Aperiodicity resulting from two-cycle coupling in the Belousov–Zhabotinskii reaction. III. Analysis of a model of the effect of spatial inhomogeneities at the input ports of a continuous-flow, stirred tank reactor

Abstract

Deterministic chaos is a well-established phenomenon in continuous-flow, stirred tank reactor (CSTR) experiments with the oscillatory Belousov–Zhabotinskii (BZ) reaction. However, it has not yet been possible to reproduce the experimentally observed, robust chaos in simulations using realistic models of the homogeneous chemical kinetics of the BZ reaction. That it may be necessary to consider spatial inhomogeneities in modeling the BZ chaos is suggested by the existence of strong stirring effects on the aperiodic behavior and by the difficulty of reproducing chaos under the same conditions in reactors of different physical configuration. Such inhomogeneity might result from a lack of perfect mixing in the CSTR, especially near the inlets, or from diffusion of species at low flow rates from the CSTR reaction mixture into the tips of the inlets. The presence of spatial inhomogeneities allows coupling between essentially independent oscillators, a well-known source of chaos. Such a model using a realistic representation of the BZ kinetics leads to an eight-variable set of ordinary differential equations. Numerical analysis of these equations by continuation methods and by numerical integration shows the existence of broad regions of chaos and various hysteresis effects involving limit cycles, a steady state and/or a strange attractor. Tristability was found in calculations in a narrow flow rate range. The computed behavior appears for parameter values closely related to the values used experimentally to obtain similar phenomena, and the visual similarity of the computed and experimental strange attractors is striking. The experimental routes to chaos, period doubling, intermittency, and secondary Hopf bifurcations are all reproduced in the simulations. The computed and experimental structures of periodic windows observed within chaotic regions also are very similar.