Spiral wave chimera states in large populations of coupled chemical oscillators

Abstract

The coexistence of coherent and incoherent dynamics in a population of identically coupled oscillators is known as a chimera state1,2. Discovered in 20023, this counterintuitive dynamical behaviour has inspired extensive theoretical and experimental activity4,5,6,7,8,9,10,11,12,13,14,15. The spiral wave chimera is a particularly remarkable chimera state, in which an ordered spiral wave rotates around a core consisting of asynchronous oscillators. Spiral wave chimeras were theoretically predicted in 200416 and numerically studied in a variety of systems17,18,19,20,21,22,23. Here, we report their experimental verification using large populations of nonlocally coupled Belousov–Zhabotinsky chemical oscillators10,18 in a two-dimensional array. We characterize previously unreported spatiotemporal dynamics, including erratic motion of the asynchronous spiral core, growth and splitting of the cores, as well as the transition from the chimera state to disordered behaviour. Spiral wave chimeras are likely to occur in other systems with long-range interactions, such as cortical tissues24, cilia carpets25, SQUID metamaterials26 and arrays of optomechanical oscillators9.

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Fig. 1: Experimental set-up and spiral wave chimera.
Fig. 2: Core dynamics of spiral wave chimera.
Fig. 3: Splitting of spiral wave chimera cores and transition to incoherence.

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Acknowledgements

The authors thank J. Sixt and F. Sielaff from TU Berlin Physics Department’s precision mechanical workshop for preparing the acrylic glass plates with micrometre-sized cavities that hold the micro-oscillators and U. Künkel for assistance in the laboratory. This work was supported by the Deutsche Forschungsgemeinschaft (grants GRK 1558 and SFB 910 to J.F.T., J.R. and H.E.), the National Science Foundation (grant CHE-1565665 to K.S. and M.R.T.) and the Alexander von Humboldt-Stiftung (to K.S.).

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J.F.T. and J.R. built and programmed the set-up and performed experiments. J.F.T., K.S. and H.E. designed the study and wrote the paper. The simulations were carried out by J.F.T. and J.R., except for those shown in Fig. 3b–i, which were done by M.R.T. All authors discussed the results and commented on the manuscript.

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Correspondence to Jan Frederik Totz or Kenneth Showalter or Harald Engel.

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Totz, J.F., Rode, J., Tinsley, M.R. et al. Spiral wave chimera states in large populations of coupled chemical oscillators. Nature Phys 14, 282–285 (2018). https://doi.org/10.1038/s41567-017-0005-8

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