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Hidden Dynamics of a New Jerk-like System with a Smooth Memristor and Applications in Image Encryption

Author

Listed:
  • Zuolei Wang

    (School of Mathematics and Statistics, Yancheng Teachers University, Yancheng 224002, China)

  • Lizhou Zhuang

    (School of Mathematics and Statistics, Yancheng Teachers University, Yancheng 224002, China)

  • Jianjiang Yu

    (School of Information Engineering, Yancheng Teachers University, Yancheng 224002, China)

  • Haibo Jiang

    (School of Mathematics and Statistics, Yancheng Teachers University, Yancheng 224002, China)

  • Wanjiang Xu

    (School of Mathematics and Statistics, Yancheng Teachers University, Yancheng 224002, China)

  • Xuerong Shi

    (School of Mathematics and Statistics, Yancheng Teachers University, Yancheng 224002, China)

Abstract

Considering the dynamic characteristics of memristors, a new Jerk-like system without an equilibrium point is addressed based on a Jerk-like system, and the hidden dynamics are investigated. When changing system parameter b and fixing other parameters, the proposed system shows various hidden attractors, such as a hidden chaotic attractor ( b = 5), a hidden period-1 attractor ( b = 3.2), and a hidden period-2 attractor ( b = 4). Furthermore, bifurcation analysis suggests that not only parameter b , but also the initial conditions of the system, have an effect on the hidden dynamics of the discussed system. The coexistence of various hidden attractors is explored and different coexistences of hidden attractors can be found for suitable system parameters. Offset boosting of different hidden attractors is discussed. It is observed that offset boosting can occur for hidden chaotic attractor, period-1 attractor, and period-2 attractor, but not for period-3 attractor and period-4 attractor. The antimonotonicity of the proposed system is debated and a full Feigenbaum remerging tree can be detected when system parameters a or b change within a certain range. On account of the complicated dynamics of the proposed system, an image encryption scheme is designed, and its encryption effectiveness is analyzed via simulation and comparison.

Suggested Citation

  • Zuolei Wang & Lizhou Zhuang & Jianjiang Yu & Haibo Jiang & Wanjiang Xu & Xuerong Shi, 2023. "Hidden Dynamics of a New Jerk-like System with a Smooth Memristor and Applications in Image Encryption," Mathematics, MDPI, vol. 11(22), pages 1-18, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4613-:d:1278042
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    References listed on IDEAS

    as
    1. A. E. Matouk & T. N. Abdelhameed & D. K. Almutairi & M. A. Abdelkawy & M. A. E. Herzallah, 2023. "Existence of Self-Excited and Hidden Attractors in the Modified Autonomous Van Der Pol-Duffing Systems," Mathematics, MDPI, vol. 11(3), pages 1-13, January.
    2. Zhang, Sen & Zeng, Yicheng, 2019. "A simple Jerk-like system without equilibrium: Asymmetric coexisting hidden attractors, bursting oscillation and double full Feigenbaum remerging trees," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 25-40.
    3. Leutcho, Gervais Dolvis & Kengne, Jacques, 2018. "A unique chaotic snap system with a smoothly adjustable symmetry and nonlinearity: Chaos, offset-boosting, antimonotonicity, and coexisting multiple attractors," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 275-293.
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