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Utilization of the Discrete Chaotic Systems as the Pseudo Random Number Generators

  • Roman Senkerik
  • Michal Pluhacek
  • Ivan Zelinka
  • Zuzana Kominkova Oplatkova
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 285)

Abstract

This paper investigates the utilization of the discrete dissipative chaotic system as the chaotic pseudo random number generators. (CPRNGs) Several discrete chaotic maps are simulated, statistically analyzed and compared within this initial research study.

Keywords

Chaos Dissipative systems Discrete maps Pseudo random number generators 

Notes

Acknowledgments

This work was supported by: Grant Agency of the Czech Republic—GACR P103/13/08195S, is partially supported by Grant of SGS No. SP2014/159, VŠB—Technical University of Ostrava, Czech Republic, by the Development of human resources in research and development of latest soft computing methods and their application in practice project, reg. no. CZ.1.07/2.3.00/20.0072 funded by Operational Programme Education for Competitiveness, co-financed by ESF and state budget of the Czech Republic, further was supported by European Regional Development Fund under the project CEBIA-Tech No. CZ.1.05/2.1.00/03.0089 and by Internal Grant Agency of Tomas Bata University under the project No. IGA/FAI/2014/010.

References

  1. 1.
    Celikovsky, S., Zelinka, I.: Chaos theory for evolutionary algorithms researchers. In: Zelinka, I., Celikovsky, S., Richter, H., Chen, G. (eds.) Evolutionary Algorithms and Chaotic Systems. Studies in Computational Intelligence, vol. 267, pp. 89–143. Springer, Berlin Heidelberg (2010)CrossRefGoogle Scholar
  2. 2.
    Lee, J.S., Chang, K.S.: Applications of chaos and fractals in process systems engineering. J. Process. Control 6(2–3), 71–87 (1996)CrossRefGoogle Scholar
  3. 3.
    Wu, J., Lu, J., Wang, J.: Application of chaos and fractal models to water quality time series prediction. Environ. Model Softw. 24(5), 632–636 (2009)CrossRefGoogle Scholar
  4. 4.
    Lozi, R.: Emergence of randomness from Chaos. Int. J. Bifurcat. Chaos 22(02), 1250021 (2012)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Persohn, K.J., Povinelli, R.J.: Analyzing logistic map pseudorandom number generators for periodicity induced by finite precision floating-point representation. Chaos, Solitons Fractals 45(3), 238–245 (2012)CrossRefGoogle Scholar
  6. 6.
    Wang, X.-Y., Qin, X.: A new pseudo-random number generator based on CML and chaotic iteration. Nonlinear Dyn. 70(2), 1589–1592 (2012)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Narendra, K.P., Vinod, P., Krishan, K.S.: A random bit generator using chaotic maps. Int. J. Netw. Secur. 10, 32–38 (2010)Google Scholar
  8. 8.
    Yang, L., Wang, X.-Y.: Design of pseudo-random bit generator based on chaotic maps. Int. J. Mod. Phys. B 26(32), 1250208 (2012)CrossRefGoogle Scholar
  9. 9.
    Bucolo, M., Caponetto, R., Fortuna, L., Frasca, M., Rizzo, A.: Does chaos work better than noise? Circuits Syst. Mag., IEEE 2(3), 4–19 (2002)CrossRefGoogle Scholar
  10. 10.
    Hu, H., Liu, L., Ding, N.: Pseudorandom sequence generator based on the Chen chaotic system. Comput. Phys. Commun. 184(3), 765–768 (2013)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Pluchino, A., Rapisarda, A., Tsallis, C.: Noise, synchrony, and correlations at the edge of chaos. Phys. Rev. E 87(2), 022910 (2013)CrossRefGoogle Scholar
  12. 12.
    Aydin, I., Karakose, M., Akin, E.: Chaotic-based hybrid negative selection algorithm and its applications in fault and anomaly detection. Expert Syst. Appl. 37(7), 5285–5294 (2010)CrossRefGoogle Scholar
  13. 13.
    Caponetto, R., Fortuna, L., Fazzino, S., Xibilia, M.G.: Chaotic sequences to improve the performance of evolutionary algorithms. IEEE Trans. Evol. Comput. 7(3), 289–304 (2003)CrossRefGoogle Scholar
  14. 14.
    Davendra, D., Zelinka, I., Senkerik, R.: Chaos driven evolutionary algorithms for the task of PID control. Comput. Math. Appl. 60(4), 1088–1104 (2010)CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Zelinka, I.: SOMA—self-organizing migrating algorithm. New Optimization Techniques in Engineering. Studies in Fuzziness and Soft Computing, vol. 141, pp. 167–217. Springer, Berlin Heidelberg (2004)CrossRefGoogle Scholar
  16. 16.
    Liang, W., Zhang, L., Wang, M.: The chaos differential evolution optimization algorithm and its application to support vector regression machine. J. Softw. 6(7), 1297–1304 (2011)CrossRefGoogle Scholar
  17. 17.
    Zhenyu, G., Bo, C., Min, Y., Binggang, C.: Self-adaptive chaos differential evolution. In: Jiao, L., Wang, L., Gao, X.-b., Liu, J., Wu, F. (eds.) Advances in Natural Computation, vol. 4221, pp. 972–975. Lecture Notes in Computer Science. Springer, Berlin Heidelberg (2006)Google Scholar
  18. 18.
    LdS, Coelho, Mariani, V.C.: A novel chaotic particle swarm optimization approach using Hénon map and implicit filtering local search for economic load dispatch. Chaos, Solitons Fractals 39(2), 510–518 (2009)CrossRefGoogle Scholar
  19. 19.
    Hong, W.-C.: Chaotic particle swarm optimization algorithm in a support vector regression electric load forecasting model. Energy Convers. Manag. 50(1), 105–117 (2009)CrossRefGoogle Scholar
  20. 20.
    Senkerik, R., Pluhacek, M., Zelinka, I., Oplatkova, Z., Vala, R., Jasek, R.: Performance of chaos driven differential evolution on shifted benchmark functions set. In: Herrero, Á., Baruque, B., Klett, F. et al. (eds.) International Joint Conference SOCO’13-CISIS’13-ICEUTE’13, vol. 239, pp. 41–50. Advances in Intelligent Systems and Computing. Springer International Publishing (2014)Google Scholar
  21. 21.
    Senkerik, R., Davendra, D., Zelinka, I., Pluhacek, M., Kominkova Oplatkova, Z.: On the differential evolution Drivan by selected discrete chaotic systems: Extended study. In: 19th International conference on soft computing, MENDEL 2013, pp. 137–144 (2013)Google Scholar
  22. 22.
    Senkerik, R., Pluhacek, M., Oplatkova, Z.K., Davendra, D., Zelinka, I.: Investigation on the differential evolution driven by selected six chaotic systems in the task of reactor geometry optimization. In: 2013 IEEE Congress on Evolutionary Computation (CEC), 20–23 June 2013, pp. 3087–3094 (2013)Google Scholar
  23. 23.
    Davendra, D., Bialic-Davendra, M., Senkerik, R.: Scheduling the lot-streaming flowshop scheduling problem with setup time with the chaos-induced enhanced differential evolution. In: 2013 IEEE Symposium on Differential Evolution (SDE), 16–19 April 2013, pp. 119–126 (2013)Google Scholar
  24. 24.
    Pluhacek, M., Senkerik, R., Davendra, D., Kominkova Oplatkova, Z., Zelinka, I.: On the behavior and performance of chaos driven PSO algorithm with inertia weight. Comput. Math. Appl. 66(2), 122–134 (2013)CrossRefMathSciNetGoogle Scholar
  25. 25.
    Pluhacek, M., Senkerik, R., Zelinka. I., Davendra, D.: Chaos PSO algorithm driven alternately by two different chaotic maps—an initial study. In: 2013 IEEE Congress on Evolutionary Computation (CEC), 20–23 June 2013, pp 2444–2449 (2013)Google Scholar
  26. 26.
    Pluhacek, M., Senkerik, R., Zelinka, I.: Multiple choice strategy based PSO algorithm with chaotic decision making—a preliminary study. In: Herrero, Á., Baruque, B., Klett, F., et al. (eds.) International Joint Conference SOCO’13-CISIS’13-ICEUTE’13, vol. 239, pp. 21–30. Advances in Intelligent Systems and Computing. Springer International Publishing (2014)Google Scholar
  27. 27.
    ELabbasy, E., Agiza, H., EL-Metwally, H., Elsadany, A.: Bifurcation analysis, chaos and control in the Burgers mapping. Int. J. Nonlinear Sci. 4(3), 171–185 (2007)MathSciNetGoogle Scholar
  28. 28.
    Sprott, J.C.: Chaos and Time-Series Analysis. Oxford University Press, Oxford (2003)MATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Roman Senkerik
    • 1
  • Michal Pluhacek
    • 1
  • Ivan Zelinka
    • 2
  • Zuzana Kominkova Oplatkova
    • 1
  1. 1.Faculty of Applied InformaticsTomas Bata University in ZlinZlinCzech Republic
  2. 2.Faculty of Electrical Engineering and Computer ScienceTechnical University of OstravaOstrava-PorubaCzech Republic

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