Skip to main content
SpringerLink
Log in

The Complexity Analysis of Chaotic Systems

  • Conference paper
Intelligent Data analysis and its Applications, Volume II

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 298))

Abstract

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.

This paper is supported by Innovated Team Project of ’Modern Sensing Technology’ in colleges and universities of Heilongjiang Province (No. 2012TD007) and Institutions of Higher Learning by the Specialized Research Fund for the Doctoral Degree (No.20132301110004).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Huang, L.L., Yin, Q.T.: A Chaos Synchronization Secure Communication system Based on Output Control. Electronics & Information Technology 31, 2402–2405 (2009)

    Google Scholar 

  2. Parlitz, U., Ergezinger, S.: Robust Communication Based Chaotic Spreading Sequences. Phys. Lett. A 188, 146–150 (1994)

    Article  Google Scholar 

  3. Kolmogrov, A.N.: Three Approaches to the Quantitative Definition of Information. Problem in Information Transmission 1, 1–7 (1965)

    Google Scholar 

  4. Lempel, A., Ziv, J.: On the Complexity of Finite Sequences. IEEE Transactions on Information Theory 22, 75–81 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  5. Pincus, S.M.: Approximate Entropy As a Measure of System Complexity. Proc. Natl. Acad. Sci. 88, 2297–2301 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  6. Bandt, C., Pompe, B.: Permulation Entropy a Natural Complexity Measure for Time Series. Phys. Rev. Lett. 88, 174102-1–174102-4 (2002)

    Google Scholar 

  7. Xiao, F.H., Yan, G.R., Han, Y.H.: A Symbolic Dynamics Approach for the Complexity Analysis of Chaotic Pseudorandom Sequences. Acta Physica Sinica 53, 2877–2880 (2004)

    Google Scholar 

  8. Larrondo, H.A., Gonzalez, C.M., Martin, M.T.: Intensive Statistical Complexity Measure of Pseudorandom Number Generators. Physica A 356, 133–138 (2005)

    Article  Google Scholar 

  9. Chen, X.J., Li, Z., Bai, B.M.: A New Complexity Metric of Chaotic Pseudorandom Sequences Based on Fuzzy Entropy. Electronics & Information Technology 147, 195–197 (1981)

    Google Scholar 

  10. Zhao, G., Fang, J.Q.: Modern Information Safety and Advances In Application Research of Chaos-Based Security Communication. Progress In Physics 23, 212–252 (2003)

    Google Scholar 

  11. Wang, Y.X., Weng, Y.F.: Study on the Complexity Analysis Methodology and Application to Logisitic Map. Beijing Technology and Business University 24, 38–41 (2006)

    Google Scholar 

  12. Pincus, S.M.: Approximate Entropy as a Measure of System Complexity. Proceedings of the National Academy of Sciences 88, 2297–2301 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  13. Sun, K.H., Tan, G.Q.: The Complexity Analysis of TD-ERCS Discrete Chaotic Pseudo-Random Sequences. Acta Physica Sinica 57, 3359–3365 (2008)

    MATH  MathSciNet  Google Scholar 

  14. Xu, W., Ding, Q., Zhang, X.G.: Detection Complexity of Chaotic Sequence. Information Technology 12, 5487–5491 (2013)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computer Science and Technology, Heilongjiang University, Harbin, 150080, China

    Wei Xu

  2. School of Electronic Engineering, Heilongjiang University, Harbin, 150080, China

    Bingbing Song, Chunlei Fan & Qun Ding

  3. School of Computer Science, Engineering and Mathematics, Flinders University, Adelaide, Australia

    Shu-Chuan Chu

Authors
  1. Wei Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bingbing Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chunlei Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Qun Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Shu-Chuan Chu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wei Xu .

Editor information

Editors and Affiliations

  1. University of Applied Sciences, Kaohsiung, Taiwan

    Jeng-Shyang Pan

  2. Department of Computer Science Faculty of Elec. Eng. & Comp. Sci., VSB-Technical University of Ostrava, Ostrava, Czech Republic

    Vaclav Snasel

  3. Departamento de Informáca y Automática Facultad de Biología, University of Salamanca, Salamanca, Spain

    Emilio S. Corchado

  4. Scientific Network for Innovation and Research Excellence, Machine Intelligence Research Labs (MIR Labs), Auburn, Washington, USA

    Ajith Abraham

  5. Department of Information Management, National University of Kaohsiung, Kaohsiung, Taiwan

    Shyue-Liang Wang

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Xu, W., Song, B., Fan, C., Ding, Q., Chu, SC. (2014). The Complexity Analysis of Chaotic Systems. In: Pan, JS., Snasel, V., Corchado, E., Abraham, A., Wang, SL. (eds) Intelligent Data analysis and its Applications, Volume II. Advances in Intelligent Systems and Computing, vol 298. Springer, Cham. https://doi.org/10.1007/978-3-319-07773-4_31

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-07773-4_31

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07772-7

  • Online ISBN: 978-3-319-07773-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation