ArticleProceedings. Mathematical, physical, and engineering sciences2015
Stability analysis and simulations of coupled bulk-surface reaction-diffusion systems.
Article in Proceedings. Mathematical, physical, and engineering sciences, 2015. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 12 papers.
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12 citing papers in PubMed.
- Cell-Size Confinement Drives Size-Dependent Scaling of Intracellular Reaction-Diffusion Waves for Robust Patterning.Small science · 2026Article
- Using Floquet theory to unravel far-from equilibrium dynamics in reaction-diffusion systems.PNAS nexus · 2026Article
- Designing reaction-cross-diffusion systems with Turing and wave instabilities.Journal of mathematical biology · 2025Article
- Turing Pattern Formation in Reaction-Cross-Diffusion Systems with a Bilayer Geometry.Bulletin of mathematical biology · 2024Article
- conditions for Turing and wave instabilities in reaction-diffusion systems.Journal of mathematical biology · 2023Article
- Modern perspectives on near-equilibrium analysis of Turing systems.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2021Review
- Turing Patterning in Stratified Domains.Bulletin of mathematical biology · 2020Article
- Influence of Curvature, Growth, and Anisotropy on the Evolution of Turing Patterns on Growing Manifolds.Bulletin of mathematical biology · 2019Article
- Article
- Local modulation of chemoattractant concentrations by single cells: dissection using a bulk-surface computational model.Interface focus · 2016Article
- Effects of 3D geometries on cellular gradient sensing and polarization.Physical biology · 2016Article
- A computational method for the coupled solution of reaction-diffusion equations on evolving domains and manifolds: Application to a model of cell migration and chemotaxis.Journal of computational physics · 2016Article
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3 authors.
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Abstract
In this article, we formulate new models for coupled systems of bulk-surface reaction-diffusion equations on stationary volumes. The bulk reaction-diffusion equations are coupled to the surface reaction-diffusion equations through linear Robin-type boundary conditions. We then state and prove the necessary conditions for diffusion-driven instability for the coupled system. Owing to the nature of the coupling between bulk and surface dynamics, we are able to decouple the stability analysis of the bulk and surface dynamics. Under a suitable choice of model parameter values, the bulk reaction-diffusion system can induce patterning on the surface independent of whether the surface reaction-diffusion system produces or not, patterning. On the other hand, the surface reaction-diffusion system cannot generate patterns everywhere in the bulk in the absence of patterning from the bulk reaction-diffusion system. For this case, patterns can be induced only in regions close to the surface membrane. Various numerical experiments are presented to support our theoretical findings. Our most revealing numerical result is that, Robin-type boundary conditions seem to introduce a boundary layer coupling the bulk and surface dynamics.
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