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Design of a New Chaotic System Based on Van Der Pol Oscillator and Its Encryption Application

Author

Listed:
  • Jianbin He

    (College of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, China
    Institute of Digital Fujian Meteorological Big Data, Minnan Normal University, Zhangzhou 363000, China)

  • Jianping Cai

    (College of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, China
    Institute of Digital Fujian Meteorological Big Data, Minnan Normal University, Zhangzhou 363000, China)

Abstract

The Van der Pol oscillator is investigated by the parameter control method. This method only needs to control one parameter of the Van der Pol oscillator by a simple periodic function; then, the Van der Pol oscillator can behave chaotically from the stable limit cycle. Based on the new Van der Pol oscillator with variable parameter (VdPVP), some dynamical characteristics are discussed by numerical simulations, such as the Lyapunov exponents and bifurcation diagrams. The numerical results show that there exists a positive Lyapunov exponent in the VdPVP. Therefore, an encryption algorithm is designed by the pseudo-random sequences generated from the VdPVP. This simple algorithm consists of chaos scrambling and chaos XOR (exclusive-or) operation, and the statistical analyses show that it has good security and encryption effectiveness. Finally, the feasibility and validity are verified by simulation experiments of image encryption.

Suggested Citation

  • Jianbin He & Jianping Cai, 2019. "Design of a New Chaotic System Based on Van Der Pol Oscillator and Its Encryption Application," Mathematics, MDPI, vol. 7(8), pages 1-12, August.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:743-:d:257330
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    References listed on IDEAS

    as
    1. Makouo, L. & Woafo, P., 2017. "Experimental observation of bursting patterns in Van der Pol oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 95-101.
    2. Vinícius Wiggers & Paulo C. Rech, 2018. "On symmetric and asymmetric Van der Pol-Duffing oscillators," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 91(7), pages 1-6, July.
    3. Wiggers, Vinícius & Rech, Paulo C., 2017. "Multistability and organization of periodicity in a Van der Pol–Duffing oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 103(C), pages 632-637.
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