From localized spots to the formation of invaginated labyrinthine structures in a Swift-Hohenberg model

The stability of a circular localized spot with respect to azimuthal perturbations is studied in a prototype variational model, namely, a Swift-Hohenberg type equation. The conditions under which the circular shape of the spot undergoes an elliptical deformation which transforms it into a rod-shaped structure are analyzed. As it elongates, the rod structure exhibits a transversal instability, generating an invaginated labyrinthine structure which invades all the space available.