Minimizing of the quadratic functional on Hopfield networks

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 constr...

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Bibliographic Details
Main Authors: Boichuk Oleksandr
Pokutnyi Oleksandr
Feruk Viktor
Bihun Dmytro
Format: Serial
Published: 2021
Series:Electronic journal of qualitative theory of differential equations
Kulcsszavak:Hopfield hálózatok, Határérték probléma - differenciálegyenletek
Subjects:
doi:10.14232/ejqtde.2021.1.92

Online Access:http://acta.bibl.u-szeged.hu/75813
Description
Summary: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.
Physical Description:20
ISSN:1417-3875