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Volume 4, Issue 3
Spatiotemporal Dynamic Analysis in a Time-Space Discrete Brusselator Model

Hongxia Liu, Ranchao Wu & Biao Liu

DOI: 10.12150/jnma.2022.539

J. Nonl. Mod. Anal., 4 (2022), pp. 539-561.

Published online: 2022-06

[An open-access article; the PDF is free to any online user.]

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  • Abstract

In this paper, we study the spatiotemporal patterns of a Brusselator model with discrete time-space by using the coupled mapping lattice (CML) model. The existence and stability conditions of the equilibrium point are obtained by using linear stability analysis. Then, applying the center manifold reduction theorem and the bifurcation theory, the parametric conditions of the flip and the Neimark-Sacker bifurcation are described respectively. Under space diffusion, the model admits the Turing instability at stable homogeneous solutions under some certain conditions. Two nonlinear mechanisms, including flip-Turing instability and Neimark-Sacker-Turing instability, are presented. Through numerical simulation, periodic windows, invariant circles, chaotic phenomenon and some interesting spatial patterns are found.

  • Keywords

Discrete Brusselator model, Bifurcation, Turing instability, Couple map lattice.

  • AMS Subject Headings

34C23, 37G10, 39A28

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-4-539, author = {Liu , HongxiaWu , Ranchao and Liu , Biao}, title = {Spatiotemporal Dynamic Analysis in a Time-Space Discrete Brusselator Model}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2022}, volume = {4}, number = {3}, pages = {539--561}, abstract = {

In this paper, we study the spatiotemporal patterns of a Brusselator model with discrete time-space by using the coupled mapping lattice (CML) model. The existence and stability conditions of the equilibrium point are obtained by using linear stability analysis. Then, applying the center manifold reduction theorem and the bifurcation theory, the parametric conditions of the flip and the Neimark-Sacker bifurcation are described respectively. Under space diffusion, the model admits the Turing instability at stable homogeneous solutions under some certain conditions. Two nonlinear mechanisms, including flip-Turing instability and Neimark-Sacker-Turing instability, are presented. Through numerical simulation, periodic windows, invariant circles, chaotic phenomenon and some interesting spatial patterns are found.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2022.539}, url = {http://global-sci.org/intro/article_detail/jnma/20724.html} }
TY - JOUR T1 - Spatiotemporal Dynamic Analysis in a Time-Space Discrete Brusselator Model AU - Liu , Hongxia AU - Wu , Ranchao AU - Liu , Biao JO - Journal of Nonlinear Modeling and Analysis VL - 3 SP - 539 EP - 561 PY - 2022 DA - 2022/06 SN - 4 DO - http://doi.org/10.12150/jnma.2022.539 UR - https://global-sci.org/intro/article_detail/jnma/20724.html KW - Discrete Brusselator model, Bifurcation, Turing instability, Couple map lattice. AB -

In this paper, we study the spatiotemporal patterns of a Brusselator model with discrete time-space by using the coupled mapping lattice (CML) model. The existence and stability conditions of the equilibrium point are obtained by using linear stability analysis. Then, applying the center manifold reduction theorem and the bifurcation theory, the parametric conditions of the flip and the Neimark-Sacker bifurcation are described respectively. Under space diffusion, the model admits the Turing instability at stable homogeneous solutions under some certain conditions. Two nonlinear mechanisms, including flip-Turing instability and Neimark-Sacker-Turing instability, are presented. Through numerical simulation, periodic windows, invariant circles, chaotic phenomenon and some interesting spatial patterns are found.

Liu , HongxiaWu , Ranchao and Liu , Biao. (2022). Spatiotemporal Dynamic Analysis in a Time-Space Discrete Brusselator Model. Journal of Nonlinear Modeling and Analysis. 4 (3). 539-561. doi:10.12150/jnma.2022.539
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