ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Kuptsov P. V., Stankevich N. V. Modeling of the Hodgkin–Huxley neural oscillators dynamics using an artificial neural network. Izvestiya VUZ. Applied Nonlinear Dynamics, 2024, vol. 32, iss. 1, pp. 72-95. DOI: 10.18500/0869-6632-003079, EDN: VCXHMY

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Modeling of the Hodgkin–Huxley neural oscillators dynamics using an artificial neural network

Kuptsov Pavel Vladimirovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Stankevich Nataliya Vladimirovna, National Research University "Higher School of Economics"

The purpose of this study — to represent a detailed description of the procedure for creating and training a neural network mapping on the example of the dynamics modeling of a neural oscillator of the Hodgkin–Huxley type; to show that the neural network mappings trained for single oscillators can be used as elements of a coupled system that simulate the behavior of coupled oscillators.

Methods. Numerical method is used for solving stiff systems of ordinary differential equations. Also a procedure for training neural networks based on the method of back propagation of error is employed together with the Adam optimization algorithm, that is a modified version of the gradient descent supplied with an automatic step adjustment.

Results. It is shown that the neural network mappings built according to the described procedure are able to reproduce the dynamics of single neural oscillators. Moreover, without additional training, these mappings can be used as elements of a coupled system for the dynamics modeling of coupled neural oscillator systems.

Conclusion. The described neural network mapping can be considered as a new universal framework for complex dynamics modeling. In contrast to models based on series expansion (power, trigonometric), neural network mapping does not require truncating of the series. Consequently, it allows modeling processes with arbitrary order of nonlinearity, hence there are reasons to believe that in some aspects it will be more effective. The approach developed in this paper based on the neural network mapping can be considered as a sort of an alternative to the traditional numerical methods of modeling of dynamics. What makes this approach topical is the current rapid development of technologies for creating fast computing equipment that supports neural network training and operation.

The study of mathematical models was carried out within the framework of the Mirror Laboratories Project of HSE University (Sections 1, 2). Development and research of the neural network mapping (Sections 3–5) was supported by the Russian Science Foundation, 20-71-10048
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