Dynamics of local map of a discrete brusselator model: Eventually trapping regions and strange attractors

被引:13
作者
Kang, Hunseok [1 ]
机构
[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA
关键词
coupled map lattice; eventually trapping region; strange attractor; brusselator model;
D O I
10.3934/dcds.2008.20.939
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The reaction-diffusion equation for the Brusselator model produces a coupled map lattice (CML) by discretization. The two-dimensional nonlinear local map of this lattice has rich and interesting dynamics. In [] we studied the dynamics of the local map, focusing on trajectories escaping to infinity, and the Julia set. In this paper we build a correspondence between CML and its local map via traveling waves, and then using this correspondence we study asymptotic properties of this CML. We show the existence of a bounded region in which every trajectory in the Julia set is eventually trapped. We also find a region where every bounded trajectory visits. Finally, we present some strange attractors that are numerically observed in the Julia set.
引用
收藏
页码:939 / 959
页数:21
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