On wellposedness of generalized neural field equations with delay

TL;DR

This paper establishes conditions for the existence and uniqueness of solutions to generalized neural field equations with delay, and examines how these solutions depend on various parameters such as kernels, delays, and firing rates.

Contribution

It provides new theoretical conditions ensuring well-posedness and analyzes the sensitivity of solutions to key model components.

Findings

Existence of unique solutions under specific conditions

Continuous dependence on kernels, delays, and firing rates

Extension to maximally extended solutions

Abstract

We obtain conditions for existence of unique global or maximally extended solutions to generalized neural field equations. We also study continuous dependence of these solutions on the spatiotemporal integration kernel, delay effects, firing rate and prehistory functions.