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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 [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.