Revealing new dynamical patterns in a reaction-diffusion model with cyclic competition via a novel computational framework
| Autor: | Andrew Morozov, Emmanuil H. Georgoulis, Oliver J. Sutton, Andrea Cangiani |
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| Rok vydání: | 2017 |
| Předmět: |
0301 basic medicine
Wave propagation Computer science General Mathematics General Physics and Astronomy Pattern formation 010103 numerical & computational mathematics 01 natural sciences 03 medical and health sciences Competition model Reaction–diffusion system FOS: Mathematics Mathematics - Numerical Analysis Statistical physics 0101 mathematics Spatial dependence Quantitative Biology - Populations and Evolution Research Articles Numerical analysis General Engineering Populations and Evolution (q-bio.PE) Numerical Analysis (math.NA) Finite element method 030104 developmental biology FOS: Biological sciences A priori and a posteriori |
| Zdroj: | Proceedings. Mathematical, physical, and engineering sciences. 474(2213) |
| ISSN: | 1364-5021 |
| Popis: | Understanding how patterns and travelling waves form in chemical and biological reaction-diffusion models is an area which has been widely researched, yet is still experiencing fast development. Surprisingly enough, we still do not have a clear understanding about all possible types of dynamical regimes in classical reaction-diffusion models such as Lotka-Volterra competition models with spatial dependence. In this work, we demonstrate some new types of wave propagation and pattern formation in a classical three species cyclic competition model with spatial diffusion, which have been so far missed in the literature. These new patterns are characterised by a high regularity in space, but are different from patterns previously known to exist in reaction-diffusion models, and may have important applications in improving our understanding of biological pattern formation and invasion theory. Finding these new patterns is made technically possible by using an automatic adaptive finite element method driven by a novel a posteriori error estimate which is proven to provide a reliable bound for the error of the numerical method. We demonstrate how this numerical framework allows us to easily explore the dynamical patterns both in two and three spatial dimensions. Comment: 24 pages, 35 figures |
| Databáze: | OpenAIRE |
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