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Turing pattern dynamics and adaptive discretization for a super-diffusive Lotka-Volterra model
| Content Provider | Semantic Scholar |
|---|---|
| Author | Bendahmane, Mostafa Ruiz-Baier, Ricardo Tian, Canrong |
| Copyright Year | 2016 |
| Abstract | In this paper we analyze the effects of introducing the fractional-in-space operator into a Lotka-Volterra competitive model describing population super-diffusion. First, we study how cross super-diffusion influences the formation of spatial patterns: a linear stability analysis is carried out, showing that cross super-diffusion triggers Turing instabilities, whereas classical (self) super-diffusion does not. In addition we perform a weakly nonlinear analysis yielding a system of amplitude equations, whose study shows the stability of Turing steady states. A second goal of this contribution is to propose a fully adaptive multiresolution finite volume method that employs shifted Grünwald gradient approximations, and which is tailored for a larger class of systems involving fractional diffusion operators. The scheme is aimed at efficient dynamic mesh adaptation and substantial savings in computational burden. A numerical simulation of the model was performed near the instability boundaries, confirming the behavior predicted by our analysis. |
| Starting Page | 1441 |
| Ending Page | 1465 |
| Page Count | 25 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s00285-015-0917-9 |
| PubMed reference number | 26219250 |
| Journal | Medline |
| Volume Number | 72 |
| Alternate Webpage(s) | http://people.maths.ox.ac.uk/ruizbaier/myPapers/brt_jmb16.pdf |
| Alternate Webpage(s) | https://doi.org/10.1007/s00285-015-0917-9 |
| Journal | Journal of mathematical biology |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
