Synchronization of time-delay coupled pulse oscillators

We present a detailed study of the dynamics of pulse oscillators with time-delayed coupling. We get the return maps, obtain strict solutions and analyze their stability. For the case of two oscillators, a periodical structure of synchronization regions is found in parameter space, and the regions corresponding to in-phase and antiphase regimes alternate with growth of time delay. Two types of switching between in-phase and antiphase regimes are studied. We also show that for different parameters coupling delay may have synchronizing or desynchronizing effect. Another novel result is that phase locked regimes exist for arbitrary large values. The specificity of system dynamics with large delay is studied.

Research highlights
► Oscillators can be synchronized via coupling with arbitrary large delay.
► Imposing of coupling delay may either result in delay-induced synchronization or delay-induced desynchronization.
► In-phase and antiphase synchronization zones alternate in parameter space.
► Two types of transitions between the in-phase and antiphase synchronization, i.e. phase-flip bifurcation and soft switching.