Spatiotemporal dynamics of reaction-diffusion equations modeling predator-prey interactions using DUNE-PDELab
| Autor: | Noaman Khan, Ishtiaq Ali |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Surface (mathematics)
0303 health sciences Computer science Numerical analysis Complex system General Physics and Astronomy Space (mathematics) 01 natural sciences 010101 applied mathematics 03 medical and health sciences Distribution (mathematics) Reaction–diffusion system Quantitative Biology::Populations and Evolution Statistical physics Boundary value problem 0101 mathematics Diffusion (business) 030304 developmental biology |
| Zdroj: | The European Physical Journal Plus. 134 |
| ISSN: | 2190-5444 |
| DOI: | 10.1140/epjp/i2019-12920-7 |
| Popis: | Reaction-diffusion systems (RDS) help us to understand the distribution of the concentration of substances in space or time under the influence of two phenomena: local chemical reactions where the substances are transmuted into one another, and diffusion which causes the substances to spread out over a surface in space. Analytical solutions for these behavioral models are still lacking, therefore it is essential to use some numerical methods to find approximate solution to these systems as the numerical results will allow us the use of parameters fitting. This study focuses on the numerical approximation based on finite-element scheme together with the powerful DUNE-PDELab package to investigate the spatio-temporal dynamics of the structure of predator-prey diffusive model. The scheme is introduced for approximation of predator-prey with Holling type-II functional response, while the growth is logistic, subject to some appropriate initial and boundary conditions. The simulations were obtained in the two-dimensional case, which demonstrate that the initial and boundary conditions play an important role in identifying the spatio-temporal dynamics of predator-prey interactions. |
| Databáze: | OpenAIRE |
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