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Article

Bifurcation and Patterns Analysis for a Spatiotemporal Discrete Gierer-Meinhardt System

by 1,* and 2
1
School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
2
School of Mathematical Sciences, Anhui University, Hefei 230601, China
*
Author to whom correspondence should be addressed.
Academic Editor: José M. Vega
Mathematics 2022, 10(2), 243; https://doi.org/10.3390/math10020243
Received: 5 December 2021 / Revised: 4 January 2022 / Accepted: 11 January 2022 / Published: 13 January 2022
(This article belongs to the Topic Dynamical Systems: Theory and Applications)
The Gierer-Meinhardt system is one of the prototypical pattern formation models. The bifurcation and pattern dynamics of a spatiotemporal discrete Gierer-Meinhardt system are investigated via the couple map lattice model (CML) method in this paper. The linear stability of the fixed points to such spatiotemporal discrete system is analyzed by stability theory. By using the bifurcation theory, the center manifold theory and the Turing instability theory, the Turing instability conditions in flip bifurcation and Neimark–Sacker bifurcation are considered, respectively. To illustrate the above theoretical results, numerical simulations are carried out, such as bifurcation diagram, maximum Lyapunov exponents, phase orbits, and pattern formations. View Full-Text
Keywords: bifurcation; patterns formation; spatiotemporal discrete; Gierer-Meinhardt system bifurcation; patterns formation; spatiotemporal discrete; Gierer-Meinhardt system
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MDPI and ACS Style

Liu, B.; Wu, R. Bifurcation and Patterns Analysis for a Spatiotemporal Discrete Gierer-Meinhardt System. Mathematics 2022, 10, 243. https://doi.org/10.3390/math10020243

AMA Style

Liu B, Wu R. Bifurcation and Patterns Analysis for a Spatiotemporal Discrete Gierer-Meinhardt System. Mathematics. 2022; 10(2):243. https://doi.org/10.3390/math10020243

Chicago/Turabian Style

Liu, Biao, and Ranchao Wu. 2022. "Bifurcation and Patterns Analysis for a Spatiotemporal Discrete Gierer-Meinhardt System" Mathematics 10, no. 2: 243. https://doi.org/10.3390/math10020243

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