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Dynamics analysis and predefined-time sliding mode synchronization of multi-scroll systems based on a single memristor model

Author

Listed:
  • Yan, Shaohui
  • Wu, Xinyu
  • Jiang, Jiawei

Abstract

To overcome the limitations of conventional designs for memristive multi-scroll chaotic systems, this paper introduces a novel memristor that relies solely on a single memristor function and a single state variable function to generate both odd and even numbers of double-scroll attractors. This design not only simplifies the memristor structure but also offers a new approach to constructing multi-scroll chaotic systems. The proposed memristor is integrate into a modified Sprott-C system to develop the one-dimensional memristive multi-scroll Sprott-C systems (1D-MMSCS), two-dimensional memristive multi-scroll Sprott-C systems (2D-MMSCS), and the three-dimensional memristive multi-scroll Sprott-C systems (3D-MMSCS). The complex dynamics of these memristive multi-scroll systems are analyzed using equilibrium points, Poincaré maps, bifurcation diagrams, and Lyapunov exponents. Interestingly, the constructed MMSCS exhibits extreme multi-stability, indicating its high sensitivity to initial conditions and enhanced unpredictability. To verify the practical feasibility of the system, it is developed a digital hardware platform based on a Field-Programmable Gate Array (FPGA) and successfully implemented both the 1D-MMSCS and 2D-MMSCS. Finally, leveraging Lyapunov stability theory and predefined-time stability theory, a novel predefined-time sliding mode control scheme (PTSMS) is proposed. This scheme is applied to achieve synchronization in the more complex 3D-MMSCS. Simulation results confirm that the proposed method ensures rapid synchronization and exhibits strong robustness against internal uncertainties and external disturbances.

Suggested Citation

  • Yan, Shaohui & Wu, Xinyu & Jiang, Jiawei, 2025. "Dynamics analysis and predefined-time sliding mode synchronization of multi-scroll systems based on a single memristor model," Chaos, Solitons & Fractals, Elsevier, vol. 196(C).
    • Handle: RePEc:eee:chsofr:v:196:y:2025:i:c:s0960077925003509
    DOI: 10.1016/j.chaos.2025.116337
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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.
    2. Zhang, Lingshuang & Li, Zhijun & Peng, Yuexi, 2024. "A hidden grid multi-scroll chaotic system coined with two multi-stable memristors," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    3. Wang, Ran & Li, Chunbiao & Kong, Sixiao & Jiang, Yicheng & Lei, Tengfei, 2022. "A 3D memristive chaotic system with conditional symmetry," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    4. Biamou, Arsene Loic Mbanda & Tamba, Victor Kamdoum & Tagne, François Kapche & Takougang, Armand Cyrille Nzeukou, 2024. "Fractional-order-induced symmetric multi-scroll chaotic attractors and double bubble bifurcations in a memristive coupled Hopfield neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    5. Chen, Qun & Li, Bo & Yin, Wei & Jiang, Xiaowei & Chen, Xiangyong, 2023. "Bifurcation, chaos and fixed-time synchronization of memristor cellular neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    6. 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.
    7. Beyhan, Selami, 2024. "An experimental set-up design for synchronization and control of coupled Hindmarsh–Rose neurons with Markov-jump dynamics: A case study on finite-time sliding-mode synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    8. Yu, Fei & Kong, Xinxin & Yao, Wei & Zhang, Jin & Cai, Shuo & Lin, Hairong & Jin, Jie, 2024. "Dynamics analysis, synchronization and FPGA implementation of multiscroll Hopfield neural networks with non-polynomial memristor," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    9. Zhang, Tianxian & Zhao, Yongqi & Xu, Xiangliang & Wu, Si & Gu, Yujuan, 2024. "Solution and dynamics analysis of fractal-fractional multi-scroll Chen chaotic system based on Adomain decomposition method," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    10. Zhou, Ping & Ma, Jun & Xu, Ying, 2023. "Phase synchronization between neurons under nonlinear coupling via hybrid synapse," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    11. 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.
    12. Rouzimaimaiti Mahemuti & Abdujelil Abdurahman, 2023. "Predefined-Time (PDT) Synchronization of Impulsive Fuzzy BAM Neural Networks with Stochastic Perturbations," Mathematics, MDPI, vol. 11(6), pages 1-18, March.
    13. Lai, Qiang & Chen, Zhijie, 2023. "Dynamical analysis and finite-time synchronization of grid-scroll memristive chaotic system without equilibrium," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    14. Xin, Zeng-Jun & Lai, Qiang, 2024. "Dynamical investigation and encryption application of a new multiscroll memristive chaotic system with rich offset boosting features," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    15. Xue, Haibo & Liu, Xinghua, 2023. "A novel fast terminal sliding mode with predefined-time synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    16. Sahoo, Shilalipi & Roy, Binoy Krishna, 2022. "Design of multi-wing chaotic systems with higher largest Lyapunov exponent," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    17. Tabekoueng Njitacke, Zeric & Tsafack, Nestor & Ramakrishnan, Balamurali & Rajagopal, Kartikeyan & Kengne, Jacques & Awrejcewicz, Jan, 2021. "Complex dynamics from heterogeneous coupling and electromagnetic effect on two neurons: Application in images encryption," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    18. Balaraman, Sundarambal & Kengne, Jacques & Kamga Fogue, M.S. & Rajagopal, Karthikeyan, 2023. "From coexisting attractors to multi-spiral chaos in a ring of three coupled excitation-free Duffing oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    19. 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).
    20. Wang, Shasha & Jian, Jigui, 2023. "Predefined-time synchronization of fractional-order memristive competitive neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
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