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

Author

Listed:
  • Biao Liu

    (School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China)

  • Ranchao Wu

    (School of Mathematical Sciences, Anhui University, Hefei 230601, China)

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.

Suggested Citation

  • Biao Liu & Ranchao Wu, 2022. "Bifurcation and Patterns Analysis for a Spatiotemporal Discrete Gierer-Meinhardt System," Mathematics, MDPI, vol. 10(2), pages 1-14, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:2:p:243-:d:724014
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    Citations

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    Cited by:

    1. Yun Liu & Lifeng Guo & Xijuan Liu, 2023. "Dynamical Behaviors in a Stage-Structured Model with a Birth Pulse," Mathematics, MDPI, vol. 11(15), pages 1-13, July.
    2. Ishtiaq Ali & Maliha Tehseen Saleem, 2023. "Spatiotemporal Dynamics of Reaction–Diffusion System and Its Application to Turing Pattern Formation in a Gray–Scott Model," Mathematics, MDPI, vol. 11(6), pages 1-17, March.

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