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Transitions between inverse anticipatory, inverse complete and inverse lagsynchronizations are shown to occur as a function of the coupling delay inunidirectionally coupled time-delay systems with inhibitory coupling. We havealso shown that the same general asymptotic stability condition obtained usingthe Krasovskii-Lyapunov functional theory can be valid for the cases where (i)both the coefficients of the $\Delta$ and $\Delta_\tau$ terms in the errorequation 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 ofsynchronization are corroborated using similarity function, probability ofsynchronization and also from changes in the spectrum of Lyapunov exponents ofthe coupled time-delay systems.

Inverse synchronizations in coupled time-delay systems with inhibitory coupling