Turing instability in reaction–diffusion models on complex networks

Yusuke Ide, Hirofumi Izuhara and Takuya Machida

Physica A: Statistical Mechanics and its Applications, 2016, vol. 457, issue C, 331-347

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 Erdős–Rényi, the Watts–Strogatz, and the threshold network models. From analysis of the Laplacian matrices of graphs generated by these models, we numerically reveal that stable and unstable regions of a homogeneous steady state on the parameter space of two diffusion coefficients completely differ, depending on the network architecture. In addition, we theoretically discuss the stable and 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.

Keywords: Turing instability; Reaction–diffusion models on networks; Complex network; Pattern formation (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:457:y:2016:i:c:p:331-347

DOI: 10.1016/j.physa.2016.03.055

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