Oscillatory reactions involving hydrogen peroxide and thiosulfate-kinetics of the oxidation of tetrathionate by hydrogen peroxide.

The reaction between tetrathionate and hydrogen peroxide forms an important part of several pH oscillators based on the oxidation of thiosulfate. The kinetics of this reaction were examined in a batch reactor by measurement of the initial pH values in the range from 8 to 10.5. Experimental data were evaluated by the method of initial reaction rates combined with the assumption of instantaneously equilibrated acid-base reactions. The rate-determining step was found to be of the first order with respect to tetrathionate, hydrogen peroxide, and OH- ions with the value of rate constant k = (1.50 +/- 0.03) x 10(2) (M2 s)(-1) at 25 degrees C. In the alkaline solution, no distinct catalytic effect of Cu2+ was observed in contrast to earlier assumptions. The waveform of measured pH over the course of the reaction indicates that thiosulfate is probably an intermediate because characteristics of the curves are very similar to those for the oxidation of thiosulfate. We also measured the time evolution of concentrations of major components by the attenuated total internal reflectance infrared spectroscopy to further elucidate the underlying reaction mechanism. These measurements confirm the suspected role of thiosulfate as an intermediate in the studied reaction and provide valuable detailed information on the time evolution of thiosulfate, sulfite, sulfate, tetrathionate, and trithionate. These experimental observations are included in a simple mechanism that accurately simulates the reaction course in an alkaline solution. The results provide considerable new insights into the nature of autocatalysis in the hydrogen peroxide-thiosulfate-Cu2+ reaction and suggest that a new role for Cu2+ in the oscillatory dynamics observed in a flow-through reactor needs to be found.

Thresholds of excitability in three-dimensional dynamical systems.

A two-dimensional threshold surface of an excitable system is found as a set of threshold trajectories calculated step by step in cross sections of the phase space. The method leads to a highly nonlinear boundary value problem that can be solved numerically with the use of adaptive multiple shooting and continuation methods. We demonstrate this technique by examining a model of a biochemical oscillator with two positive feedbacks. Generalization to arbitrary dimension is discussed.

Excitable dynamics and threshold sets in nonlinear systems.

Following our previous work [J. Zagora et al., Faraday Discuss. 120, 313 (2001)], we present a quantitative definition of a threshold that separates large-amplitude excitatory responses and small-amplitude nonexcitatory responses to a perturbation of an excitable system with a single globally attracting steady state. For systems with two variables, finding the threshold set is formulated as a boundary value problem supplemented by a condition of a maximum separation rate. For this highly nonlinear problem we formulate a numerical method based on the use of multiple shooting and continuation methods. The threshold phenomena are examined by using an example dynamical system with chemical reaction--the bromate-sulfite-ferrocyanide system. In a model of this reaction we find the threshold set, construct a bifurcation diagram and discuss how excitability can vanish. These results are compared with recent experiments. We also discuss relevance of other definitions of the excitability threshold including the concept of nullclines.