Turing instability of the periodic solutions for reaction-diffusion systems with cross-diffusion and the patch model with cross-diffusion-like coupling

In this paper, we determine how the diffusion could destabilize an otherwise stable spatially homogeneous periodic solutions for the diffusive systems. This is known as Turing instability of the periodic solutions. In a general setting, we establish a formulae in terms of the diffusion rates (not ne...

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Bibliographic Details
Published in:Journal of Differential Equations 2021-04, Vol.281, p.379-410
Main Author: Yi, Fengqi
Format: Article
Language:English
Subjects:
Spatially homogeneous periodic solutions
The Lengyel-Epstein model
The patch model of n-coupled reactors
The PDEs model with cross-diffusions
Turing instability
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Summary:In this paper, we determine how the diffusion could destabilize an otherwise stable spatially homogeneous periodic solutions for the diffusive systems. This is known as Turing instability of the periodic solutions. In a general setting, we establish a formulae in terms of the diffusion rates (not necessarily limited to either larger diffusivity or smaller diffusivity) to determine Turing instability of the Hopf bifurcating periodic solutions for reaction-diffusion systems with cross-diffusions and the patch model of n-coupled reactors with cross-diffusion-like coupling. Then, we supply an example of the Lengyel-Epstein model which is used to characterize the CIMA chemical reactions to demonstrate how our results can be applied.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2021.02.006