The purpose of this work is to rigorously prove the existence of traveling waves in neural field models with lateral inhibition synaptic coupling types and sigmoidal firing rate functions. In the case of traveling fronts, we utilize theory of linear operators and the implicit function theorem on Banach spaces, providing a variation of the homotopy approach originally proposed by Ermentrout and McLeod (1992) in their seminal study of monotone fronts in neural field models. After establishing the existence of traveling fronts, we move to a well-studied singularly perturbed system with linear feedback. For the special case where the synaptic coupling kernel is a difference of exponential functions, we are able to combine our results for the front with theory of invariant manifolds in autonomous dynamical systems to prove the existence of fast traveling pulses that are comparable to singular homoclinical orbits. Finally, using a numerical approximation scheme, we derive the ubiquitous Evan 查看全文>>