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Effective nonlocal kernels on reaction-diffusion networks

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Title: Effective nonlocal kernels on reaction-diffusion networks
Authors: Ei, Shin-Ichiro Browse this author →KAKEN DB
Ishii, Hiroshi Browse this author
Kondo, Shigeru Browse this author
Miura, Takashi Browse this author
Tanaka, Yoshitaro Browse this author
Keywords: Non-local convolution
Pattern formation
Turing pattern
Issue Date: 21-Jan-2021
Publisher: Elsevier
Journal Title: Journal of theoretical biology
Volume: 509
Start Page: 110496
Publisher DOI: 10.1016/j.jtbi.2020.110496
Abstract: A new method to derive an essential integral kernel from any given reaction-diffusion network is proposed. Any network describing metabolites or signals with arbitrary many factors can be reduced to a single or a simpler system of integro-differential equations called "effective equation" including the reduced integral kernel (called "effective kernel") in the convolution type. As one typical example, the Mexican hat shaped kernel is theoretically derived from two component activator-inhibitor systems. It is also shown that a three component system with quite different appearance from activator-inhibitor systems is reduced to an effective equation with the Mexican hat shaped kernel. It means that the two different systems have essentially the same effective equations and that they exhibit essentially the same spatial and temporal patterns. Thus, we can identify two different systems with the understanding in unified concept through the reduced effective kernels. Other two applications of this method are also given: Applications to pigment patterns on skins (two factors network with long range interaction) and waves of differentiation (called proneural waves) in visual systems on brains (four factors network with long range interaction). In the applications, we observe the reproduction of the same spatial and temporal patterns as those appearing in pre-existing models through the numerical simulations of the effective equations. (C) 2020 The Authors. Published by Elsevier Ltd.
Type: article
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

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