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

Key Points

• The research aims to explore the stability of fixed points in ordered spaces and their applications to boundary value problems in neural networks.
• Examined the ordinal structure of fixed point sets of monotone operators in partially ordered spaces.
• Derived stability conditions for fixed point sets in response to changes in monotone operators.
• Analyzed a boundary value problem and control system related to a neural network model.
• Identified specific stability conditions for fixed points under variations of monotone operators.
• Applied findings to demonstrate the behavior of a Hopfield-type neural network model with distinct activation functions.