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ORIGINAL RESEARCH article

Front. Phys.
Sec. Interdisciplinary Physics
Volume 12 - 2024 | doi: 10.3389/fphy.2024.1452077

Numerical simulation and theoretical analysis of pattern dynamics for the fractional-in-space Schnakenberg model

Provisionally accepted
Ji-Lei Wang Ji-Lei Wang 1*Yu-Xing Han Yu-Xing Han 2*Qing-Tong Chen Qing-Tong Chen 3,4*Zhi-Yuan Li Zhi-Yuan Li 1*Ming-Jing Du Ming-Jing Du 5*Yu-Lan Wang Yu-Lan Wang 4,6*
  • 1 Inner Mongolia Open University, Teaching Department, Hohhot, Hohhot, China
  • 2 Capital Medical University Second Clinical School, Capital Medical University, Beijing, China, Beijing, China
  • 3 Inner Mongolia University of Technology, Hohhot, Inner Mongolia Autonomous Region, China
  • 4 Department of Mathematics, College of Science, Inner Mongolia University of Technology, Hohhot, China
  • 5 Institute of Computer Information Management, Inner Mongolia University of Finance and Economics, Hohhot , China, Hohhot, China
  • 6 Department of Mathematics, Inner Mongolia University of Technology, Hohhot, China, Hohhot, China

The final, formatted version of the article will be published soon.

    It is always a difficult and hot topic to effectively explore the pattern dynamic behavior of reaction-diffusion models. The Schnakenberg model is a famous reaction-diffusion system, which has been widely used in many fields such as physics, chemistry and biology. In this paper, we researches the stability, Turing instability and weakly nonlinear analysis for the Schnakenberg model, and pattern dynamics of the fractional-in-space Schnakenberg model was simulated numerically based on the Fourier spectral method. The pattern patterns under different parameters, different initial conditions and different disturbances are shown, including target pattern, bar pattern and dot pattern. It is found that the pattern can not only split and spread from the bar pattern to the spot pattern, but also form the bar pattern from the broken connection of the dot pattern. The effect of fractional Laplacian operator on the pattern is also shown. In most cases, the diffusion rate of fractional model is faster than that of integer model. By comparing with different methods in other literatures, it can be found that the simulated patterns are basically consistent with the results simulated by other numerical methods in literatures, which indicates that Fourier spectral method can effectively explore the dynamic behavior of fractional Schnakenberg model. Some novel pattern dynamics behavior of the fractional-in-space Schnakenberg model are shown.

    Keywords: stability, Turing instability, Weakly nonlinear analysis, numerical simulation, Fourier spectral method

    Received: 20 Jun 2024; Accepted: 07 Aug 2024.

    Copyright: © 2024 Wang, Han, Chen, Li, Du and Wang. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

    * Correspondence:
    Ji-Lei Wang, Inner Mongolia Open University, Teaching Department, Hohhot, Hohhot, China
    Yu-Xing Han, Capital Medical University Second Clinical School, Capital Medical University, Beijing, China, Beijing, China
    Qing-Tong Chen, Inner Mongolia University of Technology, Hohhot, Inner Mongolia Autonomous Region, China
    Zhi-Yuan Li, Inner Mongolia Open University, Teaching Department, Hohhot, Hohhot, China
    Ming-Jing Du, Institute of Computer Information Management, Inner Mongolia University of Finance and Economics, Hohhot , China, Hohhot, China
    Yu-Lan Wang, Department of Mathematics, College of Science, Inner Mongolia University of Technology, Hohhot, China

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