01709nas a2200265 i 4500 acta75813 20220523133312.0 220523s2021 hu o 0|| eng d 1417-3875 10.14232/ejqtde.2021.1.92 doi SZTE Egyetemi Kiadványok Repozitórium hun eng Boichuk Oleksandr Minimizing of the quadratic functional on Hopfield networks [elektronikus dokumentum] / Boichuk Oleksandr 2021 20 Electronic journal of qualitative theory of differential equations 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. Természettudományok Matematika Hopfield hálózatok, Határérték probléma - differenciálegyenletek Pokutnyi Oleksandr aut Feruk Viktor aut Bihun Dmytro aut http://acta.bibl.u-szeged.hu/75813/1/ejqtde_2021_092.pdf Dokumentum-elérés