Standing wave patterns that arise on the surface of ferrofluids by (single frequency) parametric forcing with an ac magnetic field are investigated experimentally. Depending on the frequency and amplitude of the forcing, the system exhibits various patterns including a superlattice and subharmonic rhombuses as well as conventional harmonic hexagons and subharmonic squares. The superlattice arises in a bicritical situation where harmonic and subharmonic modes collide. The rhombic pattern arises due to the non-monotonic dispersion relation of a ferrofluid. 47.20.k; 47.54.+r; 05.70.Fh

The effect of parametric modulations on spiral waves that form in a thin layer of liquid crystal under rotating magnetic field is studied in laboratory experiments and numerical simulations. Parametric forcings that are sinusoidal in time make a simply rotating spiral tip to meander, rendering a compound tip trajectory that is composed of a main circular orbit and a satellite orbit with an unusual crescent shape. No evidence of frequency locking is found. The underlying mechanism for the unusual shape of the satellite orbit is elucidated, and the dependence of the rotation frequency of the main circular orbit f(o) on the perturbation parameters are discussed.