Turing pattern formation with two kinds of cells and a diffusive chemical

Koichiro Uriu, Yoh Iwasa

研究成果: ジャーナルへの寄稿学術誌査読

18 被引用数 (Scopus)


We study a three-variable Turing system with two kinds of cells and a diffusive chemical, considering the formation and maintenance of fish skin patterns with multiple pigment cells. The two types of cells are produced from undifferentiated cells. They inhibit the supply rate of the other cell type, forming local clusters of the same cell type. In addition, the cells of one type can be maintained only in the presence of a diffusive chemical produced by the other cell type, resulting in the coexistence of two cell types in heterogeneous spatial patterns. We assume linear interaction among cells and the chemical, and cell supply rates constrained to be positive or zero. We derive the condition for diffusion-driven instability. In one-dimensional model, we examine how the wavelength of the periodic pattern depends on parameters. In the two-dimensional model, we study the condition for spot, stripe or reversed spot pattern to emerge (pattern selection). We discuss heuristic criteria for the pattern selection.

ジャーナルBulletin of Mathematical Biology
出版ステータス出版済み - 11月 1 2007

!!!All Science Journal Classification (ASJC) codes

  • 農業および生物科学(全般)


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