Numerical bifurcation analysis of pattern formation in a cell based auxin transport model

TL;DR

This paper applies numerical bifurcation analysis to a plant hormone transport model to identify steady state patterns and their stability, offering a more efficient alternative to traditional time step simulations.

Contribution

It introduces bifurcation analysis to study steady states in a cell-based auxin transport model, revealing stability regions and pattern formation mechanisms.

Findings

Identified stability regions of uniform hormone distribution.

Discovered bifurcation scenarios leading to patterned steady states.

Showed bifurcation analysis as an effective tool for steady state solutions.

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 (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.