Title
Numerical bifurcation analysis of the pattern formation in a cell based auxin transport model Numerical bifurcation analysis of the pattern formation in a cell based auxin transport model
Author
Faculty/Department
Faculty of Sciences. Biology
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Berlin ,
Subject
Mathematics
Biology
Human medicine
Computer. Automation
Source (journal)
Journal of mathematical biology. - Berlin
Volume/pages
67(2013) :5 , p. 1279-1305
ISSN
0303-6812
ISI
000325463200011
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
Transport models of growth hormones can be used to reproduce the hormone accumulations that occur in plant organs. Mostly, these accumulation patterns are calculated using time step methods, even though only the resulting steady state patterns of the model are of interest. We examine the steady state solutions of the hormone transport model of Smith et al. (Proc Natl Acad Sci USA 103(5):13011306, 2006) for a one-dimensional row of plant cells. We search for the steady state solutions as a function of three of the model parameters by using numerical continuation methods and bifurcation analysis. These methods are more adequate for solving steady state problems than time step methods. We discuss a trivial solution where the concentrations of hormones are equal in all cells and examine its stability region. We identify two generic bifurcation scenarios through which the trivial solution loses its stability. The trivial solution becomes either a steady state pattern with regular spaced peaks or a pattern where the concentration is periodic in time.
E-info
https://repository.uantwerpen.be/docman/iruaauth/d229a5/1f5bbf239f5.pdf
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