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Extreme Multistability and Its Incremental Integral Reconstruction in a Non-Autonomous Memcapacitive Oscillator

Author

Listed:
  • Bei Chen

    (School of Microelectronics and Control Engineering, Changzhou University, Changzhou 213164, China)

  • Xinxin Cheng

    (School of Microelectronics and Control Engineering, Changzhou University, Changzhou 213164, China)

  • Han Bao

    (School of Microelectronics and Control Engineering, Changzhou University, Changzhou 213164, China)

  • Mo Chen

    (School of Microelectronics and Control Engineering, Changzhou University, Changzhou 213164, China)

  • Quan Xu

    (School of Microelectronics and Control Engineering, Changzhou University, Changzhou 213164, China)

Abstract

Extreme multistability has frequently been reported in autonomous circuits involving memory-circuit elements, since these circuits possess line/plane equilibrium sets. However, this special phenomenon has rarely been discovered in non-autonomous circuits. Luckily, extreme multistability is found in a simple non-autonomous memcapacitive oscillator in this paper. The oscillator only contains a memcapacitor, a linear resistor, a linear inductor, and a sinusoidal voltage source, which are connected in series. The memcapacitive system model is firstly built for further study. The equilibrium points of the memcapacitive system evolve between a no equilibrium point and a line equilibrium set with the change in time. This gives rise to the emergence of extreme multistability, but the forming mechanism is not clear. Thus, the incremental integral method is employed to reconstruct the memcapacitive system. In the newly reconstructed system, the number and stability of the equilibrium points have complex time-varying characteristics due to the presence of fold bifurcation. Furthermore, the forming mechanism of the extreme multistability is further explained. Note that the initial conditions of the original memcapacitive system are mapped onto the controlling parameters of the newly reconstructed system. This makes it possible to achieve precise control of the extreme multistability. Furthermore, an analog circuit is designed for the reconstructed system, and then PSIM circuit simulations are performed to verify the numerical results.

Suggested Citation

  • Bei Chen & Xinxin Cheng & Han Bao & Mo Chen & Quan Xu, 2022. "Extreme Multistability and Its Incremental Integral Reconstruction in a Non-Autonomous Memcapacitive Oscillator," Mathematics, MDPI, vol. 10(5), pages 1-13, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:754-:d:759475
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Joseph S. Najem & Md Sakib Hasan & R. Stanley Williams & Ryan J. Weiss & Garrett S. Rose & Graham J. Taylor & Stephen A. Sarles & C. Patrick Collier, 2019. "Dynamical nonlinear memory capacitance in biomimetic membranes," Nature Communications, Nature, vol. 10(1), pages 1-11, December.
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    4. Daniel A. Magallón & Rider Jaimes-Reátegui & Juan H. García-López & Guillermo Huerta-Cuellar & Didier López-Mancilla & Alexander N. Pisarchik, 2022. "Control of Multistability in an Erbium-Doped Fiber Laser by an Artificial Neural Network: A Numerical Approach," Mathematics, MDPI, vol. 10(17), pages 1-20, September.

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