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 - <p style="text-align: justify;">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.</p>