Minimizing of the quadratic functional on Hopfield networks

In this paper, we consider the continuous Hopfield model with a weakinteraction of network neurons. This model is described by a system ofdifferential equations with linear boundary conditions. Also, we considerthe questions of finding necessary and sufficient conditions of solvabilityand constructive construction of solutions of the given problem, which turninto solutions of the linear generating problem, as the parameter$\varepsilon$ tends to zero. An iterative algorithm for finding solutionshas been constructed. The problem of finding the extremum of the targetfunctions on the given problem solution is considered. To minimize afunctional, an accelerated method of conjugate gradients is used. Resultsare illustrated with examples for the case of three neurons.