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

Kuramoto model for populations of quadratic integrate-and-fire neurons with chemical and electrical coupling