Abstract
The dynamic transitions of the Brusselator model has been recently
analyzed in Y. Choi et’al (2021) and T. Ma, S. Wang (2011). Our aim in
this paper is to address the relation between the pattern formation and
dynamic transition results left open in those papers. We consider the
problem in the setting of a 2D rectangular box where an instability of
the homogeneous steady state occurs due to the perturbations in the
direction of several modes becoming critical simultaneously. Our main
results are two folds: (1) a rigorous characterization of the types and
structure of the dynamic transitions of the model from basic homogeneous
states and (2) the relation between the dynamic transitions and the
pattern formations. We observe that the Brusselator model exhibits
different transition types and patterns depending on the nonlinear
interactions of the pattern of the critical modes.