Phase-flip transition in coupled time-delayed piecewise linear electronic circuits

We study the synchronization dynamics of mutually time-delay coupled intrinsic time-delay systems. In particular, we analyze the phase synchronized states and phase-flip transitions occurring in a bi-directionally time-delay coupled electronic circuit model with threshold nonlinearity using both numerical simulations and direct experiment. By varying the coupling delay for different coupling strengths, we identify the changes in the relative phase between the oscillators from in-phase to anti-phase and vice versa. We also carry out a detailed analysis by solving the delay differential equations numerically to confirm the phase-flip transition. Finally, the numerical predictions are verified with experiments.