A Brief Survey on the Chaotic Systems as the Pseudo Random Number Generators

  • Roman SenkerikEmail author
  • Michal Pluhacek
  • Ivan Zelinka
  • Donald Davendra
  • Zuzana Kominkova Oplatkova
Part of the Emergence, Complexity and Computation book series (ECC, volume 14)


This paper briefly investigates the utilization of the both discrete dissipative chaotic system as well as the time-continuous chaotic systems as the chaotic pseudo random number generators. (CPRNGs) Several examples of chaotic systems are simulated, statistically analyzed and compared within this brief survey.


Chaos Dissipative systems Discrete maps Chaotic flows Pseudo random number generators 


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  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. SCI, vol. 267, pp. 89–143. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  2. 2.
    Lee, J.S., Chang, K.S.: Applications of chaos and fractals in process systems engineering. Journal of 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. Environmental Modelling & Software 24(5), 632–636 (2009)CrossRefGoogle Scholar
  4. 4.
    Lozi, R.: Emergence of Randomness from Chaos. International Journal of Bifurcation and 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. International Journal of Network Security 10, 32–38 (2010)Google Scholar
  8. 8.
    Yang, L., Wang, X.-Y.: Design of Pseudo-random Bit Generator Based on Chaotic Maps. International Journal of Modern Physics B 26(32), 1250208 (2012)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Bucolo, M., Caponetto, R., Fortuna, L., Frasca, M., Rizzo, A.: Does chaos work better than noise? IEEE Circuits and Systems Magazine 2(3), 4–19 (2002)CrossRefGoogle Scholar
  10. 10.
    Hu, H., Liu, L., Ding, N.: Pseudorandom sequence generator based on the Chen chaotic system. Computer Physics Communications 184(3), 765–768 (2013)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Pluchino, A., Rapisarda, A., Tsallis, C.: Noise, synchrony, and correlations at the edge of chaos. Physical Review E 87(2), 022910 (2013)Google Scholar
  12. 12.
    Aydin, I., Karakose, M., Akin, E.: Chaotic-based hybrid negative selection algorithm and its applications in fault and anomaly detection. Expert Systems with Applications 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 Transactions on Evolutionary Computation 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. Computers & Mathematics with Applications 60(4), 1088–1104 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Zelinka, I.: SOMA — Self-Organizing Migrating Algorithm. In: New Optimization Techniques in Engineering. STUDFUZZ, vol. 141, pp. 167–217. Springer, 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. Journal of Software 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.) ICNC 2006. LNCS, vol. 4221, pp. 972–975. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  18. 18.
    Coelho, L.D.S., 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 Conversion and Management 50(1), 105–117 (2009)CrossRefGoogle Scholar
  20. 20.
    Senkerik, R., Pluhacek, M., Zelinka, I., Oplatkova, Z.K., Vala, R., Jasek, R.: Performance of chaos driven differential evolution on shifted benchmark functions set. In: Herrero, A., et al. (eds.) International Joint Conference SOCO’13-CISIS’13-ICEUTE’13. AISC, vol. 239, pp. 41–50. Springer, Heidelberg (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), June 20-23, 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), April 16-19, 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. Computers & Mathematics with Applications 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), June 20-23, 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., et al. (eds.) International Joint Conference SOCO’13-CISIS’13-ICEUTE’13. AISC, vol. 239, pp. 21–30. Springer, Heidelberg (2014)Google Scholar
  27. 27.
    ELabbasy, E., Agiza, H., EL-Metwally, H., Elsadany, A.: Bifurcation Analysis, Chaos and Control in the Burgers Mapping. International Journal of Nonlinear Science 4(3), 171–185 (2007)MathSciNetGoogle Scholar
  28. 28.
    Sprott, J.C.: Chaos and Time-Series Analysis. Oxford University Press (2003)Google Scholar
  29. 29.
    Bharti, L., Yuasa, M.: Energy Variability and Chaos in Ueda Oscillator,
  30. 30.
    Kanamaru, T.: Van der Pol oscillator. Scholarpedia 2(1), 2202 (2007)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Roman Senkerik
    • 1
    Email author
  • Michal Pluhacek
    • 1
  • Ivan Zelinka
    • 2
  • Donald Davendra
    • 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 OstravaOstravaCzech Republic

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