Turing pattern in the fractional Gierer-Meinhardt model

doi:10.1088/1674-1056/28/5/050503

中国物理B ›› 2019, Vol. 28 ›› Issue (5): 50503-050503.doi: 10.1088/1674-1056/28/5/050503

Turing pattern in the fractional Gierer-Meinhardt model

Yu Wang(王语), Rongpei Zhang(张荣培), Zhen Wang(王震), Zijian Han(韩子健)

1 School of Mathematics and Systematic Sciences, Shenyang Normal University, Shenyang 110034, China;
2 College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

收稿日期:2018-12-22 修回日期:2019-03-04 出版日期:2019-05-05 发布日期:2019-05-05
通讯作者: Rongpei Zhang E-mail:rongpeizhang@163.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61573008 and 61703290) and Natural Science Foundation of Liaoning Province, China (Grant No. 20180550996).

Turing pattern in the fractional Gierer-Meinhardt model

Yu Wang(王语)¹, Rongpei Zhang(张荣培)¹, Zhen Wang(王震)², Zijian Han(韩子健)¹

1 School of Mathematics and Systematic Sciences, Shenyang Normal University, Shenyang 110034, China;
2 College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Received:2018-12-22 Revised:2019-03-04 Online:2019-05-05 Published:2019-05-05
Contact: Rongpei Zhang E-mail:rongpeizhang@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61573008 and 61703290) and Natural Science Foundation of Liaoning Province, China (Grant No. 20180550996).

摘要/Abstract

摘要： It is well-known that reaction-diffusion systems are used to describe the pattern formation models. In this paper, we will investigate the pattern formation generated by the fractional reaction-diffusion systems. We first explore the mathematical mechanism of the pattern by applying the linear stability analysis for the fractional Gierer-Meinhardt system. Then, an efficient high-precision numerical scheme is used in the numerical simulation. The proposed method is based on an exponential time differencing Runge-Kutta method in temporal direction and a Fourier spectral method in spatial direction. This method has the advantages of high precision, better stability, and less storage. Numerical simulations show that the system control parameters and fractional order exponent have decisive influence on the generation of patterns. Our numerical results verify our theoretical results.

关键词: Turing patterns, fractional Gierer-Meinhardt model, Fourier spectral method

Abstract: It is well-known that reaction-diffusion systems are used to describe the pattern formation models. In this paper, we will investigate the pattern formation generated by the fractional reaction-diffusion systems. We first explore the mathematical mechanism of the pattern by applying the linear stability analysis for the fractional Gierer-Meinhardt system. Then, an efficient high-precision numerical scheme is used in the numerical simulation. The proposed method is based on an exponential time differencing Runge-Kutta method in temporal direction and a Fourier spectral method in spatial direction. This method has the advantages of high precision, better stability, and less storage. Numerical simulations show that the system control parameters and fractional order exponent have decisive influence on the generation of patterns. Our numerical results verify our theoretical results.

Key words: Turing patterns, fractional Gierer-Meinhardt model, Fourier spectral method

中图分类号: (Fractional statistics systems)

05.30.Pr

05.65.+b (Self-organized systems) 82.40.Ck (Pattern formation in reactions with diffusion, flow and heat transfer) 02.70.Hm (Spectral methods)

王语, 张荣培, 王震, 韩子健. Turing pattern in the fractional Gierer-Meinhardt model[J]. 中国物理B, 2019, 28(5): 50503-050503.

Yu Wang(王语), Rongpei Zhang(张荣培), Zhen Wang(王震), Zijian Han(韩子健). Turing pattern in the fractional Gierer-Meinhardt model[J]. Chin. Phys. B, 2019, 28(5): 50503-050503.

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Turing pattern in the fractional Gierer-Meinhardt model

Turing pattern in the fractional Gierer-Meinhardt model

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