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arXiv · 1907.03924

Dynamics of Reaction-Diffusion Oscillators in Star Networks

Michael M. Norton·Nathan Tompkins·Baptiste Blanc·Matthew C. Cambria·Jesse Held·Seth Fraden
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Abstract

We experimentally and theoretically investigate the dynamics of inhibitory coupled self-driven oscillators on a star network in which a single central hub node is connected to $k$ peripheral arm nodes. The system consists of water-in-oil Belousov-Zhabotinsky $\sim$100$μ$m emulsion drops contained in storage wells etched in silicon wafers. We observed three dynamical attractors by varying the number of arms in the star graph and the coupling strength; ($i$) unlocked; uncorrelated phase shifts between all oscillators, ($ii$) locked; arm-hubs synchronized in-phase with a $k$-dependent phase shift between the arm and central hub, and ($iii$) center silent; central hub stopped oscillating and the arm-hubs oscillated without synchrony. We compare experiment to theory. For case ($ii$), we identified a logarithmic dependence of the phase shift on star degree, and were able to discriminate between contributions to the phase shift arising from star topology and oscillator chemistry.

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Michael M. Norton, Nathan Tompkins, Baptiste Blanc, Matthew C. Cambria, Jesse Held, Seth Fraden. 2019-07-09. Dynamics of Reaction-Diffusion Oscillators in Star Networks. https://doi.org/10.1103/physrevlett.123.148301

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