Analysis of oscillating processes in spiking neural networks
Regional Scientific and Educational Mathematical Center “Centre of Integrable Systems”, P. G. Demidov Yaroslavl State University, Sovetskaya, 14, 150003, Yaroslavl, Russia
2 P. G. Demidov Yaroslavl State University, Sovetskaya, 14, 150003, Yaroslavl, Russia
Accepted: 30 January 2023
Published online: 2 March 2023
In the classical neural networks, information is presented as a set of the stable equilibrium states. This review considers a series of papers devoted to an urgent topic of development of the neural networks models that do not have equilibrium states. Oscillatory conditions in neural networks are interpreted as patterns, i.e. a reflection of some information. Based on the physiological concepts, a model of a neural environment is proposed that is capable of storing information presented in a wave form. Effective analytical methods for the asymptotic analysis of non-linear, non-local oscillations in a system of equations with delay describing a neuronal population are described. Theoretical studies have made it possible to effectively solve important specific problems.
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