The Complexity Analysis of Chaotic Systems

  • Wei Xu
  • Bingbing Song
  • Chunlei Fan
  • Qun Ding
  • Shu-Chuan Chu
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 298)


The complexity of the sequence is an important index of quantify the performance of chaotic sequence. In order to select a higher complexity of chaotic sequence and apply it in hardware encryption system, this paper analyzes chaotic complexity quantitative analysis methods and presents the approximate entropy and permutation entropy as criterion of measuring the complexity of the chaotic sequences. Set tent, logistic and henon three kinds of chaotic systems as examples, and we analysis and comparison their complexity. It is proved that the two kinds algorithms are effective, and can distinguish different complex chaos and chaotic sequences. Researches show that the complexity of the Logistic map is greater than that of other chaotic systems. The results of the study provide the theoretical and experimental basis for the application of chaotic sequence in hardware encryption system and the information security communication.


chaos complexity approximate entropy permutation entropy 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Wei Xu
    • 1
  • Bingbing Song
    • 2
  • Chunlei Fan
    • 2
  • Qun Ding
    • 2
  • Shu-Chuan Chu
    • 3
  1. 1.School of Computer Science and TechnologyHeilongjiang UniversityHarbinChina
  2. 2.School of Electronic EngineeringHeilongjiang UniversityHarbinChina
  3. 3.School of Computer Science, Engineering and MathematicsFlinders UniversityAdelaideAustralia

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