  The production process of integrated electronic circuitry inherently leads to
large heterogeneities on the component level. For electronic clock networks
this implies detuned intrinsic frequencies and differences in coupling strength
and the characteristic time-delays associated with signal transmission,
processing and feedback. Using a phase-model description, we study the effects
of such component heterogeneity on the dynamical properties of synchronization
in networks of mutually delay-coupled Kuramoto oscillators. We test the theory
against experimental results and circuit-level simulations in a prototype
system of mutually delay-coupled electronic clocks, so called phase-locked
loops. Contrary to the hindering effects of component heterogeneity for the
synchronization in hierarchical networks, we show that clock heterogeneities
can enhance self-organized synchronization in networks with flat hierarchy.
That means that beyond the optimizations that can be achieved by tuning
homogeneous coupling strengths, time-delays and loop-filter cut-off
frequencies, heterogeneities in these system parameters enable much better
optimization of perturbation decay rates, the stabilization of synchronous
states and the tuning of phase-differences between the clocks. Our theory
enables the design of custom-fit synchronization layers according to the
specific requirements and properties of electronic systems, such as operational
frequencies, phase-relations and e.g. transmission-delays. These results are
not restricted to electronic systems, as signal transmission, processing and
feedback delays are common to networks of spatially distributed and coupled
autonomous oscillators.
