  In principle, while coupled limit cycle oscillators can overcome mismatch in
intrinsic rates and match their frequencies, but zero phase lag synchronization
is just achievable in the limit of zero mismatch, i.e., with identical
oscillators. Delay in communication, on the other hand, can exert phase shift
in the activity of the coupled oscillators. In this study, we address the
question of how phase locked, and in particular zero phase lag synchronization,
can be achieved for a heterogeneous system of two delayed coupled neurons. We
have analytically studied the possibility of inphase synchronization and near
inphase synchronization when the neurons are not identical or the connections
are not exactly symmetric. We have shown that while any single source of
inhomogeneity can violate isochronous synchrony, multiple sources of
inhomogeneity can compensate for each other and maintain synchrony. Numeric
studies on biologically plausible models also support the analytic results.
