logistic Map and the Route to Chaos (Berlin: Springer-Verlag) p36
[7] ［7］Yu Z B, Feng J C 2008 Acta Phys. Sin. 57 1409 (in Chinese) ［余振标、冯久超 2008 57 1409］
[8] ［8］Habutsu T, Nishio Y, Sasase I 1991 Advances in Cryptology Eurcrypt91 (Berlin: Springer-Verlag) p127
[9] ［9］Liu P, Yan C, Huang G X 2007 J. Commun. 28 134 (in Chinese) ［柳平、闫川、黄高显 2007 通信学报 28 134］
[10] ］Zhang Y W, Wang Y M, Shen X B 2007 Sci. Chin. Ser. E 37 183 (in Chinese) ［张翌维、王育民、沈绪榜 2007 中国科学E辑 (信息科学) 37 183］
[11] ］Zhu X J, Chen Y C, Shao Y, Wang J 2008 J. Commun. 29 122 (in Chinese) ［朱晓锦、陈艳春、邵勇、王健 2008 通信学报 29 122］
[12] ］Yang Y X, Liu D, Xin J 2008 J. Electron. Inf. Tech. 30 529 (in Chinese) ［杨延西、刘丁、辛菁 2008 电子与信息学报 30 529］
[13] ］Wang J Z, Chen Z Q, Yuan Z Z 2006 Acta Phys. Sin. 55 3956 (in Chinese) ［王杰智、陈增强、袁著祉 2006 55 3956］
[14] ］Wang X Y, Wang M J 2008 Acta Phys. Sin. 57 731 (in Chinese) ［王兴元、王明军 2008 57 731］
[15] ］Zhang Q C, Tian R L, Wang W 2008 Acta Phys. Sin. 57 2799 (in Chinese) ［张琪昌、田瑞兰、王炜 2008 57 2799］
[16] ］Wang K, Pei W J, Xia H S, Cheung Y M 2008 Phys. Lett. A 372 4388
[17] ］Yang R, Zhang B 2006 Acta Phys. Sin. 55 5667 (in Chinese) ［杨汝、张波 2006 55 5667］
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