Forma, Vol. 27 (No. 1), pp. 19-23, 2012


Three-Dimensional Specific Patterns Based on the Keller-Segel Model

Hiroto Shoji1,2*, Makiko Nonomura2,3 and Kohtaro Yamada4

1Department of Physics, Graduate School of Medicine, Kyoto Prefectural University of Medicine, Kyoto 603-8334, Japan
2PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan
3Department of Mathematical Information Engineering, College of Industrial Technology, Nihon University, 1-2-1 Izumi-cho, Narashino, Chiba 275-8575, Japan
4Liberal Arts Division, Anan National College of Technology, 265 Aoki Minobayashi, Anan, Tokushima 774-0017, Japan
*E-mail address:

(Received November 1, 2011; Accepted March 11, 2012)

Abstract. Aggregation patterns in the volume-filling Keller-Segel model are studied numerically. Three-dimensional specific patterns, such as P-surface, perforated lamellar, are appeared. These patterns never exist in lower dimensions. The relative stability analysis of these patterns is also performed numerically on the basis of the derived free energy and of the robustness against perturbation.

Keywords: Chemotaxis, Keller-Segel Model, Pattern Selection, Stability Analysis

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