Pattern Formation on Growing Square Domains 
 
by Adela Comanici (Rice University) 

Abstract:

Numerical simulations of reaction-diffusion systems with Neumann boundary
conditions on growing square domains by Maini et al. exhibit square
and stripe patterns that are usually associated with bifurcations from a
trivial equilibrium on a square lattice. However, these patterns change as
the domain grows. In this talk, I will discuss some of these
transitions ; namely, transitions between different types of squares
and between squares and stripes. I will show that these transitions can be
understood by tracing  paths through the unfoldings of certain codimension
two mode interactions.