Dynamics of Reaction-Diffusion Oscillators in Star and other Networks with Cyclic Symmetries Exhibiting Multiple Clusters

Michael M. Norton, Nathan Tompkins, Baptiste Blanc, Matthew Carl Cambria, Jesse Held, Seth Fraden

Research output: Contribution to journalArticle

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 ∼100 μm 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, a 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.

Original languageEnglish (US)
Article number148301
JournalPhysical Review Letters
Volume123
Issue number14
DOIs
StatePublished - Oct 4 2019

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hubs
oscillators
stars
phase shift
symmetry
emulsions
topology
oils
wafers
chemistry
silicon
water

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

Norton, Michael M. ; Tompkins, Nathan ; Blanc, Baptiste ; Cambria, Matthew Carl ; Held, Jesse ; Fraden, Seth. / Dynamics of Reaction-Diffusion Oscillators in Star and other Networks with Cyclic Symmetries Exhibiting Multiple Clusters. In: Physical Review Letters. 2019 ; Vol. 123, No. 14.
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Dynamics of Reaction-Diffusion Oscillators in Star and other Networks with Cyclic Symmetries Exhibiting Multiple Clusters. / Norton, Michael M.; Tompkins, Nathan; Blanc, Baptiste; Cambria, Matthew Carl; Held, Jesse; Fraden, Seth.

In: Physical Review Letters, Vol. 123, No. 14, 148301, 04.10.2019.

Research output: Contribution to journalArticle

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