Bifurcation to spatially induced chaos in a reaction-diffusion system

Abstract

A one-dimensional reaction-diffusion equation is used to model a class of experimental open chemical systems in which spatiotemporal patterns can be sustained indefinitely. Numerical simulations for the model in parameter regimes corresponding to experiment reveal only low-dimensional behavior. The observed bifurcation sequence leads from steady state concentration profiles to temporally chaotic patterns. The physical mechanism that causes this behavior is deduced from analysis of the local dynamics: localized oscillators appear at each end of the reactor and one of the oscillators acts as a periodic forcing for the other. The numerical results are in good qualitative agreement with the experiments.

Spatiotemporal patterns in a one-dimensional open reaction-diffusion system

“…3 and 9 show that the amplitude of the oscillations is large near the z = 0 (bromate) end of the reactor, but no oscillations are discernible near the other end. Although the oscillation amplitude is below the level of detectability near the z = 1 end of the reactor, the system is presumably oscillating globally; this is indeed the case for the model [14].…”

“…The boundary conditions and control parameters are not really the same for the experiment and the model, but, as argued in ref. [14], these differences should be significant mainly at high flow rates (or, in the model, high concentrations); indeed, a good correspondence between model and experiment is found only at low flow rates (low concentrations in the model). Further, the twospecies model of the'chemical kinetics is a greatly over-simplified description of even the wellstudied malonic acid BZ system with a cerium catalyst, and the relation of the model kinetics to our variant of the BZ reaction, a glucose-acetone system with a manganese catalyst, is unknown.…”

“…12a-12d) are also remarkably similar. In the model, as in the experiment, the chaotic attractors were lowdimensional (d < 3) [14].…”

“…The Couette reactor has been modeled recently by Vastano et al [6,14]. The local chemistry of the Couette reactor was modeled by an Oregonator model with two species, bromous acid and the catalyst of the BZ reaction [23].…”

“…This reactor has been recently examined in theoretical studies by Vastano et al [13,14] and Arneodo and Elezgaray [15]. Our Couette reactor with feeds at the ends differs from a Turing system where the initial state is spatially uniform.…”