Turing pattern selection for a plant-wrack model with cross-diffusion

doi:10.1088/1674-1056/acac13

Abstract We investigate the Turing instability and pattern formation mechanism of a plant-wrack model with both self-diffusion and cross-diffusion terms. We first study the effect of self-diffusion on the stability of equilibrium. We then derive the conditions for the occurrence of the Turing patterns induced by cross-diffusion based on self-diffusion stability. Next, we analyze the pattern selection by using the amplitude equation and obtain the exact parameter ranges of different types of patterns, including stripe patterns, hexagonal patterns and mixed states. Finally, numerical simulations confirm the theoretical results.

Keywords: plant-wrack model cross-diffusion Turing instability pattern selection amplitude equation

Received: 08 October 2022
Revised: 02 December 2022
Accepted manuscript online: 16 December 2022

PACS:	02.30.Oz	(Bifurcation theory)
	02.30.Hq	(Ordinary differential equations)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10971009, 11771033, and 12201046), Fundamental Research Funds for the Central Universities (Grant No. BLX201925), and China Postdoctoral Science Foundation (Grant No. 2020M670175).

Corresponding Authors: Jinliang Wang
E-mail: jlwang@buaa.edu.cn

Cite this article:

Ying Sun(孙颖), Jinliang Wang(王进良), You Li(李由), Nan Jiang(江南), and Juandi Xia(夏娟迪) Turing pattern selection for a plant-wrack model with cross-diffusion 2023 Chin. Phys. B 32 090203

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Turing pattern selection for a plant-wrack model with cross-diffusion

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