5 Irregular Wave Patterns

The complex Ginzburg–Landau (CGL) equation (1.1.6) has been derived in Sect. 1.3.3 as the amplitude equation (1.3.28) at the Hopf bifurcation that describes the evolution of the oscillation amplitude on a slow time scale far exceeding the oscillation period, as well as its modulation on an extended spatial scale. Its coefficients can be related to parameters of an underlying non-equilibrium system through a technically cumbersome but fully algorithmic procedure of multiscale expansion in the vicinity of a Hopf bifurcation, as described for a general reaction–diffusion system in Sect. 1.3.3.