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State variable mapping method for studying initial-dependent dynamics in memristive hyper-jerk system with line equilibrium

Author

Listed:
  • Chen, M.
  • Feng, Y.
  • Bao, H.
  • Bao, B.C.
  • Yu, Y.J.
  • Wu, H.G.
  • Xu, Q.

Abstract

Memristive hyper-jerk system has been reported to exhibit the initial-dependent multistability phenomenon, whose dynamical mechanism and control strategy deserve further in-depth investigations. However, a more effective method is required for the existence of line equilibrium. Inspired by the dimensionality decreasing flux-charge analysis method, we handle these problems via state variable mapping (SVM) method of integral transformation. With this method, the hyper-jerk system characterized by four autonomous differential equations can be reconstructed and a dimensionality decreasing model is obtained. In the newly formulated system, the initial conditions of the original system are mapped as standalone system parameters. Thus, the initial-dependent multi-stability phenomenon is transformed into the easily controlled parameter-relied dynamics, which facilitates physical direction of multi-stable system's operation mode in hardware circuit. Specially, the line equilibrium point exhibited in the voltage-current model is mapped as two determined equilibria. Thus, the dynamics of coexisting infinitely many attractors and their forming mechanisms are readily investigated in the newly constructed system. Moreover, a hardware circuit is designed and fabricated, whose operation mode is rigorously controlled by applying additional DC signals which are proportional to the specified initial conditions. Through circuit simulations and experimental measurements, it is demonstrated that the SVM method offers a direction for interpretation and control of multistability in memristive systems without any determined equilibrium.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:chsofr:v:115:y:2018:i:c:p:313-324
    DOI: 10.1016/j.chaos.2018.07.025
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    References listed on IDEAS

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    1. Njitacke, Z.T. & kengne, J. & Fotsin, H.B. & Negou, A. Nguomkam & Tchiotsop, D., 2016. "Coexistence of multiple attractors and crisis route to chaos in a novel memristive diode bidge-based Jerk circuit," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 180-197.
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    Cited by:

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    2. 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.
    3. Bao, B. & Peol, M.A. & Bao, H. & Chen, M. & Li, H. & Chen, B., 2021. "No-argument memristive hyper-jerk system and its coexisting chaotic bubbles boosted by initial conditions," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    4. Wu, H.G. & Ye, Y. & Bao, B.C. & Chen, M. & Xu, Q., 2019. "Memristor initial boosting behaviors in a two-memristor-based hyperchaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 121(C), pages 178-185.
    5. Zhang, Yunzhen & Liu, Zhong & Wu, Huagan & Chen, Shengyao & Bao, Bocheng, 2019. "Two-memristor-based chaotic system and its extreme multistability reconstitution via dimensionality reduction analysis," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 354-363.
    6. Bao, Bocheng & Zhang, Xi & Bao, Han & Wu, Pingye & Wu, Zhimin & Chen, Mo, 2019. "Dynamical effects of memristive load on peak current mode buck-boost switching converter," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 69-79.
    7. Guo, Yeye & Wang, Chunni & Yao, Zhao & Xu, Ying, 2022. "Desynchronization of thermosensitive neurons by using energy pumping," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 602(C).
    8. Makenne, Y.L. & Kengne, R. & Pelap, F.B., 2019. "Coexistence of multiple attractors in the tree dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 70-82.
    9. 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.
    10. 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).
    11. 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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