English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we present computational techniques to investigate thesolutions of two-component, nonlinear reaction-diffusion (RD) systems onarbitrary surfaces. We build on standard techniques for linear and nonlinearanalysis of RD systems, and extend them to operate on large-scale meshes forarbitrary surfaces. In particular, we use spectral techniques for a linearstability analysis to characterize and directly compose patterns emerging fromhomogeneities. We develop an implementation using surface finite elementmethods and a numerical eigenanalysis of the Laplace-Beltrami operator onsurface meshes. In addition, we describe a technique to explore solutions ofthe nonlinear RD equations using numerical continuation. Here, we present amultiresolution approach that allows us to trace solution branches of thenonlinear equations efficiently even for large-scale meshes. Finally, wedemonstrate the working of our framework for two RD systems with applicationsin biological pattern formation: a Brusselator model that has been used tomodel pattern development on growing plant tips, and a chemotactic model forthe formation of skin pigmentation patterns. While these models have been usedpreviously on simple geometries, our framework allows us to study the impact ofarbitrary geometries on emerging patterns.

Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces