Stability of Fixed Points in Ordered Spaces. Applications to Boundary Value Problems for Hopfield-Type Equations of a Neural Network

Key Points

• The research investigates conditions for the stability of fixed points of monotone operators in ordered spaces.
• Analyzing the ordinal structure of fixed points of a monotone operator in a partially ordered space.
• Investigating stability under changes in monotone operators.
• Exploring boundary value problems for Hopfield-type models in neural networks.
• Established conditions for the stability of sets of fixed points under operator changes.
• Demonstrated how stability conditions apply to boundary value problems in neural networks.
• Examined control systems related to the differential equations of neural network activity.