Synchronization in Cartesian-Product Networks of Time-Delay Coupled Systems

We present a theoretical result about synchronization in Cartesian-product networks of coupled semipassive systems interconnected through diffusive time-delay couplings. First, for two diffusively time-delay coupled systems, we give sufficient conditions that guarantee the existence of a region S* in the parameter space (coupling strength vs. time delay), such that if these parameters belong to the region, the two coupled systems synchronize. Then, using this region S* and the spectral properties of the Cartesian-product, we derive a method to predict the values of coupling strength and time-delay for which diffusive time-delay coupled systems on Cartesian-product networks synchronize. The obtained theoretical results are experimentally validated using an experimental setup built around electronic circuit realizations of the Hindmarsh-Rose neuron model.