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

Ivan Kipelkin (), Svetlana Gerasimova, Davud Guseinov, Dmitry Pavlov, Vladislav Vorontsov, Alexey Mikhaylov and Victor Kazantsev
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Ivan Kipelkin: Laboratory of Stochastic Multistable Systems, National Research Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod 603022, 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
Victor Kazantsev: Laboratory of Stochastic Multistable Systems, National Research Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod 603022, Russia

Mathematics, 2023, vol. 11, issue 5, 1-17

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.

Keywords: supercritical Andronov–Hopf bifurcation; memristor-based nonlinearity; neuron-like oscillator; self-oscillation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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