This paper presents a mathematical model and hardware implementation of synaptically coupled neurons, realized by two modified FitzHugh-Nagumo oscillators interconnected via an inorganic memristive device. Our study focuses on the adaptive characteristics of the memristive device as a function of the driving signal parameters, thereby capturing key features of synaptic plasticity observed in biological systems. We provide experimental measurements of the average relative change in memristive resistance, which serves as the effective coupling coefficient in our mathematical model. Furthermore, we identify the optimal duty cycle of the master oscillator and demonstrate its direct impact on both the coupling strength and the oscillation amplitude. Through a combination of computational modeling and experimental validation, we reveal synchronization regimes at the natural frequency, as well as at harmonic and subharmonic frequencies. The corresponding phase-space structures of the coupled system are analyzed in detail, providing insight into the underlying dynamical mechanisms governing memristive synaptic interaction.

In this work, we investigate the adaptive dynamics in spiking neural networks with a novel memristive STDP approach based on pulse-width modulation. We propose a memristor state control scheme in which pre- and post-synaptic neuronal spikes, owing to their low amplitude, do not directly change the memristor state but instead activate an additional block that influences the memristor. The memristor state is effectively controlled with a single discrete rectangular pulse, the width and polarity of which are determined by the pre–post spike timing difference. We conduct numerical simulations based on a second-order memristor model to study the proposed approach and experimentally validate the method. The resulting changes in the memristor state parameter obtained from both experimental measurements and numerical simulations closely resemble classical STDP rules of synaptic plasticity. We test this approach by demonstrating cluster formation under external stimulation, similar to classical STDP. We also investigate the learning capabilities in a spiking neural network with the proposed approach and demonstrate successful detection of a repeating temporal pattern embedded in noise through self-organization of memristive STDP connections. The obtained results contribute to biologically plausible implementations of memristive plasticity and to the advancement of neuromorphic technologies based on energy-efficient information processing.

In this work, we investigate the possibility of learning in spiking neural network with connections based on the model of Au/Ta/ZrO2(Y)/Ta2O5/TiN/Ti memristive devices. These memristive connections demonstrate STDP obtained by pulse-width modulation. We demonstrate that the output neuron successfully learns a temporal pattern by self-organization of memristive connections with proposed STDP mechanism. The output neuron is capable to learn a pattern interspersed with noise due to memristive STDP with pulse-width modulation. We have noted that the efficiency of neuron learning depends on the frequency of pattern presentation in this model, which is due to the fact that the model is based on memristive devices with spike-rate-dependent plasticity. The obtained results suggest that similar self-learning process could be implemented using physical memristive devices and allow to develop neuromorphic technologies that implement the principles of energy-efficient information processing.

In this study we have investigated the impact of the changes induced by ion irradiation on the performance and reliability of Au/Ta/ZrO2(Y)/Pt/Ti memristive devices. A comprehensive experimental approach was employed, involving irradiation with various ion species, including H+, Ne+, O+, and Kr+ to simulate different radiation environments. Thus, advanced statistical and modeling techniques to analyze the effects of irradiation on the resistive switching (RS) characteristics of the devices have been employed. Results revealed alterations in the post-irradiation RS parameters, including set and reset voltages and currents. These changes were found to depend on the ion species and dosage, with heavier ions such as Kr+ causing more pronounced effects. The findings are supported by detailed Monte Carlo simulations, which provided insights into the distribution of vacancies within the memristive devices under neutron irradiation. The experimental data, combined with the modeling results, indicate that RS is generally tolerant to radiation, although ion irradiation can lead to the formation of defect structures that affect the switching parameters of memristive devices.

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.

The influence of spin-flip scattering on the generation of spin currents in n-type silicon is studied. Doping of silicon by heavy donors, such as bismuth or antimony, leads to an additional spin scattering of conduction electrons on the impurity-induced spin-orbit potential. Based on the diffusion model and the theory of spin pumping spin current and inverse-spin-Hall effect voltage are considered for different types of donors with various concentrations and spin diffusion lengths. Calculations yield the dependence of the inverse spin-Hall effect signal on the parameters of bismuth-doped silicon layers and also explain the absence of such signal for silicon layers doped by phosphorus or antimony.

