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

Abstract

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.