PERIOD-DOUBLING GEOMETRY OF THE BELOUSOV-ZHABOTINSKY REACTION DYNAMICS
The intricate geometry of stable and unstable manifolds of a saddle cycle arising from a super-critical period-doubling bifurcation is explored experimentally for the Belousov-Zhabotinsky (BZ) reaction in a CSTR (Continuous flow Stirred Tank Reactor). We find clear experimental evidence that the stable manifold winds round the stable period-doubled orbit arising at the bifurcation. The stable manifold is probed experimentally by perturbations from the period-doubled limit cycle. The method provides a model-independent experimental test for species essential for the complexity, as well as quantitative information about the geometry of the limit cycles, the associated manifolds, and their embedding in the concentration space. The results are supported by simulations of the experiments with a four-dimensional model of the BZ reaction. Here stable manifold has several branches showing some tendency of curling. However the branches may end on the boundary of the positive orthant of the concentration space.