Study on Spatiotemporal Pattern Evolution Mechanism of Schnakenberg System

被引：0
作者：
Dong, Shun-Ke [1 ]
Xiao, Min [1 ]
Yu, Wen-Wu [2 ]
机构：
[1] College of Automation, College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing
[2] School of Mathematics, Southeast University, Nanjing
来源：
Zidonghua Xuebao/Acta Automatica Sinica | 2024年 / 50卷 / 08期
基金：
中国国家自然科学基金;
关键词：
circular wave; Cross-diffusion; Schnakenberg system; spatiotemporal patterns; stability;
D O I：
10.16383/j.aas.c230637
中图分类号：
学科分类号：
摘要：
Schnakenberg system is a typical chemical reaction-diffusion control system. Currently, research both domestically and internationally is limited to Turing instability and bifurcation of such system, with relatively fewer reports on the evolution mechanism of its chemical patterns. Pattern mechanism analysis can accurately reveal the generation of self-organization phenomena and the evolution of spatial patterns in chemical reactions. This paper investigates the structural transformation, evolution speed, and time-dependence of patterns of Schnakenberg system under cross-diffusion driving, and focuses on exploring the response mechanism of cross-diffusion to its kinetics and pattern evolution. The findings indicate that when a system induced by self-diffusion is stable, cross-diffusion can trigger pattern formation. When a system induced by self-diffusion is unstable, cross-diffusion can lead to the transformation of pattern structures. For circular wave structures, different components of cross-diffusion can influence their evolution speed. In the context of temporal dependence, cross-diffusion can trigger the generation of patterns that vary periodically with time and can transform such patterns into relatively stable ones over time. Therefore, cross-diffusion plays a crucial role in the pattern generation, transformation, evolution speed, and temporal dependence of Schnakenberg system. © 2024 Science Press. All rights reserved.
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页码：1620 / 1630
页数：10
相关论文
共 44 条
  • [1] Turing A M., The chemical basis of morphogenesis, Philosophical Transactions of the Royal Society B: Biological Sciences, 237, 641, (1952)
  • [2] Page K M, Maini P K, Monk N A M., Complex pattern formation in reaction-diffusion systems with spatially varying parameters, Physica D: Nonlinear Phenomena, 202, 1−2, pp. 95-115, (2005)
  • [3] Qi Jie, Qi Jin-Peng, Boundary stabilization for a 2-D reaction-diffusion equation with symmetrical initial data, Acta Automatica Sinica, 41, 1, pp. 209-214, (2015)
  • [4] Qi Jie, Wang Chuan, Pan Feng, Boundary observer and output-feedback control for a class of n-dimensional symmetric advection-diffusion equations, Acta Automatica Sinica, 41, 7, pp. 1356-1364, (2015)
  • [5] Zhuang Bo, Cui Bao-Tong, Lou Xu-Yang, Chen Juan, Backstepping-based output feedback boundary control for coupled fractional reaction-diffusion systems, Acta Automatica Sinica, 48, 11, pp. 2729-2743, (2022)
  • [6] Du L L., Blow-up for a degenerate reaction-diffusion system with nonlinear nonlocal sources, Journal of Computational and Applied Mathematics, 202, 2, (2007)
  • [7] Yang R., Cross-diffusion induced spatiotemporal patterns in Schnakenberg reaction-diffusion model, Nonlinear Dynamics, 110, 2, pp. 1753-1766, (2022)
  • [8] Lu Y X, Xiao M, Huang C D, Cheng Z S, Wang Z X, Cao J D., Early warning of tipping in a chemical model with cross-diffusion via spatiotemporal pattern formation and transition, Chaos, 33, 7, (2023)
  • [9] Al Saadi F, Champneys A., Unified framework for localized patterns in reaction-diffusion systems
  • [10] the Gray-Scott and Gierer-Meinhardt cases, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 379, 2213, (2021)
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