Stationary and oscillatory fronts in a two-component genetic regulatory network model
type: Item
instance of: scholarly article
title: Stationary and oscillatory fronts in a two-component genetic regulatory network model
zbMATH Open document ID: 1201.37113
author: Heather Hardway
author: Yue-Xian Li
published in: Physica D
publication date: 2010-09-24T00:00:00Z
review text: The authors investigate a two-component gene network model, originally used to describe the spatiotemporal patterning of the gene products in early Drosophila development and found both stable stationary and time-oscillatory fronts can occur in the reaction-diffusion system. Through reducing this system, the authors obtain explicit formula for all steady-state solutions and their linear eigenvalues. The authors also explore the range in which a monotone, stationary front is stable and show it can lose stability through a Hopf bifurcation, giving rise to oscillatory fronts. They also discuss the existence and stability of steady-state and time-oscillatory solutions with multiple extrema.
reviewed by: Fengqin Zhang
Mathematics Subject Classification ID: 37N25
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 92D10
Mathematics Subject Classification ID: 92C42
Mathematics Subject Classification ID: 35B32
zbMATH DE Number: 5791153
zbMATH Keywords: oscillatory front
zbMATH Keywords: reaction-diffusion
zbMATH Keywords: bifurcation
zbMATH Keywords: genetic network
MaRDI profile type: Publication
full work available at URL: j.physd.2010.04.009
OpenAlex ID: W2053404756
cites work: Q4856151
cites work: The geometry of biological time.
cites work: Mathematical biology. Vol. 2: Spatial models and biomedical applications.
cites work: Layer Oscillations in Reaction-Diffusion Systems
cites work: Study of propagation along nonuniform excitable fibers
cites work: Reflected Waves in an Inhomogeneous Excitable Medium
cites work: Front-bifurcations in reaction-diffusion systems with inhomogeneous parameter distributions
cites work: Analytic solutions for monotonic and oscillating fronts in a reaction-diffusion system under external fields
cites work: Tango waves in a bidomain model of fertilization calcium waves
cites work: Stability of front solutions in inhomogeneous media
cites work: Propagation of Waves in an Excitable Medium with Discrete Release Sites
cites work: Inhomogeneity-induced bifurcation of stationary and oscillatory pulses
cites work: Dynamics of traveling pulses in heterogeneous media
cites work: Modeling the precision and robustness of Hunchback border during \textit{Drosophila} embryonic development
cites work: Bifurcation phenomena from standing pulse solutions in some reaction-diffusion systems
cites work: Asymptotic behavior for solutions of a one-dimensional parabolic equation with homogeneous Neumann boundary conditions
cites work: Monotonicity of stable solutions in shadow systems
DOI: 10.1016/J.PHYSD.2010.04.009
description: scientific article; zbMATH DE number 5791153