Minimizing of the quadratic functional on Hopfield networks

Boichuk Oleksandr and Pokutnyi Oleksandr and Feruk Viktor and Bihun Dmytro: Minimizing of the quadratic functional on Hopfield networks. (2021)

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In this paper, we consider the continuous Hopfield model with a weak interaction of network neurons. This model is described by a system of differential equations with linear boundary conditions. Also, we consider the questions of finding necessary and sufficient conditions of solvability and constructive construction of solutions of the given problem, which turn into solutions of the linear generating problem, as the parameter ε tends to zero. An iterative algorithm for finding solutions has been constructed. The problem of finding the extremum of the target functions on the given problem solution is considered. To minimize a functional, an accelerated method of conjugate gradients is used. Results are illustrated with examples for the case of three neurons.

Item Type: Journal
Publication full: Electronic journal of qualitative theory of differential equations
Date: 2021
Number: 92
ISSN: 1417-3875
Number of Pages: 20
Language: English
Place of Publication: Szeged
DOI: 10.14232/ejqtde.2021.1.92
Uncontrolled Keywords: Hopfield hálózatok, Határérték probléma - differenciálegyenletek
Additional Information: Bibliogr.: p. 17-20. ; összefoglalás angol nyelven
Subjects: 01. Natural sciences
01. Natural sciences > 01.01. Mathematics
Date Deposited: 2022. May. 23. 13:33
Last Modified: 2022. May. 23. 13:33

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