  Axisymmetric and nonaxisymmetric patterns in the cubic-quintic
Swift-Hohenberg equation posed on a disk with Neumann boundary conditions are
studied via numerical continuation and bifurcation analysis. Axisymmetric
localized solutions in the form of spots and rings known from earlier studies
persist and snake in the usual fashion until they begin to interact with the
boundary. Depending on parameters, including the disk radius, these states may
or may not connect to the branch of domain-filling target states. Secondary
instabilities of localized axisymmetric states may create multi-arm localized
structures that grow and interact with the boundary before broadening into
domain filling states. High azimuthal wavenumber wall states referred to as
daisy states are also found. Secondary bifurcations from these states include
localized daisies, i.e., wall states localized in both radius and angle.
Depending on parameters, these states may snake much as in the one-dimensional
Swift-Hohenberg equation, or invade the interior of the domain, yielding states
referred to as worms, or domain-filling stripes.
