Splitting instability of cellular structures in the Ginzburg-Landau model under the feedback control

We study numerically a Ginzburg-Landau type equation for micelles in two dimensions. The domain size and the interface length of a cellular structure are controlled by two feedback terms. The deformation and the successive splitting of the cellular structure are observed when the controlled interface length is increased. The splitting instability is further investigated using coupled mode equations to understand the bifurcation structure.