Relaxation and hysteresis in a periodically forced Swift-Hohenberg system

The relaxation and hysteresis of a periodically forced Swift-Hohenberg (SH) equation as a phenomenological model for the magnetic domains of a garnet thin film in an oscillating magnetic field are studied. It is already known that the unforced SH equation settles down to a single type of spatial structure called a stripe pattern, and that the relaxation process yields a scaling law for the structure factor. Two types of temporally oscillating spatial structure consisting of stripe and polka-dot patterns have also been asymptotically observed in the case of a periodically forced SH equation. Relaxation scaling behaviors are studied for these two patterns. It is also shown for the forced case that a hysteresis is observed in the vicinity of the boundary between two different spatial patterns in the phase diagram.