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Mathematical and Experimental Model of Neuronal Oscillator Based on Memristor-Based Nonlinearity

Author

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  • Ivan Kipelkin

    (Laboratory of Stochastic Multistable Systems, National Research Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod 603022, Russia
    Institute of Nanotechnologies Electronics and Equipment Engineering, Southern Federal University, Taganrog 347922, Russia)

  • Svetlana Gerasimova

    (Laboratory of Stochastic Multistable Systems, National Research Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod 603022, Russia)

  • Davud Guseinov

    (Laboratory of Stochastic Multistable Systems, National Research Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod 603022, Russia)

  • Dmitry Pavlov

    (Laboratory of Stochastic Multistable Systems, National Research Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod 603022, Russia)

  • Vladislav Vorontsov

    (Laboratory of Stochastic Multistable Systems, National Research Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod 603022, Russia)

  • Alexey Mikhaylov

    (Laboratory of Stochastic Multistable Systems, National Research Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod 603022, Russia
    Institute of Nanotechnologies Electronics and Equipment Engineering, Southern Federal University, Taganrog 347922, Russia)

  • Victor Kazantsev

    (Laboratory of Stochastic Multistable Systems, National Research Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod 603022, Russia
    Institute of Nanotechnologies Electronics and Equipment Engineering, Southern Federal University, Taganrog 347922, Russia)

Abstract

This article presents a mathematical and experimental model of a neuronal oscillator with memristor-based nonlinearity. The mathematical model describes the dynamics of an electronic circuit implementing the FitzHugh–Nagumo neuron model. A nonlinear component of this circuit is the Au/Zr/ZrO 2 (Y)/TiN/Ti memristive device. This device is fabricated on the oxidized silicon substrate using magnetron sputtering. The circuit with such nonlinearity is described by a three-dimensional ordinary differential equation system. The effect of the appearance of spontaneous self-oscillations is investigated. A bifurcation scenario based on supercritical Andronov–Hopf bifurcation is found. The dependence of the critical point on the system parameters, particularly on the size of the electrode area, is analyzed. The self-oscillating and excitable modes are experimentally demonstrated.

Suggested Citation

  • Ivan Kipelkin & Svetlana Gerasimova & Davud Guseinov & Dmitry Pavlov & Vladislav Vorontsov & Alexey Mikhaylov & Victor Kazantsev, 2023. "Mathematical and Experimental Model of Neuronal Oscillator Based on Memristor-Based Nonlinearity," Mathematics, MDPI, vol. 11(5), pages 1-17, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1268-:d:1088956
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    References listed on IDEAS

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    1. Minati, L. & Gambuzza, L.V. & Thio, W.J. & Sprott, J.C. & Frasca, M., 2020. "A chaotic circuit based on a physical memristor," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    2. Lin, Yi & Liu, Wenbo & Hang, Cheng, 2023. "Revelation and experimental verification of quasi-periodic bursting, periodic bursting, periodic oscillation in third-order non-autonomous memristive FitzHugh-Nagumo neuron circuit," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    3. Suhas Kumar & John Paul Strachan & R. Stanley Williams, 2017. "Chaotic dynamics in nanoscale NbO2 Mott memristors for analogue computing," Nature, Nature, vol. 548(7667), pages 318-321, August.
    4. Gerasimova, S.A. & Lebedeva, A.V. & Fedulina, A. & Koryazhkina, M. & Belov, A.I. & Mishchenko, M.A. & Matveeva, M. & Guseinov, D. & Mikhaylov, A.N. & Kazantsev, V.B. & Pisarchik, A.N., 2021. "A neurohybrid memristive system for adaptive stimulation of hippocampus," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
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    Cited by:

    1. Takaishvili, Lev V. & Ponomarenko, Vladimir I. & Sysoev, Ilya V., 2025. "Simple tunable generator of neuron-like activity," Chaos, Solitons & Fractals, Elsevier, vol. 196(C).
    2. Sergey V. Stasenko & Alexey N. Mikhaylov & Victor B. Kazantsev, 2023. "Control of Network Bursting in a Model Spiking Network Supplied with Memristor—Implemented Plasticity," Mathematics, MDPI, vol. 11(18), pages 1-14, September.

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