Madzvamuse_Chung_Venkataraman_PRSA_2015.pdf (919.33 kB)
Download fileStability analysis and simulations of coupled bulk-surface reaction–diffusion systems
journal contribution
posted on 2023-06-08, 20:01 authored by Anotida Madzvamuse, Andy H W Chung, Chandrasekhar VenkataramanChandrasekhar VenkataramanIn 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.
Funding
Unravelling new mathematics for 3D cell migration; G1438; LEVERHULME TRUST; RPG-2014-149
Mathematical Modelling and Analysis of Spatial Patterning on Evolving Surfaces; G0872; EPSRC-ENGINEERING & PHYSICAL SCIENCES RESEARCH COUNCIL; EP/J016780/1
History
Publication status
- Published
File Version
- Published version
Journal
Proceedings of the Royal Society AISSN
1364-5021Publisher
The Royal SocietyExternal DOI
Issue
2175Volume
471Article number
a20140546Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes