Synchronization of two delayed coupled neurons in presence of inhomogeneity

In principle coupled oscillators can overcome mismatch in intrinsic firing rates and match their frequencies, but with a nonzero phase lag. Delay in communication, on the other hand, can exert phase shifts in the concerted activity of the coupled oscillators. In this study, we address the question of how synchronization can be achieved for a two neurons system, in presence of mismatch and delay in communication. Analytic and numeric results are presented to inspect general conditions for synchronization and in particular, the possibility of inphase synchronization and near inphase synchronization is studied when a source of inhomogeneity (in the neurons or in the couplings parameters) is present. Our general results match in special cases given by other authors for symmetric configurations.