The article presents a study on a new type of an oscillatory neural network (ONN) that uses multilevel neurons for pattern recognition on the basis of high order synchronization effect. The feature of this network architecture is a single oscillator (neuron) at the output with multilevel variation of its synchronization value with the main oscillator thus allowing classifications of an input pattern into a set of classes. ONN model is realized on thermally-coupled VO2-oscillators. ONN training was performed by using the trial-and-error method for the network parameters selection. It is shown that ONN is capable to classify 512 visual patterns (as a cell array 3x3, distributed by symmetry into 102 classes) into a set of classes with the maximum number of elements up to P=11. Classification capability of a network is studied depending on the interior noise level and synchronization effectiveness parameter. The obtained results allow designing multilevel output cascades of neural networks with high net data throughput and it may be applied in ONNs with various coupling mechanisms and oscillators topology.

We explore a prototype of an oscillatory neural network (ONN) based on vanadium dioxide switching devices. The model system under study represents two oscillators based on thermally coupled VO2 switches. Numerical simulation shows that the effective action radius RTC of coupling depends both on the total energy released during switching and on the average power. It is experimentally and numerically proved that the temperature change ΔT commences almost synchronously with the released power peak and T-coupling reveals itself up to a frequency of about 10 kHz. For the studied switching structure configuration, the RTC value varies over a wide range from 4 to 45 μm, depending on the external circuit capacitance C and resistance Ri, but the variation of Ri is more promising from the practical viewpoint. In the case of a "weak" coupling, synchronization is accompanied by attraction effect and decrease of the main spectra harmonics width. In the case of a "strong" coupling, the number of effects increases, synchronization can occur on subharmonics resulting in multilevel stable synchronization of two oscillators. An advanced algorithm for synchronization efficiency and subharmonic ratio calculation is proposed. It is shown that of the two oscillators the leading one is that with a higher main frequency, and, in addition, the frequency stabilization effect is observed. Also, in the case of a strong thermal coupling, the limit of the supply current parameters, for which the oscillations exist, expands by ~ 10 %. The obtained results have a universal character and open up a new kind of coupling in ONNs, namely, T-coupling, which allows for easy transition from 2D to 3D integration. The effect of subharmonic synchronization hold promise for application in classification and pattern recognition.

In the present paper, we report on the switching dynamics of both single and coupled VO2-based oscillators, with resistive and capacitive coupling, and explore the capability of their application in oscillatory neural networks. Based on these results, we further select an adequate SPICE model to describe the modes of operation of coupled oscillator circuits. Physical mechanisms influencing the time of forward and reverse electrical switching, that determine the applicability limits of the proposed model, are identified. For the resistive coupling, it is shown that synchronization takes place at a certain value of the coupling resistance, though it is unstable and a synchronization failure occurs periodically. For the capacitive coupling, two synchronization modes, with weak and strong coupling, are found. The transition between these modes is accompanied by chaotic oscillations. A decrease in the width of the spectrum harmonics in the weak-coupling mode, and its increase in the strongcoupling one, is detected. The dependences of frequencies and phase differences of the coupled oscillatory circuits on the coupling capacitance are found. Examples of operation of coupled VO2 oscillators as a central pattern generator are demonstrated.

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