  We derive the Kuramoto model (KM) corresponding to a population of weakly
coupled, nearly identical quadratic integrate-and-fire (QIF) neurons with both
electrical and chemical coupling. The ratio of chemical to electrical coupling
determines the phase lag of the characteristic sine coupling function of the KM
and critically determines the synchronization properties of the network. We
apply our results to investigate chimera states in two coupled populations of
identical QIF neurons. We find that the presence of both electrical and
chemical coupling is a necessary condition for chimera states to exist.
Finally, we numerically demonstrate that chimera states gradually disappear as
coupling strengths cease to be weak.
