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Two oscillatory Belousov-Zhabotinsky reactions are serially mass coupled to generate additional periodic states, period doubling, phase locking, quasiperiodicity, and chaos. The time series for these states are characterized in terms of their power spectra, attractors (reconstructed by singular value decomposition), Poincare sections, return maps, Lyapunov exponents, and various dimensionalities (Dq spectra). Adding trace impurities to the system does not alter the observed chaos. Model calculations using a partially reversible Oregonator model qualitatively agree with the experimental findings for the coupled oscillators.

plexed to either the solvent or the electrode surface (or both). There is no evidence from the PMV data to suggest that surface effects are responsible for the long lifetime of the intermediate. It is, however, possible that the estimated lifetime is that of the nitrilium ion formed by reaction of acetonitrile with the diphenylmethyl cation provided that the nitrilium ion is electroactive (presumably by dissociative reduction to form the radical and acetonitrile).It is possible to estimate the potential for the dissociative reduction of the nitrilium ion. Steenken and McClelland showed that the formation of this species is reversible.* Under conditions where it is formed almost exclusively, the major product is actually diphenylmethanol with the Ritter product always a minor component of the mixture. The equilibrium constant for this process must be >1000,35 giving a free energy change of <-4 kcal mol-' (<0.18 eV). Saveant and co-workers have suggested that the overpotential for a dissociative electron-transfer reaction will be essentially equivalent to the enthalpy change for the bond dissociation of the bond in the oxidized form of the electroactive specie^.'^ Using this reasoning, the reduction of the nitrilium ion is expected near 0.17 V vs SCE. A mechanism consistent with all of the experimental data is shown in Scheme I. (35) Steenken, S., private communication. (36) Saveant, J. M. J . Am. Chem. Soc. 1987, 109, 6788. ConclusionsImplicit finitedifference simulation of photomodulation voltammograms can be used to obtain lifetimes of radicals and product ions as well as values for the heterogeneous electron-transfer rate and Eo for redox reactions of radicals. Our experimental setup restricts lifetime measurement to an upper limit of ca. 300 ps (due to the limiting time response of the electrochemical cell). The effects of changes in the kinetic parameters can be summarized as follows:(1) At high potentials (above the diffusion limit) the phase of the electrochemical signal depends only on the lifetime of the radical.(2) Changes in the lifetime of the ion affect the quadrature signals more than those signals that are in phase with the excitation lamp. The effect of changes in ion lifetime, however, is to shift the position of E,/* but not to change the shape of the wave (Le., the breadth of the wave does not change).(3) Decreases in the heterogeneous electron-transfer rate (k,) increase the breadth and ElFor the oxidation of the dipienylmethyl radical the data suggest that nitrilium ion, which is formed in a reaction between the carbocation and acetonitrile, will either undergo a dissociative electron transfer to form the radical or slowly react to form products with a rate that depends on the concentration of water in the solvent system.of the voltammetric waves.The dynamical behavior of the methylene blue-oxygen-sulfide oscillator in a continuous flow stirred tank reactor is investigated. At low flow rates oscillations of period one emerge at a supercritical Hopf bifurcation, whereas a subcritical Hopf bifur...

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.

We present experimental and theoretical investigations of the nonlinear resonance behavior of a focal steady state in the Belousov-Zhabotinsky (BZ) reaction which is perturbed by its own dynamics. For this purpose the outputs of two independent BZ-oscillators of incommensurate frequencies are linearly combined in analogy to a simple feed-forward net to achieve the quasiperiodic driving of a third BZ-reactor which is in a focal steady state. For low amplitudes of the quasiperiodic flow-rate perturbations the response is also quasiperiodic in the focal BZ-reactor. Above a threshold value of the quasiperiodic amplitudes, however, single bursts are observed at small phase differences between the two perturbing oscillators. A further increase in the amplitude leads to groups of bursts with small oscillations in between. Aperiodic stochastic bursting in the BZ-reactor is observed when the flow-rate into the focal reactor is perturbed by Gaussian distributed white noise of sufficiently high amplitude and pulse length. The experiments are shown to agree with computer simulations using the Showalter-Noyes-Bar-Eli (SNB) model. At high amplitudes of quasiperiodic forcing the SNBmodel gives evidence for the existence of an attractor which is strange but nonchaotic (information dimension = 2.0).