Turing pattern dynamics and adaptive discretization for a superdiffusive Lotka-Volterra system
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN] | |
| dc.contributor.author | BENDAHMANE, Mostafa | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Ecole Polytechnique Fédérale de Lausanne [EPFL] | |
| dc.contributor.author | RUIZ-BAIER, Ricardo | |
| hal.structure.identifier | Yancheng Institute of Technology [YIT] | |
| dc.contributor.author | TIAN, Canrong | |
| dc.date.accessioned | 2024-04-04T03:12:49Z | |
| dc.date.available | 2024-04-04T03:12:49Z | |
| dc.date.issued | 2016 | |
| dc.identifier.issn | 0303-6812 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193899 | |
| dc.description.abstractEn | We focus our attention on the effects of introducing the fractional-in-space operator into a Lotka-Volterra competitive model describing population superdiffusion. First, we address the weak solvability of the coupled problem employing the Faedo-Galerkin method and compactness arguments. In addition, we are interested in how cross superdiffusion influences the formation of spatial patterns: a linear stability analysis has been carried out, showing that cross superdiffusion triggers Turing instabilities, whereas classical self superdiffusion suppresses Turing instability. We have also performed 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 (MRFV) method that employs shifted Grunwald gradient approximations, and which is tailored for a larger class of systems involving fractional diffusion operators, and 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. | |
| dc.language.iso | en | |
| dc.publisher | Springer | |
| dc.subject.en | Turing instability | |
| dc.subject.en | Pattern formation | |
| dc.subject.en | Amplitude equations | |
| dc.subject.en | Superdiffusion | |
| dc.subject.en | Finite volume approximation | |
| dc.subject.en | Fully adaptive multiresolution | |
| dc.subject.en | PhD Yangzhou | |
| dc.subject.en | Jiangsu Province CHINA Corresponding Author Secondary Information: Corresponding Author's Institution: Corresponding Author's Secondary Institution: | |
| dc.title.en | Turing pattern dynamics and adaptive discretization for a superdiffusive Lotka-Volterra system | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math] | |
| bordeaux.journal | Journal of Mathematical Biology | |
| bordeaux.page | 1441-1465 | |
| bordeaux.volume | 6 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01403081 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01403081v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Mathematical%20Biology&rft.date=2016&rft.volume=6&rft.spage=1441-1465&rft.epage=1441-1465&rft.eissn=0303-6812&rft.issn=0303-6812&rft.au=BENDAHMANE,%20Mostafa&RUIZ-BAIER,%20Ricardo&TIAN,%20Canrong&rft.genre=article |
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