Global attractivity of affine-periodic solutions for generalized ODEs with application to a Hopfield neural network model

Key Points

• The study aims to establish the existence and uniqueness of a global attractor in generalized ordinary differential equations.
• Demonstrated the existence of a $(Q, heta)$ -affine periodic solution.
• Analyzed generalized ODEs under $(Q, heta)$ -affine conditions.
• Derived an analogue for measure differential equations with a zero-average condition.
• Illustrated the findings using a Hopfield neural network model.
• Confirmed the existence of a global attractor for the stated equations.
• Showed uniqueness of the $(Q, heta)$ -affine periodic solution.
• Illustrated the practical applications in a Hopfield neural network framework.

Abstract