  We present a systematic approach to reveal the correspondence between time
delay dynamics and networks of coupled oscillators. After early demonstrations
of the usefulness of spatio-temporal representations of time-delay system
dynamics, extensive research on optoelectronic feedback loops has revealed
their immense potential for realizing complex system dynamics such as chimeras
in rings of coupled oscillators and applications to reservoir computing.
Delayed dynamical systems have been enriched in recent years through the
application of digital signal processing techniques. Very recently, we have
showed that one can significantly extend the capabilities and implement
networks with arbitrary topologies through the use of field programmable gate
arrays (FPGAs). This architecture allows the design of appropriate filters and
multiple time delays which greatly extend the possibilities for exploring
synchronization patterns in arbitrary topological networks. This has enabled us
to explore complex dynamics on networks with nodes that can be perfectly
identical, introduce parameter heterogeneities and multiple time delays, as
well as change network topologies to control the formation and evolution of
patterns of synchrony.
