BENDAHMANE, Mostafa; RUIZ-BAIER, Ricardo; TIAN, Canrong

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BENDAHMANE, Mostafa
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]

TIAN, Canrong
Yancheng Institute of Technology [YIT]

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Ce document a été publié dans

Journal of Mathematical Biology. 2016, vol. 6, p. 1441-1465

Springer

Résumé en anglais

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.< Réduire

Mots clés en anglais

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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Turing pattern dynamics and adaptive discretization for a superdiffusive Lotka-Volterra system

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