Turing pattern dynamics and adaptive discretization for a superdiffusive Lotka-Volterra system
BENDAHMANE, Mostafa
Institut de Mathématiques de Bordeaux [IMB]
Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
Institut de Mathématiques de Bordeaux [IMB]
Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
RUIZ-BAIER, Ricardo
Institut de Mathématiques de Bordeaux [IMB]
Ecole Polytechnique Fédérale de Lausanne [EPFL]
Institut de Mathématiques de Bordeaux [IMB]
Ecole Polytechnique Fédérale de Lausanne [EPFL]
BENDAHMANE, Mostafa
Institut de Mathématiques de Bordeaux [IMB]
Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
Institut de Mathématiques de Bordeaux [IMB]
Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
RUIZ-BAIER, Ricardo
Institut de Mathématiques de Bordeaux [IMB]
Ecole Polytechnique Fédérale de Lausanne [EPFL]
< Leer menos
Institut de Mathématiques de Bordeaux [IMB]
Ecole Polytechnique Fédérale de Lausanne [EPFL]
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en
Article de revue
Este ítem está publicado en
Journal of Mathematical Biology. 2016, vol. 6, p. 1441-1465
Springer
Resumen en inglés
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 ...Leer más >
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.< Leer menos
Palabras clave en inglés
Turing instability
Pattern formation
Amplitude equations
Superdiffusion
Finite volume approximation
Fully adaptive multiresolution
PhD Yangzhou
Jiangsu Province CHINA Corresponding Author Secondary Information: Corresponding Author's Institution: Corresponding Author's Secondary Institution:
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