We show that for large coupling delays the synchronizability of delay-coupled networks of identical units relates in a simple way to the spectral properties of the network topology. The master stability function used to determine stability of synchro
nous solutions has a universal structure in the limit of large delay: it is rotationally symmetric around the origin and increases monotonically with the radius in the complex plane. We give details of the proof of this structure and discuss the resulting universal classification of networks with respect to their synchronization properties. We illustrate this classification by means of several prototype network topologies.
Stability of synchronization in delay-coupled networks of identical units generally depends in a complicated way on the coupling topology. We show that for large coupling delays synchronizability relates in a simple way to the spectral properties of
the network topology. The master stability function used to determine stability of synchronous solutions has a universal structure in the limit of large delay: it is rotationally symmetric around the origin and increases monotonically with the radius in the complex plane. This allows a universal classification of networks with respect to their synchronization properties and solves the problem of complete synchronization in networks with strongly delayed coupling.
pydelay is a python library which translates a system of delay differential equations into C-code and simulates the code using scipy weave.
We theoretically study chaos synchronization of two lasers which are delay-coupled via an active or a passive relay. While the lasers are synchronized, their dynamics is identical to a single laser with delayed feedback for a passive relay and identi
cal to two delay-coupled lasers for an active relay. Depending on the coupling parameters the system exhibits bubbling, i.e., noise-induced desynchronization, or on-off intermittency. We associate the desynchronization dynamics in the coherence collapse and low frequency fluctuation regimes with the transverse instability of some of the compound cavitys antimodes. Finally, we demonstrate how, by using an active relay, bubbling can be suppressed.
