Skip to main content
SpringerLink
Log in

Implementation of FPGA-based real time novel chaotic oscillator

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Currently, chaotic systems and chaos-based applications are commonly used in the engineering fields. One of the main structures used in these applications is the chaos-based signal generators. Chaotic signal generators have an important role, particularly in chaotic communication and cryptology. In this study, the Pehlivan-Wei chaotic system, which is a recently developed chaotic system, has been implemented with FPGA using three distinct algorithms (the Euler, Heun, and RK4) for the first time in literature. Numerical and HDL approaches are implemented by these three algorithms to compare the performance of each model for use in chaotic generators. In addition, the Lyapunov exponents and phase portraits of the system have been extracted for chaos analysis. RMSE analysis has been conducted on the chaotic generators, which are modeled using the Euler, Heun, and RK4 algorithms in order to observe error rates of each numerical algorithm in a comparative aspect. The performance of new chaotic system with various data sets has been analyzed. The operation frequency of the chaotic oscillators synthesized and tested for the Virtex-6 FPGA chip has been able to reach up to 463.688 MHz and the chaotic system has been able to calculate 300,000 data sets in 0.0284 s. However, PC-based algorithm having highest performance score can calculate 300,000 data sets in a period of 75.363 s. A comparison study has been performed on the performance of the FPGA-based and PC-based solutions to evaluate each approach.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Lorenz, E.N.: Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130–141 (1963)

    Article  Google Scholar 

  2. Li, T.Y., Yorke, J.A.: Period three implies chaos. Am. Math. Mon. 82(10), 985–992 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  3. Rössler, O.E.: An equation for continuous chaos. Phys. Lett. A 57(5), 397–398 (1976)

    Article  Google Scholar 

  4. Rössler, O.E.: Continuous choas-four prototype equations. Ann. N.Y. Acad Sci. 316, 376–392 (1979)

    Article  Google Scholar 

  5. Matsumoto, T., Chua, L.O., Tanaka, S.: Simplest chaotic nonautonomous circuit. Phys. Rev. A 30(2), 1155–1157 (1984)

    Article  Google Scholar 

  6. Pehlivan, I., Uyaroglu, Y.: A new chaotic attractor from general Lorenz system family and its electronic experimental implementation. Turk. J. Electr. Eng. Comput. Sci. 18(2), 171–184 (2010)

    Google Scholar 

  7. Wu, J.G., Wu, Z.M., Liu, Y.R., Fan, L., Tang, X., Xia, G.Q.: Simulation of bidirectional long-distance chaos communication performance in a novel fiber-optic chaos synchronization system. J. Lightwave Technol. 31(3), 461–467 (2013)

    Article  Google Scholar 

  8. Özkaynak, F., Yavuz, S.: Designing chaotic s-boxes based on time-delay chaotic system. Nonlinear Dyn. 74(3), 551–557 (2013)

    Article  Google Scholar 

  9. Sundarapandian, V., Pehlivan, I.: Analysis, control, synchronization and circuit design of a novel chaotic system. Math. Comput. Model. 55(7–8), 1904–1915 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  10. Zhang, G.D., Shen, Y., Wang, L.M.: Global anti-synchronization of a class of chaotic memristive neural networks with time-varying delays. Neural Netw. 46, 1–8 (2013)

    Article  Google Scholar 

  11. Li, N., Yuan, H.Q., Sun, H.Y., Zhang, Q.L.: An impulsive multi-delayed feedback control method for stabilizing discrete chaotic systems. Nonlinear Dyn. 73, 1187–1199 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  12. Yu, J., Yu, H.: Chen, Bing., Gao, Junwei., Qin, Yong.: Direct adaptive neural control of chaos in the permanent magnet synchronous motor. Nonlinear Dyn. 70(3), 1879–1887 (2012)

    Article  Google Scholar 

  13. Rafikov, M., José, M.B.: On control and synchronization in chaotic and hyperchaotic systems via linear feedback control. Commun. Nonlinear Sci. Numer. Simul. 13, 1246–1255 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  14. Cho, S., Jin, M., Kuc, T.Y., Lee, J.S.: Control and synchronization of chaos systems using time-delay estimation and supervising switching control. Nonlinear Dyn. (2013). doi:10.1007/s11071-013-1084-4

  15. Farahani, M., Ganjefar, S., Alizadeh, M.: PID controller adjustment using chaotic optimization algorithm for multi-area load frequency control. IET Control Theory Appl. 6, 1984–1992 (2012)

    Article  MathSciNet  Google Scholar 

  16. Wang, Y., Wong, K.W., Liao, X., Chen, G.: A new chaos-based fast image encryption algorithm. Appl. Soft Comput. 11, 514–522 (2011)

    Article  Google Scholar 

  17. Tong, X., Minggen, C.: Image encryption scheme based on 3D baker with dynamical compound chaotic sequence cipher generator. Signal Process. 89, 480–491 (2009)

