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. 2019 Mar 8;9:3935. doi: 10.1038/s41598-019-40373-4

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© The Author(s) 2019

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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(a) The shaded area indicates where spontaneous centers can be observed, depending on cell density. Blue dots indicate the degradation rate at which 75% of the simulations presented spontaneous centers. Error bar extends up to 50%. Lower boundary marks the maximum degradation rate at which the homogeneous system presents bulk oscillations. (b) Dispersion relations for different densities. 5 · 10⁵ cells/cm² (0.5 mono-layer) in red circles, 4 · 10⁵ cells/cm² (0.4 mono-layer) in black squares, and 3 · 10⁵ cells/cm² (0.3 mono-layer) in blue triangles. k_e = 5.0 min⁻¹. (c) Center frequency for different degradation values. 1-D simulations with density = 4 · 10⁵ cells/cm², 100 simulations used for each k_e value.