Experimental Equivariant Dynamics in a Network of Reaction-Diffusion Oscillators*

Does form follow function in natural coupled-oscillator networks? Symmetry controls both the steady-state and the transient spatiotemporal patterns that form in mathematically ideal networks to a remarkable degree. But what happens in the real-world networks, with imperfections in their nodes and connections? To address these questions, we developed a model experimental reaction-diffusion network formed by an oscillatory chemical reaction confined to a square symmetric ring of 4 diffusively coupled microfluidic reactors. We compared experimental dynamics to theory assuming perfect symmetry and theory incorporating slight heterogeneity. We observed that even slight heterogeneity selectively modifies and eliminates some patterns, while preserving others. This work demonstrates that a surprising degree of the natural network’s dynamics are constrained by symmetry in spite of the breakdown of the assumptions of perfect symmetry and raises the question of why heterogeneity destabilizes some symmetry predicted states, but not others.