Synchronization transitions in coupled time-delay electronic circuits with a threshold nonlinearity

Experimental observations of typical kinds of synchronization transitions are reported in unidirectionally coupled time-delay electronic circuits with a threshold nonlinearity and two time delays, namely feedback delay $\tau_1$ and coupling delay $\tau_2$. We have observed transitions from anticipatory to lag via complete synchronization and their inverse counterparts with excitatory and inhibitory couplings, respectively, as a function of the coupling delay $\tau_2$. The anticipating and lag times depend on the difference between the feedback and the coupling delays. A single stability condition for all the different types of synchronization is found to be valid as the stability condition is independent of both the delays. Further, the existence of different kinds of synchronizations observed experimentally is corroborated by numerical simulations, and from the changes in the Lyapunov exponents of the coupled time-delay systems.