Spatiotemporal patterns induced by cross-diffusion on vegetation model

Shuo Xu; Chunrui Zhang; Shuo Xu; Chunrui Zhang

doi:10.3934/math.2022776

AIMS Mathematics

2022, Volume 7, Issue 8: 14076-14098. doi: 10.3934/math.2022776

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Research article

Spatiotemporal patterns induced by cross-diffusion on vegetation model

Shuo Xu ,
Chunrui Zhang ^,

Department of Mathematics, Northeast Forestry University, Harbin 150040, China

Received: 09 March 2022 Revised: 28 April 2022 Accepted: 16 May 2022 Published: 27 May 2022
MSC : 34K18, 35B32

This paper considers the influence of cross-diffusion on semi-arid ecosystems based on simplified Hardenberg's reaction diffusion model. In the square region, we analyze the properties of this model and give the relaxation time correspond to the system to prejudge the approximate time of this system stabilization process. The numerical results are constant with the theory very well.
- semi-arid ecosystems,
- Turing bifurcation,
- steady-state bifurcation,
- cross-diffusion,
- relaxation time
Citation: Shuo Xu, Chunrui Zhang. Spatiotemporal patterns induced by cross-diffusion on vegetation model[J]. AIMS Mathematics, 2022, 7(8): 14076-14098. doi: 10.3934/math.2022776

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Abstract

This paper considers the influence of cross-diffusion on semi-arid ecosystems based on simplified Hardenberg's reaction diffusion model. In the square region, we analyze the properties of this model and give the relaxation time correspond to the system to prejudge the approximate time of this system stabilization process. The numerical results are constant with the theory very well.

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