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

doi:10.1088/1674-1056/acac13

中国物理B ›› 2023, Vol. 32 ›› Issue (9): 90203-090203.doi: 10.1088/1674-1056/acac13

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

Ying Sun(孙颖)¹, Jinliang Wang(王进良)^1,†, You Li(李由)², Nan Jiang(江南)¹, and Juandi Xia(夏娟迪)¹

1 LMIB and School of Mathematics and Science, Beihang University, Beijing 100191, China;
2 College of Science, Beijing Forestry University, Beijing 100083, China

收稿日期:2022-10-08 修回日期:2022-12-02 接受日期:2022-12-16 发布日期:2023-08-28
通讯作者: Jinliang Wang E-mail:jlwang@buaa.edu.cn
基金资助:
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).

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

Ying Sun(孙颖)¹, Jinliang Wang(王进良)^1,†, You Li(李由)², Nan Jiang(江南)¹, and Juandi Xia(夏娟迪)¹

1 LMIB and School of Mathematics and Science, Beihang University, Beijing 100191, China;
2 College of Science, Beijing Forestry University, Beijing 100083, China

Received:2022-10-08 Revised:2022-12-02 Accepted:2022-12-16 Published:2023-08-28
Contact: Jinliang Wang E-mail:jlwang@buaa.edu.cn
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: plant-wrack model, cross-diffusion, Turing instability, pattern selection, amplitude equation

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.

Key words: plant-wrack model, cross-diffusion, Turing instability, pattern selection, amplitude equation

中图分类号: (Bifurcation theory)

02.30.Oz

02.30.Hq (Ordinary differential equations)

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[J]. 中国物理B, 2023, 32(9): 90203-090203.

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[J]. Chin. Phys. B, 2023, 32(9): 90203-090203.

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

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

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