Aperiodicity and deterministic chaos in the Belousov-Zhabotinskii reaction

Abstract

Deterministic chaos in the Belousov-Zhabotinsky reaction is well-known to occur at low flow rates.Id However, the source of aperiodicity in the high flow rate region has remained a controversial issue. We reproduced the aperiodicity found by Hudson7v8 and, more recently, by Noszticzius et al.9 under practically identical experimental conditions. We interpret the observed aperiodicity at high flow rates as nonchaotic on the basis of the 1-D maps and Renyi dimensions (calculated with the nearest neighbor method' from single value decomposition reconstructed'O attractors), including the Hausdorff dimension.The observed aperiodicity at high flow rates is most probably a noisy time series of the 1 ' l 2 state and the adjoining Farey ordered states.

Charge-transfer in the photodissociation of metal ion-benzene complexes

“…Metal-benzene ion-molecule complexes are produced by laser vaporization at 532 nm (Nd:YAG second harmonic) in a pulsed nozzle cluster source using methods described previously.17" 19 The complexes are mass-selected one at a time from the distribution produced by the source in a reflectron time-of-flight mass spectrometer. 23 Laser excitation of selected ions takes place in the reflection field at the turning point in the ion trajectory. Photodissociation products and parent ion depletion are measured with a second stage of time-of-flight mass analysis.…”

“…The operation of the reflectron instrument for photodissociation experiments has been described previously. 23 The wavelength dependence of photodissociation processes is investigated with a Nd:YAG pumped tunable dye laser (Spectra Physics PDL-2). Fragment ion intensity is recorded as a function of the laser wavelength to obtain photofragment excitation spectra.…”

Chaos in batch Belousov-Zhabotinskii systems

“…The operation of the reflectron instrument for photodissociation experiments has been described previously. 23 The wavelength dependence of photodissociation processes is investigated with a NdtYAG pumped tunable dye laser (Spectra Physics PDL-2). Fragment ion intensity is recorded as a function of the laser wavelength to obtain photofragment excitation spectra.…”

Neural nets and the local predictor method used to predict the time series of chemical reactions

“…The optimal prediction time is lower than 150 s (Figure 6d), for which the predicted and the actual data nearly coincide. The reason for the high quality of the predictions is the relatively low dimensionality (Hausdorff dimension = 2.55) 50 of the experimental chaotic motion. The correlation of the predicted time series of the driven chaotic Brusselator (Figure 5b) also decreases exponentially; however, it does not converge toward zero for long prediction times but toward a limiting value.…”

“…BZ reaction. Parts of experimentally measured (solid line, 6000 s) data and predicted time series with a neural net (dashed line), prediction time 100 s: (a) periodic (P3),43 (c) chaotic (low flow rate),22 and (e) aperiodic (high flow rate) regime 50. The actual and the predicted time series almost coincide for T = 100 s. The periodic and the chaotic time series were recorded spectrophotometrically, the aperiodic electrochemically with a Pt electrode.…”