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 is described by system differential equations linear boundary conditions. Also, questions finding necessary and sufficient conditions solvability constructive construction solutions given problem, which turn into generating as parameter $\varepsilon$ tends to zero. An iterative algorithm for has been constructed. The problem extremum target functions on solution considered. To minimize functional, an accelerated method conjugate gradients used. Results are illustrated examples case three