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

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/ZrO2(Y)/TiN...

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Bibliographic Details
Published in:Mathematics (Basel) 2023-03, Vol.11 (5), p.1268
Main Authors: Kipelkin, Ivan, Gerasimova, Svetlana, Guseinov, Davud, Pavlov, Dmitry, Vorontsov, Vladislav, Mikhaylov, Alexey, Kazantsev, Victor
Format: Article
Language:English
Subjects:
Circuit design
Circuits
Critical point
Design and construction
Differential equations
Electronic circuits
Hopf bifurcation
Magnetron sputtering
Mathematical models
Memory devices
memristor-based nonlinearity
Memristors
Methods
neuron-like oscillator
Neurons
Nonlinearity
Oscillators
Oscillators (Electronics)
Self oscillation
Semiconductors
Silicon substrates
supercritical Andronov–Hopf bifurcation
Transmission electron microscopy
Zirconium dioxide
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Summary: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/ZrO2(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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11051268