Spatio-temporal chaos in a chemotaxis model
type: Item
instance of: scholarly article
title: Spatio-temporal chaos in a chemotaxis model
zbMATH Open document ID: 1255.37026
author: Kevin J. Painter
author: Thomas Hillen
published in: Physica D
publication date: 2011-03-08T00:00:00Z
review text: In this paper, the dynamics of a one-dimensional Keller-Segel type model for chemotaxis incorporating a logistic cell growth term was explore. The capacity of the model to self-organise into multiple cellular aggregations was demonstrated, which, according to position in parameter space, either form a stationary pattern or undergo a sustained spatio-temporal sequence of merging (two aggregations coalesce) and emerging (a new aggregation appears). This spatio-temporal patterning can be further subdivided into either a time-periodic or time-irregular fashion. Numerical explorations into the latter indicate a positive Lyapunov exponent (sensitive dependence to initial conditions) together with a rich bifurcation structure. In particular, it was found that stationary patterns that bifurcate onto a path of periodic patterns which, prior to the onset of spatio-temporal irregularity, undergo a ``periodic-doubling'' sequence. Based on these results and comparisons with other systems, it was argued that the spatio-temporal irregularity observed here describes a form of spatio-temporal chaos. Brief discussion on the results in the context of previous applications of chemotaxis models, including tumour invasion, embryonic development and ecology was followed.
reviewed by: Shengqiang Liu
Mathematics Subject Classification ID: 37N25
Mathematics Subject Classification ID: 92C17
Mathematics Subject Classification ID: 92C37
Mathematics Subject Classification ID: 35Q92
Mathematics Subject Classification ID: 37M25
zbMATH DE Number: 5862557
zbMATH Keywords: chemotaxis
zbMATH Keywords: continuous models
zbMATH Keywords: pattern formation
zbMATH Keywords: spatio-temporal chaos
zbMATH Keywords: morphogenesis
describes a project that uses: ROWMAP
MaRDI profile type: Publication
full work available at URL: j.physd.2010.09.011
OpenAlex ID: W2023884962
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DOI: 10.1016/J.PHYSD.2010.09.011
description: scientific article; zbMATH DE number 5862557