Limit cycles and chaos in realistic models of the Belousov-Zhabotinskii reaction system

Effects of spatial variation in the Belousov-Zhabotinskii reaction is studied numerically by adopting the Field-Noyes kinetics (Oregonator) and the Zhabotinskii-Zaikin-Korzukhin-Kreitser kinetics. This is carried out for a spatially-discrete model composed ofN equivalent cells interacting through gradient coupling. When the system is near the boundary at which a uniform steady state bifurcates into a limit cycle, it is found with the aid of a perturbation expansion that the above models withN=3 exhibit various types of oscillations depending on the interaction strength between cells. Chaotic characteristics are also observed for a certain region of parameters. It is shown that the ZZKK model withN=2 exhibits a different kind of chaos when the size of the limit cycle becomes sensitive to external parameters, e.g., the concentrations of bromate ion or bromomalonic acid. Although each cell is equivalent, symmetry about cell numbers usually breaks down in a periodic state. It is found, however, that symmetry is recovered for the former kind of chaos, while the latter kind of chaos, there exists an asymmetric chaos as well as symmetric chaos. This has been examined by the time evolution of a certain concentration variable and by its Lorenz plot. In the asymmetric chaos, the Lorenz plot constitutes approximately a one-dimensional map. Furthermore, possible connections of the present limit cycles and chaos with the experiments of Zhabotinskii and Vavilin-Zhabotinskii-Zaikin are suggested.