中国物理B ›› 2015, Vol. 24 ›› Issue (10): 100501-100501.doi: 10.1088/1674-1056/24/10/100501

• GENERAL • 上一篇    下一篇

A perturbation method to the tent map based on Lyapunov exponent and its application

曹绿晨a, 罗玉玲a, 丘森辉a, 刘俊秀b   

  1. 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
  • 收稿日期:2015-03-25 修回日期:2015-04-28 出版日期:2015-10-05 发布日期:2015-10-05
  • 基金资助:

    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).

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   

  1. 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
  • Received:2015-03-25 Revised:2015-04-28 Online:2015-10-05 Published:2015-10-05
  • Contact: Luo Yu-Ling E-mail:yuling0616@gxnu.edu.cn
  • Supported by:

    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).

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摘要：

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.

关键词: perturbation, tent map, Lyapunov exponent, finite precision

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.

Key words: perturbation, tent map, Lyapunov exponent, finite precision

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
05.45.Pq (Numerical simulations of chaotic systems)