Collapse of Spatiotemporal Chaos

The transient nature of spatiotemporal chaos is examined in reaction-diffusion systems with coexisting stable states. We find the apparent asymptotic spatiotemporal chaos of the Gray-Scott system to be transient, with the average transient lifetime increasing exponentially with medium size. The collapse of spatiotemporal chaos arises when statistical spatial correlations produce a quasihomogeneous medium, and the system obeys its zero-dimensional dynamics to relax to its stable asymptotic state

Trigger waves in the acidic bromate oxidation of ferroin

The acidic bromate oxidation of ferroin in batch reaction proceeds with slow consumption of bromide until a critical bromide concentration is attained. At that point ferroin is suddenly oxidized to ferriin in a process involving autocatalytic generation of bromous acid. Prior to the transition, in an unstirred thin f i l m of solution, a single trigger wave of chemical reactivity may develop and subsequently propagate, converting the reaction mixture from the reduced state to the oxidized state. Because the reaction is nonoscillatory, the trigger wave represents a propagating front. Waves were electrochemically initiated by local depletion of bromide and effects of reactant concentrations on propagation velocity were investigated. The dependence of wave velocity on [Br-] ahead of the advancing wave was investigated and the critical bromide concentration for wave propagation, [Br-I,,, was determined. The coexistence of kinetic states and spatial bistability are considered. Introduction Experimental study of chemical wave behavior has been confined primarily to the Belousovl-Zhabotinsky2 (BZ) reaction. Trigger waves3 represent a particularly fascinating behavior of the BZ reaction. In an unstirred reaction mixture, waves of chemical reactivity travel at an almost constant velocity by triggering their own propagation. Velocity dependence on reactant concentrations has been systematically investigated and explained4 in terms of the Field-Koros-Noyes (FKN) mechanism6 for the BZ reaction. Reusser and Field6 have modeled the reaction-diffusion behavior using the Oregonator,' a mathematical model containing the essential kinetic features of the FKN mechanism. A recent study of electrochemical initiation of trigger waves8 demonstrated that initiation dependence on reactant concentrations and a variety of other features are also accounted for by the FKN mechanism. A reaction closely related to the oscillating BZ reaction is the acidic bromate oxidation of Ce(II1) and other weak one-electron reducing agents. In a batch reactor, the reaction has the features of a clock reaction: a long induction period followed by a sudden oxidation of the metal ion. In a continuously stirred tank reactor (CSTR), the reaction exhibits bistability: and the concentrations of certain intermediate species differ by orders of magnitude in each of the stationary states. The bistability behavior has been modeledlo almost quantitatively by using bromate chemistry from the FKN mechanism. Noyes" has recently developed a reduced model similar to the Oregonator that faithfully reproduces the essential features of the CSTR experiment. In this paper, we consider the reaction-diffusion behavior of the acidic bromate oxidation of ferroin. Just as trigger wave behavior is the spatial analogue of temporal oscillations in the BZ reaction, trigger wave behavior in th

Extreme multistability in a chemical model system

Coupled systems can exhibit an unusual kind of multistability, namely, the coexistence of infinitely many attractors for a given set of parameters. This extreme multistability is demonstrated to occur in coupled chemical model systems with various types of coupling. We show that the appearance of extreme multistability is associated with the emergence of a conserved quantity in the long-term limit. This conserved quantity leads to a slicing of the state space into manifolds corresponding to the value of the conserved quantity. The state space slices develop as t→∞ and there exists at least one attractor in each of them. We discuss the dependence of extreme multistability on the coupling and on the mismatch of parameters of the coupled systems