Nonlinear aspects of chemotaxis

S. Childress, J. K. 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 - Oct 1981

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

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