Journal of Physical Chemistry, Vol.98, No.24, 6128-6135, 1994
Normal-Form Analysis of the Belousov-Zhabotinsky Reaction Close to a Hopf-Bifurcation
The applicability of the Hopf normal form equations for describing the flow in concentration space, which is observed for a real chemical system close to a supercritical Hopf bifurcation, has been investigated experimentally for the Belousov-Zhabotinsky reaction in a continuous flow stirred tank reactor. The parameters of the unsealed normal form have previously been determined experimentally by a special pulse perturbation technique called quenching analysis. In this paper, the validity of the normal form description is tested experimentally for a large number of perturbations from the associated limit cycle with the species HBrO2, Br, and Ce4+ by a series of concentration changes p and perturbation phases cp. The experimental results are compared directly with trajectories calculated from the normal form equations, and the asymptotic phases are determined and used for a map showing curves of isochronous perturbations. This map has a phase singularity for characteristic values of p and cp which are identical to the concentration changes and phases used for producing perfect quenchings. By this correspondence, quenching studies are directly related to previous investigations of phase singularities for relaxation oscillations in the Belousov-Zhabotinsky system.