In-phase, out-of-phase and T/4 synchronization of square waves in delay-coupled non-identical optoelectronic oscillators

We model two non-identical delay-line optoelectronic oscillators mutually coupled through delayed cross-feedback. The system can generate multi-stable nanosecond periodic square-wave solutions which arise through a Hopf instability. We show that for suitable ratios between self and cross delay times, the two oscillators generate square waves with different amplitude but synchronized in-phase, out-of-phase or with a dephasing of
a quarter of the period. We also show that the synchronization is robust to small mismatches in the delay times.