STABILITY OF FIXED POINTS IN ORDERED SPACES. APPLICATIONS TO BOUNDARY VALUE PROBLEMS FOR HOPFIELD-TYPE EQUATIONS OF A NEURAL NETWORK
Evgeny Semenovich Zhukovskiy · Дифференциальные уравнения / Differential Equations · 2025
The ordinal structure of the set of fixed points of a monotone operator acting in a partially ordered space is investigated. The conditions for the stability of the set of fixed points to changes in the monotone operator are obtained. Based on these results, a boundary value problem and a control system for the differential equation of a neural network — a Hopfield-type model of the electrical activity of the brain with a continuous and discontinuous activation function — are investigated.