Boichuk Oleksandr and Pokutnyi Oleksandr and Feruk Viktor and Bihun Dmytro: Minimizing of the quadratic functional on Hopfield networks. (2021)
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Abstract
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 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/75813 |
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