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Chaotic Attractors Generated by a Memristor-Based Chaotic System and Julia Fractal

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  • Yan, Dengwei
  • Wang, Lidan
  • Duan, Shukai
  • Chen, Jiaojiao
  • Chen, Jiahao

Abstract

A chaotic system has many applications in random number generator, image encryption, and secure communication. It is essential to present abundant chaotic attractors in a single chaotic system. Thus a novel 3D chaotic system based on memristor is designed and analyzed. The system's key advantages are as follows: firstly, both the multi-scroll and extended chaotic attractors are produced by merely modifying system parameters. The complex dynamical phenomena, such as coexisting multiple multi-scroll chaotic attractors, transient phenomenon and state transformation, can be observed; secondly, the proposed system combines with the classical Julia fractal and Julia deformation forms, respectively, and fascinating and various circular chaotic attractors are generated, which take good advantage of the combination of a memristor-based chaotic system and Julia fractal. Meanwhile, by applying both dynamic analysis and numerical simulation, basic behaviors of the system, such as stability of equilibrium point, dissipation and symmetry, Poincare maps, instantaneous phase, 0-1 test and power spectrum are employed to illustrate the superiority of the system. Some rather impressive and promising applications of the proposed chaotic system to chaotic confidential communication and image encryption will be achieved later.

Suggested Citation

  • Yan, Dengwei & Wang, Lidan & Duan, Shukai & Chen, Jiaojiao & Chen, Jiahao, 2021. "Chaotic Attractors Generated by a Memristor-Based Chaotic System and Julia Fractal," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    • Handle: RePEc:eee:chsofr:v:146:y:2021:i:c:s0960077921001259
    DOI: 10.1016/j.chaos.2021.110773
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    References listed on IDEAS

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    1. Bao, B.C. & Bao, H. & Wang, N. & Chen, M. & Xu, Q., 2017. "Hidden extreme multistability in memristive hyperchaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 102-111.
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    3. Dmitri B. Strukov & Gregory S. Snider & Duncan R. Stewart & R. Stanley Williams, 2008. "The missing memristor found," Nature, Nature, vol. 453(7191), pages 80-83, May.
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    Cited by:

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    2. Zhao, Hongyu & Wang, Shengsheng & Wang, Xingyuan, 2022. "Fast image encryption algorithm based on multi-parameter fractal matrix and MPMCML system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Sahoo, Shilalipi & Roy, Binoy Krishna, 2022. "Design of multi-wing chaotic systems with higher largest Lyapunov exponent," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    4. Liu, Hongwei & He, Ping & Li, Guodong & Xu, Xiangliang & Zhong, Huiyan, 2022. "Multi-directional annular multi-wing chaotic system based on Julia fractals," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    5. Mohamed, Sara M. & Sayed, Wafaa S. & Said, Lobna A. & Radwan, Ahmed G., 2022. "FPGA realization of fractals based on a new generalized complex logistic map," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    6. Yang, Min & Dong, Chengwei & Pan, Hepeng, 2024. "Generating multi-directional hyperchaotic attractors: A novel multi-scroll system based on Julia fractal," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
    7. Hairong Lin & Chunhua Wang & Fei Yu & Jingru Sun & Sichun Du & Zekun Deng & Quanli Deng, 2023. "A Review of Chaotic Systems Based on Memristive Hopfield Neural Networks," Mathematics, MDPI, vol. 11(6), pages 1-18, March.

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