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.

In this manuscript, we investigate the memristor-based implementation of neuronal ion channels in a mathematical model and an experimental circuit for a neuronal oscillator. We used a FitzHugh-Nagumo equation system describing neuronal excitability. Non-linearities introduced by the voltage-gated ion channels were modeled using memristive devices. We implemented three basic neuronal excitability modes including the excitable mode corresponding to a single spike generation, self-oscillation stable limit cycle mode with periodic spike trains and bistability between a fixed point and a limit cycle. We also found the spike-burst activity of mathematical and experimental models under certain system parameters. Modeling synaptic transmission, we simulated postsynaptic response triggered by periodic pulse stimulation. We found that due to the charge accumulation effect in the memristive device, the electronic synapse implemented a qualitatively bio-plausible synapse with a potentiation effect with increasing amplitude of the response triggered by a spike sequence.

This article presents a unified benchmark of energy consumption per synaptic event across five classes of neuro-computational substrates: graphics processing units, neural processing units, field-programmable gate arrays, digital spiking processors, and in-memory/memristive devices, with biological synapses used as reference bands. The main contribution is methodological as well as empirical. Methodologically, we introduce a common event-level metric that makes heterogeneous systems directly comparable despite major differences in architecture, coding scheme, and learning dynamics. Empirically, we combine measurements obtained by the authors with carefully normalized literature data to map the present energy landscape of artificial and biological neural computation. The results reveal three robust regimes. Dense von Neumann ANN implementations on GPUs, NPUs, and FPGA operate mainly in the $10^{5}$ to $10^{8}$ fJ range per synaptic event. Digital spiking processors reduce this requirement to about $10^{3}$ to $10^{4}$ fJ per event. Memristive and transistor-based artificial synapses span a much broader interval, from array-level values near $10^{6}$ fJ down to a few femtojoules in the most efficient device-level realizations. In particular, the best organic PANI memristive samples approach ~2 fJ per synaptic event, entering the biological vicinity and, in some cases, surpassing the rat reference range. Taken together, the benchmarked landscape spans up to ten orders of magnitude across the full set of systems considered in this study. This result clarifies where current AI hardware stands relative to biological efficiency, identifies event-driven and in-memory computation as the most promising routes toward sustainable AI, and provides a quantitatively grounded reference framework for future neuromorphic benchmarking. INDEX TERMS Artificial neural networks, energy consumption, energy efficiency, memristive devices, neuromorphic computing, spiking neural networks, sustainable AI.