  Transitions between inverse anticipatory, inverse complete and inverse lag
synchronizations are shown to occur as a function of the coupling delay in
unidirectionally coupled time-delay systems with inhibitory coupling. We have
also shown that the same general asymptotic stability condition obtained using
the Krasovskii-Lyapunov functional theory can be valid for the cases where (i)
both the coefficients of the $\Delta$ and $\Delta_\tau$ terms in the error
equation corresponding to the synchronization manifold are time independent and
(ii) the coefficient of the $\Delta$ term is time independent while that of the
$\Delta_\tau$ term is time dependent. The existence of different kinds of
synchronization are corroborated using similarity function, probability of
synchronization and also from changes in the spectrum of Lyapunov exponents of
the coupled time-delay systems.
