Abstract
Pattern formation within complex networks surrounds us. The screen in front of you as read this text is powered by power grids and your thoughts by large networks of neurons. Within these systems, if the coupled power generators and neurons do or do not oscillate with the same frequencies or with particular phase-shifts between them, power outages and seizures can occur, respectively. In these two important examples, and hundreds of others, we wonder how form of these networks influences their function or whether or not we can systematically adapt them. This thesis introduces a model experimental microfluidic reaction-diffusion made out of the Belousov-Zhabotinsky (BZ) reaction placed in PDMS, allowing investigation of synchronization in networks in a controlled, well-characterized platform. Building off of previous work, care is taken to characterize the individual reactors and pairwise interactions within these networks. The core result presented derives from using this system to study a small symmetric experimental network. A detailed comparison between a contemporary theory that predict pattern formation in networks on the basis of symmetry and the symmetric experiments confirm its usefulness but indicate fundamentally new directions of research. This promising theory is further experimentally tested in the context of large networks with few symmetries. In this study, we find proof that frustration within dynamical networks is fundamentally different than in statistical mechanics and is a key tool towards qualitatively understanding large networks. Finally, preliminary results show how BZ functionalized hydrogels, which can act as synthetic muscles, can oscillate regularly, burst like neurons, or stay in steady-states depending on their size.