Synchronization analysis of resonate-and-fire neuron models with delayed resets

We analyzed the synchronization properties of coupled resonate-and-fire neuron models with delayed resets. The conventional phase reduction method cannot be applied to the system as it shows periodicity only under time-delayed feedback and cannot be treated as a dynamical system. Therefore, we generalized the conventional phase reduction method to include dynamics with delay-induced periodicity. Then we applied the theory to the system and utilized the reduced phase dynamics for analyzing the synchronization properties.