ArticleJournal of mathematical biology2017
Instability of turing patterns in reaction-diffusion-ODE systems.
Article in Journal of mathematical biology, 2017. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 9 papers.
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Who cites it
9 citing papers in PubMed.
- FR-BINN: Biologically Informed Neural Networks for Enhanced Biomarker Discovery and Pathway Analysis.International journal of molecular sciences · 2025Article
- Linking discrete and continuous models of cell birth and migration.Royal Society open science · 2024Article
- Network representation and analysis of energy coupling mechanisms in cellular metabolism by a graph-theoretical approach.Theory in biosciences = Theorie in den Biowissenschaften · 2022Article
- Pattern Formation in a Spatially Extended Model of Pacemaker Dynamics in Smooth Muscle Cells.Bulletin of mathematical biology · 2022Article
- Optimal control of networked reaction-diffusion systems.Journal of the Royal Society, Interface · 2022Article
- Mathematical models of nitrogen-fixing cell patterns in filamentous cyanobacteria.Frontiers in cell and developmental biology · 2022Review
- Modern perspectives on near-equilibrium analysis of Turing systems.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2021Review
- Signaling gradients in surface dynamics as basis for planarian regeneration.Journal of mathematical biology · 2021Article
- Post-Turing tissue pattern formation: Advent of mechanochemistry.PLoS computational biology · 2018Article
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Authors and funding
3 authors.
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Abstract
The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of interactions between cellular processes such as cell growth, differentiation or transformation and diffusing signaling factors. We focus on stability analysis of solutions of a prototype model consisting of a single reaction-diffusion equation coupled to an ordinary differential equation. We show that such systems are very different from classical reaction-diffusion models. They exhibit diffusion-driven instability (turing instability) under a condition of autocatalysis of non-diffusing component. However, the same mechanism which destabilizes constant solutions of such models, destabilizes also all continuous spatially heterogeneous stationary solutions, and consequently, there exist no stable Turing patterns in such reaction-diffusion-ODE systems. We provide a rigorous result on the nonlinear instability, which involves the analysis of a continuous spectrum of a linear operator induced by the lack of diffusion in the destabilizing equation. These results are extended to discontinuous patterns for a class of nonlinearities.
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