Relation between the complex Ginzburg--Landau equation and reaction--diffusion system

The complex Ginzburg--Landau equation (CGLE) has been used to describe the travelling wave behaviour in reaction--diffusion (RD) systems. We argue that this description is valid only when the RD system is close to the Hopf bifurcation, and is not valid when a RD system is away from the onset. To test this, we study spirals and anti-spirals in the chlorite-iodide-malonic acid (CIMA) reaction and the corresponding CGLE. Numerical simulations confirm that the CGLE can only be applied to the CIMA reaction when it is very near the Hopf onset.