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.
CITATION STYLE
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
Mendeley helps you to discover research relevant for your work.