ON CONNECTION BETWEEN CONTINUOUS AND DISCONTINUOUS NEURAL FIELD MODELS WITH MICROSTRUCTURE I. GENERAL THEORY
We suggest a method allowing to investigate existence and the measure of proximity between the stationary solutions to continuous and discontinuous neural fields with microstructure. The present part involves a theorem on solvability of such equations based on topological degree theory, and a theorem on continuous dependence of the solutions under the transition from continuous to discontinuous activation function using compactness in a special topology.