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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  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.