Composite “zigzag” structures in the 1D complex Ginzburg–Landau equation

We study the dynamics of the one-dimensional complex Ginzburg–Landau equation (CGLE) in the regime where holes and defects organize themselves into composite superstructures which we call zigzags. Extensive numerical simulations of the CGLE reveal a wide range of dynamical zigzag behavior which we summarize in a “phase diagram”. We have performed a numerical linear stability and bifurcation analysis of regular zigzag structures which reveals that traveling zigzags bifurcate from stationary zigzags via a pitchfork bifurcation. This bifurcation changes from supercritical (forward) to subcritical (backward) as a function of the CGLE coefficients, and we show the relevance of this for the “phase diagram”. Our findings indicate that in the zigzag parameter regime of the CGLE, the transition between defect-rich and defect-poor states is governed by bifurcations of the zigzag structures.