Amplitude equations for description of chemical reaction–diffusion systems

We consider a new method for modeling waves in complex chemical systems close to bifurcation points. The method overcomes numerical problems connected with the high dimensional configuration phase space of realistic chemical systems without sacrificing the quantitative accuracy of the calculations. The efficiency is obtained by replacing the conventional use of kinetic equations considering just a few species by the use of amplitude equations for determining the evolution of the state. Coupled with calculation of an explicit function connecting the amplitude space and the concentration space this method permits the quantitative determination of the concentrations of all species. We also introduce a new method for calculating the boundaries of convective and absolute stability of waves for a chemical model at an operating point close to a supercritical Hopf bifurcation and with a slow stable mode.