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A novel chaotic circuit with coexistence of multiple attractors and state transition based on two memristors

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  • Ma, Xujiong
  • Mou, Jun
  • Xiong, Li
  • Banerjee, Santo
  • Cao, Yinghong
  • Wang, Jieyang

Abstract

A novel chaotic circuit that includes two memristors, an inductor, and a capacitor in parallel is planned, then the dimensionless mathematical model is built. Seven kinds of different attractors are found in the system. Using traditional dynamical analysis methods, the circuit system's equilibrium point and stability are analyzed, and under certain conditions, this system not only has infinite equilibrium points but also has no equilibrium point. Then, the dynamical behaviors with the changing parameter of the system are analyzed in-depth. A wealth of special phenomena has been discovered, such as the multi-state transition and the coexisting attractors. At last, the circuit system is implemented by using the DSP platform, and the theoretical analysis is verified by the results. Theoretical analysis and simulation results show this novel memristive chaotic system has abundant dynamic behaviors. Based on these abundant dynamical characteristics and its self-excited attractors or hidden attractors under different conditions, this circuit system has the potential application in secure communication and image encryption.

Suggested Citation

  • Ma, Xujiong & Mou, Jun & Xiong, Li & Banerjee, Santo & Cao, Yinghong & Wang, Jieyang, 2021. "A novel chaotic circuit with coexistence of multiple attractors and state transition based on two memristors," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921007177
    DOI: 10.1016/j.chaos.2021.111363
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    References listed on IDEAS

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    1. Wang, Jieyang & Mou, Jun & Xiong, Li & Zhang, Yingqian & Cao, Yinghong, 2021. "Fractional-order design of a novel non-autonomous laser chaotic system with compound nonlinearity and its circuit realization," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Wu, Jiening & Wang, Lidan & Chen, Guanrong & Duan, Shukai, 2016. "A memristive chaotic system with heart-shaped attractors and its implementation," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 20-29.
    3. Singh, Jay Prakash & Roy, B.K., 2016. "The nature of Lyapunov exponents is (+, +, −, −). Is it a hyperchaotic system?," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 73-85.
    4. Liu, Tianming & Yan, Huizhen & Banerjee, Santo & Mou, Jun, 2021. "A fractional-order chaotic system with hidden attractor and self-excited attractor and its DSP implementation," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    5. 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.
    6. Fanqi Meng & Xiaoqin Zeng & Zuolei Wang & Xinjun Wang, 2020. "Anti-Synchronization of Fractional-Order Chaotic Circuit with Memristor via Periodic Intermittent Control," Advances in Mathematical Physics, Hindawi, vol. 2020, pages 1-8, January.
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    Cited by:

    1. Du, Chuanhong & Liu, Licai & Zhang, Zhengping & Yu, Shixing, 2022. "A mem-element Wien-Bridge circuit with amplitude modulation and three kinds of offset boosting," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    2. Yildirim, Melih, 2022. "Optical color image encryption scheme with a novel DNA encoding algorithm based on a chaotic circuit," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    3. Wu, Rui & Gao, Suo & Wang, Xingyuan & Liu, Songbo & Li, Qi & Erkan, Uğur & Tang, Xianglong, 2022. "AEA-NCS: An audio encryption algorithm based on a nested chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    4. Lin, Hairong & Wang, Chunhua & Du, Sichun & Yao, Wei & Sun, Yichuang, 2023. "A family of memristive multibutterfly chaotic systems with multidirectional initial-based offset boosting," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

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