Eur. Phys. J. Special Topics 222, 729-744 (2013)
https://doi.org/10.1140/epjst/e2013-01876-1

Regular Article

Zero-lag synchronization in coupled time-delayed piecewise linear electronic circuits

¹ Centre for Nonlinear Dynamics, Department of Physics, Bharathidasan University, Tiruchirapalli 620 024, India
² Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany
³ Department of Physics, B. S. Abdur Rahman University, Chennai 600 048, India
⁴ Department of Physics, Anna University, Chennai 600 025, India
⁵ Institute of Physics, Humboldt University, 12489 Berlin, Germany
⁶ Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3UE, UK

^a e-mail: lakshman@cnld.bdu.ac.in

Received: 22 March 2013
Revised: 3 May 2013
Published online: 11 July 2013

Abstract

We investigate and report an experimental confirmation of zero-lag synchronization (ZLS) in a system of three coupled time-delayed piecewise linear electronic circuits via dynamical relaying with different coupling configurations, namely mutual and subsystem coupling configurations. We have observed 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 whereas the central and outer units exhibit inverse phase synchronization (IPS). We find that in the case of mutual coupling configuration ZLS occurs both in periodic and hyperchaotic regimes, while in the subsystem coupling configuration it occurs only in the hyperchaotic regime. Snapshots of the time evolution of outer circuits as observed from the oscilloscope confirm the occurrence of ZLS experimentally. The quality of ZLS is numerically verified by correlation coefficient and similarity function measures. Further, the transition to ZLS is verified from the changes in the largest Lyapunov exponents and the correlation coefficient as a function of the coupling strength. IPS is experimentally confirmed using time series plots and also can be visualized using the concept of localized sets which are also corroborated by numerical simulations. In addition, we have calculated the correlation of probability of recurrence to quantify the phase coherence. We have also analytically derived a sufficient condition for the stability of ZLS using the Krasovskii-Lyapunov theory.