Nonlinear aspects of chemotaxis

S. Childress, Jerome Percus

Research output: Contribution to journalArticle

Abstract

A simplified Keller-Segel model for the chemotactic movements of cellular slime mold is reconsidered. In particular, we ask for the circumstances under which the cell distribution can autonomously develop a δ-function singularity. By the use of suitable differential inequalities, we show that this cannot happen in the case of one-dimensional aggregation. For three or more dimensions, we produce time developments which do become singular, while in the important special case of two-dimensional motion, we advance arguments that the possibility of chemotactic collapse requires a threshold number of cells in the system.

Original languageEnglish (US)
Pages (from-to)217-237
Number of pages21
JournalMathematical Biosciences
Volume56
Issue number3-4
DOIs
StatePublished - 1981

Fingerprint

Dictyosteliida
slime mould
chemotaxis
Chemotaxis
Fungi
Agglomeration
Cell Count
Keller-Segel Model
Cell
Differential Inequalities
Aggregation
Singularity
cells
Motion
distribution

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Ecology, Evolution, Behavior and Systematics

Cite this

Nonlinear aspects of chemotaxis. / Childress, S.; Percus, Jerome.

In: Mathematical Biosciences, Vol. 56, No. 3-4, 1981, p. 217-237.

Research output: Contribution to journalArticle

Childress, S & Percus, J 1981, 'Nonlinear aspects of chemotaxis', Mathematical Biosciences, vol. 56, no. 3-4, pp. 217-237. https://doi.org/10.1016/0025-5564(81)90055-9
Childress, S. ; Percus, Jerome. / Nonlinear aspects of chemotaxis. In: Mathematical Biosciences. 1981 ; Vol. 56, No. 3-4. pp. 217-237.
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