Attractor symmetry and stability in symmetric self-driven oscillator networks

The dynamics governing networks of identical oscillators are unchanged by node interchange symmetries, or automorphisms, of the network. Equivariant dynamical system theory predicts such networks consequently must possess steady states, and flow invariant manifolds where particular nodes, exchanged by subgroups of network symmetries, are synchronized. Homogeneous microreactors containing the oscillatory Belousov Zhabotinsky (BZ) reaction, coupled by diffusion, allow the experimental study of symmetric self-driven oscillator networks. A ring of 4 inhibitory-coupled BZ reactors was studied as a model system. This system exhibits symmetric gaits found in quadrupedal animals as its attractors. Experimental invariant manifolds, steady states, and stabilities are compared to those theoretically predicted using methods generalizable to other networks.