Mikhail A. Mishchenko

Bursting is a special dynamic mode of neurons that consists of several consecutive spikes separated by a period of quiescence. This paper considers the synchronization of two non-identical neurons capable of both spiking and bursting behavior connected by a unidirectional pulse coupling. Unlike most studies, which focus on purely mathematical modeling and numerical simulations, we use simulation modeling of a neuron based on a phase-locked loop (PLL) in addition to the conventional solving of ODEs. Using these two approaches, we demonstrate the fundamental possibility of synchronizing two neurons operating in different dynamic modes. Synchronization regions are constructed in the system parameter space. It is shown that synchronization is achieved both for two spiking neurons and for neurons generating bursting activity. The results obtained are of interest from either a fundamental perspective, as an example of a complex nonlinear system with rich dynamic behavior, or from an applied perspective. In particular, the proposed model can be used in the field of neuromorphic electronics, where not only biological plausibility is important but also the possibility of simple hardware implementation. Differences between the simulation model and the results of numerical solution of ODEs are also demonstrated, revealing the importance of proper simulation frameworks at different design levels of neuromorphic electronics.

Study of spiking neural networks is a promising scientific direction of modern interdisciplinary research. Spiking networks have demonstrated high efficacy in processing and classification tasks on various datasets (pictures, acoustic signals, biological signals) and in robotics (navigation, movement control, interaction with media etc.) One of the main problems of this type of neural networks is high computational and implementational cost. This problem rises from computational complexity of many nonlinearities in neuronal models and nonlinear synaptic functions. Novel lowcomputational-cost models of spiking neurons and synapses could be a possible decision of this problem. Here, we propose a new discrete recursive neuron model. The model demonstrates rich spiking and bursting dynamic repertoire and requires relatively small computational resources. Moreover, the proposed model could be implemented by standard discrete logic elements.

Working memory (WM) is a brain system for short-term storage and manipulation of information and plays an important role in complex cognitive tasks. In the synaptic theory of WM memorized elements are stored in the form of short-term potentiated connections in a sample population of neurons. In this paper, we show that such populations can be formed due to the mechanisms of spike-timing-dependent plasticity (STDP) – the phase dependence associated with the ratio of the pulse times of the interacting neurons. We propose a WM model considering two types of plasticity: short-term plasticity and STDP. We have shown formation of neuronal clusters encoding items in the WM model, that can be formed by external stimulation of a group of neurons due to the mechanisms of STDP and hold and reactivated by short-term plasticity mechanisms. The dynamic formation of neuronal clusters instead of pre-formed clusters gives additional flexibility to the model.

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.

Experimental implementation of neuron-like generator on the basis of phase-locked loop (PLL) with band-pass filter is proposed. The generator is able to generate oscillations that are typical for neuronal dynamics like spikes and bursts, both regular and chaotic, and demonstrate excitable (non-oscillating) behavior. Excitable mode is typical for the most of brain neurons that remains silent until activated by external signal. Previous PLL-based neuron-like models couldn't demonstrate excitable dynamics. Therefore, the proposed neuron-like generator could be a basic block for electronic spiking neural networks to mimic brain neural networks. Keywords: electronic neuron, generator, excitation of oscillations, phase-locked loop.