Abstract
Pattern formation is one of the most surprising natural phenomena in real life. Analysis of spatiotemporal reaction-diffusion system can
lead to understanding the pattern dynamics. However, the periodic traveling wave solutions resulting from the reaction-diffusion system can play
an important role to explain the pattern dynamics. In this study, we analyze a system of nonlinear reaction-diffusion equations called the Brusselator model. We establish a parameter plane to investigate the existence of
periodic traveling waves as well as stability results of the model using the
method of continuation. We also find an Eckhaus type stability boundary
where we confirm the stability change by calculating the essential spectra
of the solutions of the model. As a result, we obtain a pattern transition
from stripe pattern to spot pattern of the model in the two spatial dimensions numerically
A. K. M. Nazimuddin, Md. Showkat Ali. (2019) Pattern Formation in the Brusselator Model Using Numerical Bifurcation Analysis, Punjab University Journal of Mathematics, Volume 51, Issue 11.
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