Fundamental relations between the symmetry of excitation and the existence of spatiotemporal subharmonic structures in a pattern-forming dynamic system.

In electrohydrodynamic convection of nematics, excitation with sine or square waves of period T leads to convection structures in which the charge density, director, and velocity fields perform T-periodic oscillations. Nonconventional waveforms such as sawtooth excitation can lead to patterns with T-periodic as well as T-antiperiodic (subharmonic) dynamics. We consider different classes of excitation fields E(t): such with antisymmetry in the two half periods E(t)=-E(t+T/2), such with time inversion symmetry E(t)=E(-t), and dichotomous waveforms (two alternating values E1, E2) and discuss their influence on the pattern dynamics. From the analysis of linear differential equations that describe the system near threshold, we show analytically that each of these conditions inhibits subharmonic dynamics at onset. Numerical and experimental support of these predictions is provided.