Development of new non-toxic pigments of a wide range of applications (from coloring of bone cements to aesthetic cosmetology, including tattooing) of blue and green shades is an urgent task. In the present work, colored compounds with apatite structure were synthesized by solid-phase method. The obtained products were crystallized in hexagonal syngony of P6(3)/m space group. The alloying elements - chromophores Mn5+ and Cr5+ in tetrahedrally coordinated positions - were responsible for sky-blue and turquoise colors of the compounds, respectively. The conducted complex study (crystal structure, IR spectroscopy, color measurements, diffuse reflectance spectroscopy, electron paramagnetic resonance, cytotoxicity, surface morphology) of the colored compounds opens new opportunities for the development of alternative pigments of similar color range and expansion of the field of application of pigments based on compounds of apatite structural type. The results of in vitro study of cytotoxicity demonstrated the potential suitability of sky-blue color compound (Mn-containing apatite) for further creation of cold pigments on its basis for tattoo ink and bone cement coloring.

The lithium donor centers in Si 1– x Ge x ( x = 0.0039–0.05) single crystals enriched in spinless 28 Si and 72 Ge isotopes (99.998 and 99.984%, respectively) are studied by electron spin resonance at temperatures of T = 3.5–30 K and compared with its behavior in Si crystals. It is shown that lithium center with trigonal ([111]) symmetry has a most stable configuration in bulk Si 1– x Ge x for different values of x < 5 at %. Axial symmetry is explained by the distortion of the lithium central position and their neighboring atoms. The spin relaxation rates were studied in temperature range 4–30 K and it was shown that transverse and longitudinal relaxation consist of two components with rates differ by almost an order of magnitude. Together with Raman processes for 1/T 1 , a decrease in the exponent below T 5 is observed. This behavior is explained by cross-relaxation through states of the distorted configuration of lithium, which arise due to modulation of the crystal field potential by random distribution of Ge atoms.

The lithium donor centers in Si1–xGex (x = 0.0039–0.05) single crystals enriched in spinless 28Si and 72Ge isotopes (99.998 and 99.984

A transition is made from piecemeal functions of the memristor model with threshold type switching to differentiable functions described by a single formula. Systems of equations are obtained and numerically solved for circuit sections in which the memristive device is connected in series with other discrete elements, a conventional resistor, diode, inductor, and capacitor. For the case of a serial connection of a memristor and a resistor, the calculated data are compared with the experiment. The case of series connection of a memristor and a semiconductor diode has been studied in detail. The assumptions concerning the mathematical description and physical interpretation of the influence of the electroforming process on the memristive system are presented.

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 brief, we classify the instantaneous response of resistors with memory into three types: linear (L), separable nonlinear (SN), and non-separable nonlinear (NSN). A particular model of an NSN-type memristive device is introduced and used to demonstrate the possibility of rich dynamics in the memristor-capacitor circuit subjected to a sinusoidal voltage. In particular, our numerical simulations reveal the regimes of double period oscillations, multiple period oscillations, and chaotic oscillations. The comparison with L-type and SN-type memristive devices described by the same differential state equation indicates the importance of the NSN-type response to achieve such complex dynamics in the memristor-capacitor circuit with a first-order memristive device. Moreover, we demonstrate that a compound NSN-type memristive device can be assembled using one L-type memristive device, two resistors, and two diodes. The complex behavior of such compound devices is verified using SPICE modeling.

