October  2008, 20(4): 939-959. doi: 10.3934/dcds.2008.20.939

Dynamics of local map of a discrete Brusselator model: eventually trapping regions and strange attractors

1. 

Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, United States

Received  April 2007 Revised  October 2007 Published  January 2008

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 [7] 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.
Citation: Hunseok Kang. Dynamics of local map of a discrete Brusselator model: eventually trapping regions and strange attractors. Discrete and Continuous Dynamical Systems, 2008, 20 (4) : 939-959. doi: 10.3934/dcds.2008.20.939
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