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Keywords = symmetry of impulsive and differential compartments

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17 pages, 722 KB  
Article
Dynamics of Symmetrical Discontinuous Hopfield Neural Networks with Poisson Stable Rates, Synaptic Connections and Unpredictable Inputs
by Marat Akhmet, Zakhira Nugayeva and Roza Seilova
Symmetry 2024, 16(6), 740; https://doi.org/10.3390/sym16060740 - 13 Jun 2024
Cited by 2 | Viewed by 1438
Abstract
The purpose of this paper is to study the dynamics of Hopfield neural networks with impulsive effects, focusing on Poisson stable rates, synaptic connections, and unpredictable external inputs. Through the symmetry of impulsive and differential compartments of the model, we follow and extend [...] Read more.
The purpose of this paper is to study the dynamics of Hopfield neural networks with impulsive effects, focusing on Poisson stable rates, synaptic connections, and unpredictable external inputs. Through the symmetry of impulsive and differential compartments of the model, we follow and extend the principal dynamical ideas of the founder. Specifically, the research delves into the phenomena of unpredictability and Poisson stability, which have been examined in previous studies relating to models of continuous and discontinuous neural networks with constant components. We extend the analysis to discontinuous models characterized by variable impulsive actions and structural ingredients. The method of included intervals based on the B-topology is employed to investigate the networks. It is a novel approach that addresses the unique challenges posed by the sophisticated recurrence. Full article
(This article belongs to the Special Issue Application of Symmetry in Equations)
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