Interdisciplinary Applied Mathematics

  • Shclick T
  • Torquato S
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Abstract

In this paper, the Turing instability in reaction-diffusion models defined on complex networks is studied. Here, we focus on three types of models which generate complex networks, i.e. the Erd\H{o}s-R\'enyi, the Watts-Strogatz and the threshold network models. From analysis of the Laplacian matrices of graphs generated by these models, we reveal that the stable-unstable regions of a spatially homogeneous solution completely differ, depending on network structures. In particular, we approximately argue the existence of the stable-unstable regions in the cases of regular enhanced ring lattices which include regular circles, and networks generated by the threshold network model when the number of vertices is large enough.

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Shclick, T., & Torquato, S. (2013). Interdisciplinary Applied Mathematics. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics (Vol. 82, p. 476). https://doi.org/10.1016/j.camwa.2013.03.019

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