Periodic Dynamics and Multidelays Effects in Neural Field Models: A Semi-Fredholm Approach

Abstract

This work studies the existence and attractivity of periodic solutions in a class of reaction–diffusion systems with distributed multi-delays, motivated by neural field models and population dynamics. We consider a class of linear partial differential equation with multidelays. By combining semi-Fredholm operator perturbation and fixed-point methods, we derive sufficient conditions for the existence of periodic solutions under non-compacity assumption on the semigroup generated by the linear part of the equation. As a concrete application, we analyze a spatially extended neural field model with synaptic delays and provide numerical simulations to illustrate our results.