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Spatiotemporal Dynamic Analysis in a Time-space Discrete Brusselator Mode
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KeyWord:Discrete Brusselator model  Bifurcation  Turing instability  Couple map lattice
Author NameAffiliation
Hongxia Liu School of Mathematics Science, Anhui University, Hefei, Anhui 230601, China 
Ranchao Wu School of Mathematics Science, Anhui University, Hefei, Anhui 230601, China 
Biao Liu School of Mathematics and Physics, Anhui Jianzhu University, Hefei, Anhui 230601, China 
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      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.