Amplitude equations for reaction–diffusion systems with a Hopf bifurcation and slow real modes

Abstract

Using a normal form approach described in a previous paper we derive an amplitude equation for a reaction–diffusion system with a Hopf bifurcation coupled to one or more slow real eigenmodes. The new equation is useful even for systems where the actual bifurcation underlying the description cannot be realized, which is typical of chemical systems. For a fold-Hopf bifurcation, the equation successfully handles actual chemical reactions where the complex Ginzburg–Landau equation fails. For a realistic chemical model of the Belousov–Zhabotinsky reaction, we compare solutions to the reaction–diffusion equation with the approximations by the complex Ginzburg–Landau equation and the new distributed fold-Hopf equation.