We investigate the effect of resonant temporal forcing on an anisotropic system that exhibits a Hopf bifurcation to obliquely traveling waves in the absence of this forcing. We find that the forcing can excite various phase-locked standing-wave structures: rolls, rectangles, and cross rolls. At onset, at most one of the two-rolls or rectangles-is stable. The cross rolls can arise in a secondary bifurcation and can be stable. Experimentally, they would appear as a periodic switching between a structure in which the "zig" component dominates and one with a dominating "zag" structure. Since there are two symmetry-related states of this kind, one may expect disordered structures to arise due to the breakup of the pattern into domains. The results are consistent with recent experiments on electroconvection in nematic liquid crystals by de la Torre Juárez and Rehberg [Phys. Rev. A 42, 2096 (1990)]. We also apply the general analysis to a model of the behavior near a Lifshitz point, where the angle of obliqueness vanishes. This analysis indicates that phase-locked standing rectangles are always unstable in this parameter regime.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics