Turing instability in reaction–diffusion models on complex networks
| Autor: | Hirofumi Izuhara, Takuya Machida, Yusuke Ide |
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| Rok vydání: | 2016 |
| Předmět: |
Statistics and Probability
Discrete mathematics Ring (mathematics) Network architecture Probability (math.PR) FOS: Physical sciences Pattern Formation and Solitons (nlin.PS) Parameter space Complex network Condensed Matter Physics Nonlinear Sciences - Pattern Formation and Solitons 01 natural sciences 010305 fluids & plasmas 0103 physical sciences Reaction–diffusion system FOS: Mathematics Statistical physics Diffusion (business) 010306 general physics Laplace operator Mathematics - Probability Network model Mathematics |
| Zdroj: | Physica A: Statistical Mechanics and its Applications. 457:331-347 |
| ISSN: | 0378-4371 |
| DOI: | 10.1016/j.physa.2016.03.055 |
| Popis: | 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 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. Comment: Physica A (in press) |
| Databáze: | OpenAIRE |
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