We develop a model of Au/Ta/ZrO2(Y)/Ta2O5/TiN/Ti memristive devices and demonstrate, both experimentally and numerically, an inverted spike-rate-dependent plasticity effect. The effect consists of the reduction of the learning rate with an increase in the frequency of spikes generated by the phase-locked loop neuron. The memristor model uses two internal state variables representing the number of complete filaments and the concentration of the charged traps. While the former state variable defines the device resistance and is associated with the distribution of oxygen vacancies, the latter affects the internal electric field and modulates the migration of vacancies. Several neural circuit configurations that include pairs and populations of memristively coupled neurons are analyzed numerically. The results of this study may contribute to the development of large-scale self-organized artificial cognitive systems based on neural synchrony.

We propose a mathematical model of the Fitzhugh-Nagumo neuron employing memristor-based nonlinearity. The model implements excitable and oscillatory regimes of neuron-like firing. We obtain and analyze various dynamical modes of the memristor-based FitzHugh-Nagumo neuron.

The memristor is a simple two-terminal device that can be realized as a capacitor-like thin film stack demonstrating the effect of resistive switching (resistive memory) due to atomic (defect) reconstruction, when a voltage of a certain polarity and magnitude is applied. The main physicochemical phenomena associated with the diffusion and drift of oxygen ions (vacancies), local processes of formation and reduction-oxidation of conducting channels (filaments) in different metal-oxide materials are considered in this chapter. The conclusions about the filamentary nature of resistive switching are supported by the local electrical characterization of thin oxide films with scanning probe microscopy techniques and multiscale simulation of electroforming and switching by using phenomenological approaches, ab initio, molecular dynamics and kinetic Monte Carlo methods.

Предложена оригинальная модель резистивного переключения металлооксидных мемристивных устройств. Эффективность и гибкость подхода продемонстрированы на примере экспериментально реализованных структур Au/oxide/TiN.

Doping of silicon with bismuth leads to additional spin scattering of the conduction electron by the spin-orbit potential introduced by a heavy donor. In this paper, we discuss spin flip scattering influence on the generation of spin currents in silicon with electronic conductivity. Based on the theory of spin pumping and the diffusion model, the values of spin currents and voltages of the ISHE are calculated with varying the type of donor and its concentration and the spin diffusion lengths. Calculations made it possible to find the dependences of the magnitudes of the effects on the parameters of silicon layers doped with bismuth, and to explain the absence of ISHE signals when the silicon layer is doped only with phosphorus or antimony with a concentration of Nd> 1019 cm-3.

We propose a hybrid memristve neuromorphic system for stimulating hippocampus regions bypassing damaged areas. Synaptic plasticity properties of the system allow close-loop adaptive control of neural dynamics. We implement the simplest version of this system which consists of two neuron-like generators coupled by a memristive device, and two fiber-optic channels to transmit signals from the generators directly to living cells to stimulate hippocampus regions. The adaptive stimulation nature of the neural cells is provided by a stochastic response of the self-learning memristive device to the signal of the neuron-like generator. A biological model of impaired functioning of the perforating pathway in the rat hippocampus is implemented by damaging the CA3 region, on the base of the electrophysiological signal changes in normal and pathological conditions. The proposed adaptive stimulation technology demonstrates the possibility of restoring the functionality of the perforating pathway by introducing the neuromorphic system into the hippocampus to replace lost areas.

We investigate the constructive role of an external noise signal, in the form of a low-rate Poisson sequence of pulses supplied to all inputs of a spiking neural network, consisting in maintaining for a long time or even recovering a memory trace (engram) of the image without its direct renewal (or rewriting). In particular, this unique dynamic property is demonstrated in a single-layer spiking neural network consisting of simple integrate-and-fire neurons and memristive synaptic weights. This is carried out by preserving and even fine-tuning the conductance values of memristors in terms of dynamic plasticity, specifically spike-timing-dependent plasticity-type, driven by overlapping pre- and postsynaptic voltage spikes. It has been shown that the weights can be to a certain extent unreliable, due to such characteristics as the limited retention time of resistive state or the variation of switching voltages. Such a noise-assisted persistence of memory, on one hand, could be a prototypical mechanism in a biological nervous system and, on the other hand, brings one step closer to the possibility of building reliable spiking neural networks composed of unreliable analog elements.