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
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.
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
[1] Wang D 1990Advances in Math19 38 [2] Zhang C X and Ouyang Q 2002Science (Shanghai)75 17 [3] Turing A M 1952Bulletin of Mathematical Biology641 37 [4] Marsden J E and McCracken M 1978Springer-Verlag, New York20 410 [5] Wiggins 1991New York:Springer-Verlag31 1 [6] Murray J D 2002Springer-Verlag, New York17 187 [7] Zheng L X, Guo B Z and Yan L 2019Acta Phys. Sin.68 068201(in Chinese) [8] Qi Q, Zhang D J, Zhang M Y, Tong S Z and Zhu G L 2021STE780 146630 [9] Koppel J V D and Crain C M 2006The American Naturalist168 136 [10] Yu B G 2010Commun Nonlinear Sci Numer Simulat15 2201 [11] Liu Z H, Wang A L, Wang B and Liu Y J 2010AMC216 983 [12] Wang J L, Li Y and Hou X J 2019Mathematical Analysis26 231 [13] Hou X J, Wang J L and Li Y 2019Applicable Analysis101 2022 [14] Li Y, Cao J, Sun Y, Song D and Wu X 2021ADE539 399 [15] Zhou J 2016Mathematical Biosciences and Engineering13 857 [16] Kerner E H 1957Bull. Math. Biol.19 121 [17] Holmes E E, Lewis M A, Banks J E and Veit R R 1994Ecol.75 17 [18] Chattopadhyay J and Tapaswi P K 1997Acta Appl. Math.48 112 [19] Okubo A and Levin S 2001Springer, Berlin14 591 [20] Xie Z 2012J. Math. Anal. Appl.388 539 [21] Guin L N, Haque M and Mandal P K 2012Appl. Math. Model.36 1825 [22] Guin L N 2014Appl. Math. Comput.226 320 [23] Haile D and Xie Z 2015Math. Biosci.267 134 [24] Fang L and Wang J 2016Appl. Math. Lett.58 49 [25] Ghorai S and Poria S 2016Chaos Solit. Fract.91 421 [26] Wen Z and Fu S M 2016Chaos Solit. Fract.91 379 [27] Iida M, Mimura M and Ninomiya H 2006JMB53 617 [28] Banerjee M, Ghorai S, Mukherjee and Nayana 2018AMM55 383 [29] Li L, Jin Z and Sun G Q 2008Chin. Phys. Lett.25 3500 [30] Wang W M, Wang W J, Lin Y Z and Tan Y J 2011Chin. Phys. B20 034702 [31] Banerjee M and Abbas S 2015Ecological Complexity21 199 [32] Han R J and Dai B X 2017IJBC27 1750088 [33] Sun G Q, Wang C H and Wu Z Y 2017Nonlinear Dyn88 1385 [34] Zheng Q Q, Wang Z J and Shen J W 2017Chin. Phys. B26 020501 [35] Zheng Q Q and Shen J W 2020Applied Mathematics and Computation381 125304 [36] Batabyal S, Jana D and Upadhyay R 2021CSF147 110929 [37] Arnab M, Ranjit K, Argha M and Sanjeev K 2022AMC423 127010
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