We investigate and report an experimental confirmation of zero-lagsynchronization (ZLS) in a system of three coupled time-delayed piecewiselinear electronic circuits via dynamical relaying with different couplingconfigurations, namely mutual and subsystem coupling configurations. We haveobserved that when there is a feedback between the central unit (relay unit)and at least one of the outer units, ZLS occurs in the two outer units whereasthe central and outer units exhibit inverse phase synchronization (IPS). Wefind that in the case of mutual coupling configuration ZLS occurs both inperiodic and hyperchaotic regimes, while in the subsystem couplingconfiguration it occurs only in the hyperchaotic regime. Snapshots of the timeevolution of outer circuits as observed from the oscilloscope confirm theoccurrence of ZLS experimentally. The quality of ZLS is numerically verified bycorrelation coefficient and similarity function measures. Further, thetransition to ZLS is verified from the changes in the largest Lyapunovexponents and the correlation coefficient as a function of the couplingstrength. IPS is experimentally confirmed using time series plots and also canbe visualized using the concept of localized sets which are also corroboratedby numerical simulations. In addition, we have calculated the correlation ofprobability of recurrence to quantify the phase coherence. We have alsoanalytically derived a sufficient condition for the stability of ZLS using theKrasovskii-Lyapunov theory.
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