Unusual spiral wave tip trajectories in a parametrically forced nonequilibrium system

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 f̃_o on the perturbation parameters are discussed.