The current study uses a novel method of multilevel neurons and high order synchronization effects described by a family of special metrics, for pattern recognition in an oscillatory neural network (ONN). The output oscillator (neuron) of the network has multilevel variations in its synchronization value with the reference oscillator, and allows classification of an input pattern into a set of classes. The ONN model is implemented on thermally-coupled vanadium dioxide oscillators. The ONN is trained by the simulated annealing algorithm for selection of the network parameters. The results demonstrate that ONN is capable of classifying 512 visual patterns (as a cell array 3 × 3, distributed by symmetry into 102 classes) into a set of classes with a maximum number of elements up to fourteen. The classification capability of the network depends on the interior noise level and synchronization effectiveness parameter. The model allows for designing multilevel output cascades of neural networks with high net data throughput. The presented method can be applied in ONNs with various coupling mechanisms and oscillator topology.

This brief presents a concept of leaky integrate-and-fire neuron (LIF) based on oscillator circuit for a spike neural network with firing rate coding. The circuit contains a switching element with an S-shaped current-voltage characteristic and two capacitors; a control resistor shunts one of the capacitors. The circuit is characterized by a strong dependence of the frequency of relaxation oscillations on the magnitude of the control resistor. The dependence has a sigmoid-like form, and we present an analytical method for dependence calculation. The circuit provides theoretical perspectives for the pairing of resistive sensors with a neural network and for creating neuromorphic devices with artificial intelligence.

In this paper, we present circuit solutions based on a switch element with the S-type I–V characteristic implemented using the classic FitzHugh–Nagumo and FitzHugh–Rinzel models. Using the proposed simplified electrical circuits allows the modeling of the integrate-and-fire neuron and burst oscillation modes with the emulation of the mammalian cold receptor patterns. The circuits were studied using the experimental I–V characteristic of an NbO₂ switch with a stable section of negative differential resistance (NDR) and a VO₂ switch with an unstable NDR, considering the temperature dependences of the threshold characteristics. The results are relevant for modern neuroelectronics and have practical significance for the introduction of the neurodynamic models in circuit design and the brain–machine interface. The proposed systems of differential equations with the piecewise linear approximation of the S-type I–V characteristic may be of scientific interest for further analytical and numerical research and development of neural networks with artificial intelligence.

Development of neuromorphic systems based on new nanoelectronics materials and devices is of immediate interest for solving the problems of cognitive technology and cybernetics. Computational modeling of two- and three-oscillator schemes with thermally coupled VO₂-switches is used to demonstrate a novel method of pattern storage and recognition in an impulse oscillator neural network (ONN), based on the high-order synchronization effect. The method allows storage of many patterns, and their number depends on the number of synchronous states N_s. The modeling demonstrates attainment of N_s of several orders both for a three-oscillator scheme N_s ~ 650 and for a two-oscillator scheme N_s ~ 260. A number of regularities are obtained, in particular, an optimal strength of oscillator coupling is revealed when N_s has a maximum. Algorithms of vector storage, network training, and test vector recognition are suggested, where the parameter of synchronization effectiveness is used as a degree of match. It is shown that, to reduce the ambiguity of recognition, the number coordinated in each vector should be at least one unit less than the number of oscillators. The demonstrated results are of a general character, and they may be applied in ONNs with various mechanisms and oscillator coupling topology.

Understanding and quantifying chaos from data remains challenging. We present a data-driven method for estimating the largest Lyapunov exponent (LLE) from one-dimensional chaotic time series using machine learning. A predictor is trained to produce out-of-sample, multi-horizon forecasts; the LLE is then inferred from the exponential growth of the geometrically averaged forecast error across the horizon, which serves as a proxy for trajectory divergence. We validate the approach on four canonical 1D maps—logistic, sine, cubic, and Chebyshev—achieving Rpos2 > 0.99 against reference LLE curves with series as short as M = 450. Among baselines, k-nearest neighbor (KNN) yields the closest fits (KNN-R comparable; random forest larger deviations). By design the estimator targets positive exponents: in periodic/stable regimes, it returns values indistinguishable from zero. Noise robustness is assessed by adding zero-mean white measurement noise and summarizing performance vs the average signal-to-noise ratio (SNR) over parameter sweeps: accuracy saturates for SNRm ≳ 30 dB and collapses below ≈27 dB, a conservative sensor-level benchmark. The method is simple, computationally efficient, and model-agnostic, requiring only stationarity and the presence of a dominant positive exponent. It offers a practical route to LLE estimation in experimental settings where only scalar time-series measurements are available, with extensions to higher-dimensional and irregularly sampled data left for future work.