TIME-DELAYED INTERACTIONS AND SYNCHRONIZATION OF IDENTICAL LOHE OSCILLATORS

We study time-delay effects on the synchronous dynamics of identical Lohe oscillators on the unit sphere. Time delays in the interactions between Lohe oscillators are induced by the finite propagation speed of information or communication, and generate some oscillatory phenomena in the initial time-layer near the initial time. From the viewpoint of synchronization, we provide a sufficient framework for the complete positional synchronization of Lohe oscillators in terms of their initial configuration, time delay, and coupling strength. As long as the time delay is sufficiently small, there is no qualitative effect on synchronization.