  The brain is composed of complex networks of interacting neurons that express
considerable heterogeneity in their physiology and spiking characteristics. How
does neural heterogeneity affect macroscopic neural dynamics and how does it
contribute to neurodynamic functions? In this letter, we address these
questions by studying the macroscopic dynamics of networks of heterogeneous
Izhikevich neurons. We derive mean-field equations for these networks and
examine how heterogeneity in the spiking thresholds of Izhikevich neurons
affects the emergent macroscopic dynamics. Our results suggest that the level
of heterogeneity of inhibitory populations controls resonance and hysteresis
properties of systems of coupled excitatory and inhibitory neurons. Neural
heterogeneity may thus serve as a means to control the dynamic repertoire of
mesoscopic brain circuits.
