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

Biao Liu and Ranchao Wu
Additional contact information
Biao Liu: School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
Ranchao Wu: School of Mathematical Sciences, Anhui University, Hefei 230601, China

Mathematics, 2022, vol. 10, issue 2, 1-14

Abstract: 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.

Keywords: bifurcation; patterns formation; spatiotemporal discrete; Gierer-Meinhardt system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/2/243/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/2/243/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:2:p:243-:d:724014

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().