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Hybrid State Variable Incremental Integral for Reconstructing Extreme Multistability in Memristive Jerk System with Cubic Nonlinearity

Author

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  • Mo Chen
  • Yang Feng
  • Han Bao
  • Bocheng Bao
  • Huagan Wu
  • Quan Xu

Abstract

Memristive system with infinitely many equilibrium points has attracted much attention for the generation of extreme multistability, whose initial-dependent dynamics can be interpreted in a reduced-order model through incremental integral transformation of state variables. But, the memristive system with any extra nonlinear terms besides the memristor ones cannot be handled directly using this method. In addition, the transformed state variables could be divergent due to the asymmetry of the original system. To solve these problems, a hybrid state variable incremental integral (HSVII) method is proposed in this paper. With this method, the extreme multistability in a four-dimensional (4D) memristive jerk system with cubic nonlinearity is successfully reconstituted in a three-dimensional (3D) model and the divergent state variables are eliminated through ingenious linear state variable mapping. Thus, mechanism analysis and physical control of the special extreme multistability can readily be performed. A hardware circuit is finally designed and fabricated, and the theoretical and numerical results are verified by the experimental measurements. It is demonstrated that this HSVII method is effective for the analysis of multistable system with high-order nonlinearities.

Suggested Citation

  • Mo Chen & Yang Feng & Han Bao & Bocheng Bao & Huagan Wu & Quan Xu, 2019. "Hybrid State Variable Incremental Integral for Reconstructing Extreme Multistability in Memristive Jerk System with Cubic Nonlinearity," Complexity, Hindawi, vol. 2019, pages 1-16, June.
    • Handle: RePEc:hin:complx:8549472
    DOI: 10.1155/2019/8549472
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    References listed on IDEAS

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    1. Chen, M. & Feng, Y. & Bao, H. & Bao, B.C. & Yu, Y.J. & Wu, H.G. & Xu, Q., 2018. "State variable mapping method for studying initial-dependent dynamics in memristive hyper-jerk system with line equilibrium," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 313-324.
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    Cited by:

    1. Huagan Wu & Han Bao & Quan Xu & Mo Chen, 2019. "Abundant Coexisting Multiple Attractors’ Behaviors in Three-Dimensional Sine Chaotic System," Complexity, Hindawi, vol. 2019, pages 1-11, December.
    2. Wang, Zhen & Ahmadi, Atefeh & Tian, Huaigu & Jafari, Sajad & Chen, Guanrong, 2023. "Lower-dimensional simple chaotic systems with spectacular features," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    3. Yunzhen Zhang & Zhong Liu & Mo Chen & Huagan Wu & Shengyao Chen & Bocheng Bao, 2019. "Dimensionality Reduction Reconstitution for Extreme Multistability in Memristor-Based Colpitts System," Complexity, Hindawi, vol. 2019, pages 1-12, November.
    4. Chen, Mo & Wang, Chao & Bao, Han & Ren, Xue & Bao, Bocheng & Xu, Quan, 2020. "Reconstitution for interpreting hidden dynamics with stable equilibrium point," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. Chen, Mo & Ren, Xue & Wu, Huagan & Xu, Quan & Bao, Bocheng, 2020. "Interpreting initial offset boosting via reconstitution in integral domain," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).

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