Effective nonlocal kernels on reaction–diffusion networks

Shin Ichiro Ei, Hiroshi Ishii, Shigeru Kondo, Takashi Miura, Yoshitaro Tanaka

研究成果: Contribution to journalArticle査読

1 被引用数 (Scopus)


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.

ジャーナルJournal of Theoretical Biology
出版ステータス出版済み - 1 21 2021

All Science Journal Classification (ASJC) codes

  • 統計学および確率
  • モデリングとシミュレーション
  • 生化学、遺伝学、分子生物学(全般)
  • 免疫学および微生物学(全般)
  • 農業および生物科学(全般)
  • 応用数学


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