Phase transformation and synchrony for a network of coupled Izhikevich neurons

Recent studies have used the Lorentzian ansatz to obtain mean-field reductions of Izhikevich neuron networks, but these approaches stop short of connecting microscopic dynamics to synchrony measures. In this work, we construct an equivalent phase model for the Izhikevich neuron and apply the Ott-Antonsen ansatz to derive mean-field equations in terms of the Kuramoto order parameter. This provides governing equations for the evolution of synchrony in networks of Izhikevich neurons. We further demonstrate that the conformal mapping originally derived for quadratic integrate-and-fire neurons remains valid for the Izhikevich model, thereby extending the link between voltage-firing-rate and phase-based descriptions to a broader and more biologically realistic neuron class. Using this mapping, we challenge the common assumption that high firing rates indicate strong synchrony, and instead show that high-amplitude oscillations in firing rate are the true signature of synchrony. This result holds across excitatory and inhibitory populations and suggests that EEG and MEG spectral power could serve as noninvasive biomarkers of underlying neuronal synchrony. Together, these findings extend mean-field reduction techniques to richer neuronal models, strengthen the bridge between mathematical theory and experimental observables, and provide new insight into the relationship between firing activity and collective neural dynamics.