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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.
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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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