OREGONATOR-BASED SIMULATION OF THE BELOUSOV–ZHABOTINSKII REACTION

Abstract

Some observations are made on the Belousov–Zhabotinskii reaction simulated via the Field–Noyes model, also referred to as the Oregonator, and its modification. The simulation is performed with the aid of a cell-to-cell mapping for global analysis. Regarding the standard Oregonator, a two-dimension-like region in the three-dimensional phase space is detected showing the sensitive dependence of short-term ODE integrations on initial conditions. Trajectories with initial conditions closely located in this region may experience a phase lag if they eventually approach the same stable limit cycle connected with a subcritical Hopf bifurcation. When a flow term is added to the Oregonator, chaos can be brought about to mimic the experimental finding by suitably pleating the slow manifold. Coexistent attractors now may have a chaotic member and a fractal separatrix detected by the global analysis. The above mentioned sensitive region is found to play a significant role in shaping the pleating in order for chaos to happen in a manner analogous to the "screw-type" proposed by [Rössler, 1977] as one of the two prototypes for three-variable systems. Some relevant calculations of Lyapunov exponents, fractal dimensions and power spectra are also included.