Wavenumber locking and pattern formation in spatially forced systems

We study wavenumber locking and pattern formation resulting from weak spatially periodic one-dimensional forcing of two-dimensional systems. We consider systems that produce stationary or traveling stripe patterns when unforced and apply forcing aligned with the stripes. Forcing at close to twice the pattern wavenumber selects, stabilizes, or creates resonant stripes locked at half the forcing wavenumber. If the mismatch between the forcing and pattern wavenumber is high we find that the pattern still locks but develops a wave vector component perpendicular to the forcing direction and forms rectangular and oblique patterns. When the unforced system supports traveling waves, resonant rectangular patterns remain stationary but oblique patterns travel in a direction orthogonal to the traveling waves.