Ordered and self-disordered dynamics of holes and defects in the one-dimensional complex Ginzburg-Landau equation

We study the dynamics of holes and defects in the 1D complex Ginzburg–Landau equation in ordered and chaotic cases. Ordered hole–defect dynamics occurs when an unstable hole invades a plane wave state and periodically nucleates defects from which new holes are born. The results of a detailed numerical study of these periodic states are incorporated into a simple analytic description of isolated “edge” holes. Extending this description, we obtain a minimal model for general hole–defect dynamics. We show that interactions between the holes and a self–disordered background are essential for the occurrence of spatiotemporal chaos in hole–defect states.