SECONDARY INSTABILITIES FORM A CODIMENSION-2 POINT ACCOMPANIED BY A HOMOCLINIC BIFURCATION

A study of secondary instabilities in ac-driven electroconvection of a planarly aligned nematic liquid crystal is presented. At low frequenc ies one has a transition from normal rolls to a zigzag pattern and at high frequencies a direct transition from normal to abnormal rolls. Th e crossover defines a codimension-2 point. This point is also the orig in of a line of homoclinic bifurcations, which enable the transition f rom zigzags to abnormal rolls at lower frequencies.