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Chin. Phys. B, 2015, Vol. 24(10): 100501    DOI: 10.1088/1674-1056/24/10/100501
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A perturbation method to the tent map based on Lyapunov exponent and its application

Cao Lv-Chen (曹绿晨)a, Luo Yu-Ling (罗玉玲)a, Qiu Sen-Hui (丘森辉)a, Liu Jun-Xiu (刘俊秀)b
a Guangxi Key Laboratory of Multi-source Information Mining & Security, Faculty of Electronic Engineering, Guangxi Normal University, Guilin 541004, China;
b School of Computing and Intelligent Systems, University of Ulster, Derry, Northern Ireland BT48 7JL, UK
Abstract  

Perturbation imposed on a chaos system is an effective way to maintain its chaotic features. A novel parameter perturbation method for the tent map based on the Lyapunov exponent is proposed in this paper. The pseudo-random sequence generated by the tent map is sent to another chaos function – the Chebyshev map for the post processing. If the output value of the Chebyshev map falls into a certain range, it will be sent back to replace the parameter of the tent map. As a result, the parameter of the tent map keeps changing dynamically. The statistical analysis and experimental results prove that the disturbed tent map has a highly random distribution and achieves good cryptographic properties of a pseudo-random sequence. As a result, it weakens the phenomenon of strong correlation caused by the finite precision and effectively compensates for the digital chaos system dynamics degradation.

Keywords:  perturbation      tent map      Lyapunov exponent      finite precision  
Received:  25 March 2015      Revised:  28 April 2015      Accepted manuscript online: 
PACS:  05.45.-a (Nonlinear dynamics and chaos)  
  05.45.Pq (Numerical simulations of chaotic systems)  
Fund: 

Project supported by the Guangxi Provincial Natural Science Foundation, China (Grant No. 2014GXNSFBA118271), the Research Project of Guangxi University, China (Grant No. ZD2014022), the Fund from Guangxi Provincial Key Laboratory of Multi-source Information Mining & Security, China (Grant No. MIMS14-04), the Fund from the Guangxi Provincial Key Laboratory of Wireless Wideband Communication & Signal Processing, China (Grant No. GXKL0614205), the Education Development Foundation and the Doctoral Research Foundation of Guangxi Normal University, the State Scholarship Fund of China Scholarship Council (Grant No. [2014]3012), and the Innovation Project of Guangxi Graduate Education, China (Grant No. YCSZ2015102).

Corresponding Authors:  Luo Yu-Ling     E-mail:  yuling0616@gxnu.edu.cn

Cite this article: 

Cao Lv-Chen (曹绿晨), Luo Yu-Ling (罗玉玲), Qiu Sen-Hui (丘森辉), Liu Jun-Xiu (刘俊秀) A perturbation method to the tent map based on Lyapunov exponent and its application 2015 Chin. Phys. B 24 100501

[1] Luo Y L, Du M H and Liu J X 2015 Commun. Nonliner Sci. Numer. Simul. 20 447
[2] Yuen C, Lui O and Wong K 2012 Int. Symp., Circuits Syst., May 20-23, 2012, Seoul, Korea
[3] Lima J and Novaes L 2014 Signal Processing 94 521
[4] Li S J, Chen G R and Mou X Q 2005 Int. J. Bifur. Chaos 15 3119
[5] Bergamo P, DArco P, De Santis A and Kocarev L 2005 IEEE Trans. Circuits Syst. 52 1382
[6] Wang X Y and Wang L L 2011 Chin. Phys. B 20 050509
[7] Wang S H, Liu W R, Lu H P, Kuang J Y and Hu G 2004 Int. J. Mod. Phys. B 18 2617
[8] Heidari-Bateni G and McGillem C D 1994 IEEE Trans. Commun. 42 1524
[9] Azzaz M, Tanougast C, Sadoudi S, Fellah R and Dandache A 2013 Commun. Nonliner Sci. Numer. Simul. 18 1792
[10] Tong X J 2013 Commun. Nonliner Sci. Numer. Simul. 18 1725
[11] Hu H P, Deng Y S and Liu L F 2014 Commun. Nonliner Sci. Numer. Simul. 19 1970
[12] Dabal P and Pelka R 2012 19th Int. Conf. Mix. Des. Integr. Circuits Syst., May 24, 2012, Warsaw, Poland, p. 260
[13] Chung H and Miri A 2012 11th Inernational Conf. Inf. Sci. Signal Process. Their Appl., October 21-25, 2012, Beijing, China, p. 460
[14] Liu S B, Sun J, Xu Z Q and Liu J S 2009 Chin. Phys. B 18 5219
[15] Persohn K J and Povinelli R J 2012 Chaos, Solitons and Fractals 45 238
[16] Liu N S 2011 Commun. Nonliner Sci. Numer. Simul. 16 761
[17] Luo Y L and Du M H 2013 Chin. Phys. B 22 080503
[18] Hu H P, Xu Y and Zhu Z Q 2008 Chaos, Solitons and Fractals 38 439
[19] Rukhin A, Soto J, Nechvatal J, Smid M, Barker E, Leigh S, Levenson M, Vangel M, Banks D, Heckert A, Dray J and Vo S 2001 A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications, NIST Special Publication 800-22
[20] Dabal P and Pelka R 2011 IEEE 14th International Symposium on Design and Diagnostics of Electronic Circuits & Systems.April, 13-15, 2011, Cottbus, German
[21] Wang X Y and Wang Q 2014 Chin. Phys. B 23 030503
[22] Wang X Y, Zhao J F and Liu H J 2012 Opt. Commun. 285 562
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