Secondary instabilities form a codimension-2 point accompanied by a homoclinic bifurcation

Abstract

A study of secondary instabilities in ac-driven electroconvection of a planarly aligned nematic liquid crystal is presented. At low frequencies one has a transition from normal rolls to a zig-zag pattern and at high frequencies a direct transition from normal to abnormal rolls. The crossover defines a codimension-2 point. This point is also the origin of a line of homoclinic bifurcations, which enable the transition from zig-zags to abnormal rolls at lower frequencies.

4 pages, 4 figures, submitted to PRL

References in corpus (1)

• Weakly Nonlinear Theory of Pattern-Forming Systems with Spontaneously Broken Isotropy

Cited by in corpus (6)

• Self-Organized Networks and Lattice Effects in High Temperature Superconductors
• Abnormal Rolls and Regular Arrays of Disclinations in Homeotropic Electroconvection
• Modulated structures in electroconvection in nematic liquid crystals
• Direct observation of twist mode in electroconvection in I52
• Spatiotemporal complexity of electroconvection patterns in nematic liquid crystals
• Optical analysis of spatially periodic patterns in nematic liquid crystals: diffraction and shadowgraphy