Dynamics for a Charge Transfer Model with Cross-Diffusion: Turing Instability of Periodic Solutions

This paper is devoted to a charge transfer model with cross-diffusion under Neumann boundary conditions. We investigate how the cross-diffusion could destabilize the stable periodic solutions bifurcating from the unique positive equilibrium point. By the implicit function theorem and Floquet theory,...

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Bibliographic Details
Published in:Acta applicandae mathematicae 2024-08, Vol.192 (1), p.2, Article 2
Main Authors: Guo, Gaihui, You, Jing, Du, Xinhuan, Li, Yanling
Format: Article
Language:English
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Summary:This paper is devoted to a charge transfer model with cross-diffusion under Neumann boundary conditions. We investigate how the cross-diffusion could destabilize the stable periodic solutions bifurcating from the unique positive equilibrium point. By the implicit function theorem and Floquet theory, we obtain some conditions on the self-diffusion and cross-diffusion coefficients under which the stable periodic solutions can become unstable. New irregular Turing patterns then generate by the destabilization of stable spatially homogeneous periodic solutions. We also present some numerical simulations to further support the results of theoretical analysis.
ISSN:0167-8019
1572-9036
DOI:10.1007/s10440-024-00666-x