    Article  MATH  Google Scholar 

  18. Chen, G., Yaobin, M., Charles, K.C.: A symmetric image encryption scheme based on 3D chaotic cat maps. Chaos Solut Fractals 21, 749–761 (2004)

    Article  MATH  Google Scholar 

  19. Alatas, B.: Chaotic bee colony algorithms for global numerical optimization. Expert Syst. Appl. 37, 5682–5687 (2010)

    Article  Google Scholar 

  20. Soltanpour, M.R., Khooban, M.H.: A particle swarm opti-mization approach for fuzzy sliding mode control for track-ing the robot manipulator. Nonlinear Dyn. 74(1–2), 467–478 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  21. Coelho, L.S., Lee, C.S.: Solving economic load dispatch problems in power systems using chaotic and Gaussian particle swarm optimization approaches. Int. J. Electr. Power Energy Syst. 30, 297–307 (2008)

    Article  Google Scholar 

  22. Valenza, G., Lanata, A., Scilingo, E.P.: Oscillations of heart rate and respiration synchronize during affective visual stimulation. IEEE Trans. Inf. Technol. Biomed. 16, 683–690 (2012)

    Article  Google Scholar 

  23. Huimin, L., Monti, A., Ponci, F.A.: Fuzzy-based sensor validation strategy for AC motor drives. IEEE Trans. Ind. Inf. 8, 839–848 (2012)

    Article  Google Scholar 

  24. Wang, Y., Bingjie, W., Anbang, W.: Chaotic correlation optical time domain reflectometer utilizing laser diode. IEEE Trans. Photon. Technol. Lett. 20, 1636–1638 (2008)

    Article  Google Scholar 

  25. Nianqiang, L., Wei, P., Shuiying, X., Lianshan, Y., Bin, L., Xihua, Z.: Loss of time delay signature in broadband cascade-coupled semiconductor lasers. IEEE Trans. Photon. Technol. Lett. 24, 2187–2190 (2012)

    Article  Google Scholar 

  26. Kilic, R., Dalkiran, F.Y.: Programmable design and implementation of a chaotic system utilizing multiple nonlinear functions. Turk. J. Electr. Eng. Comput. Sci. 18(4), 647–655 (2010)

    Google Scholar 

  27. Pande, A., Zambreno, J.: Design and hardware implementation of a chaotic encryption scheme for real-time embedded systems. In: International Conference on Signal Processing and Communications (SPCOM). pp. 1–5 (2010)

  28. Zhang, Y., Zexiang, L., Xinjian, Z.: A chaos-based image encryption ASIC using reconfigurable logic. In: IEEE Asia Pacific Conference on Circuits and Systems (APCCAS). pp. 1782–1785 (2008)

  29. Zhang, Z., Guanrong, C., Simin, Y.: Hyperchaotic signal generation via DSP for efficient perturbations to liquid mixing. Int. J. Circuit Theory Appl. 37, 31–41 (2009)

    Article  Google Scholar 

  30. Azzaz, M.S., Tanougast, C., Sadoudi, S., Fellah, R., Dandache, A.: A new auto-swiched chaotic system and its FPGA implementation. Commun. Nonlinear Sci. Numer. Simul. 18(7), 1792–1804 (2012)

    Article  MathSciNet  Google Scholar 

  31. Sadoudi, S., Azzaz, M.S., Djeddou, M., Benssalah, M.: An FPGA real-time implementation of the Chen’s chaotic system for securing chaotic communications. Int. J. Nonlinear Sci. 7(4), 467–474 (2009)

    MathSciNet  Google Scholar 

  32. Wang, G.Y., Bao, X.L., Wang, Z.L.: Design and FPGA Implementation of a new hyperchaotic system. Chin. Phys. B 17(10), 3596–3602 (2008)

    Article  Google Scholar 

  33. Ding, Q., Pang, J., Fang, J., Peng, X.U.: Designing of chaotic system output sequence circuit based FPGA and its application in network encryption card. Int. J. Innov. Comput. Inf. Control 3(2), 449–456 (2007)

    Google Scholar 

  34. Pehlivan, I., Wei, Z.: Analysis, nonlinear control and circuit design of another strange chaotic system. Turk. J. Electr. Eng. Comput. Sci. 20, 1229–1239 (2012)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Control and Automation, Duzce University, Uzunmustafa Mah., Duzce, 81010, Turkey

    Ismail Koyuncu

  2. Department of Computer Engineering, Sakarya University, Serdivan, Sakarya, 54187, Turkey

    Ahmet Turan Ozcerit

  3. Department of Electrical and Electronics Engineering, Sakarya University, Serdivan, Sakarya, 54187, Turkey

    Ihsan Pehlivan

Authors
  1. Ismail Koyuncu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ahmet Turan Ozcerit
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ihsan Pehlivan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ismail Koyuncu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Koyuncu, I., Ozcerit, A.T. & Pehlivan, I. Implementation of FPGA-based real time novel chaotic oscillator. Nonlinear Dyn 77, 49–59 (2014). https://doi.org/10.1007/s11071-014-1272-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-014-1272-x

Keywords

Search

Navigation