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

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.