Determination of the largest lyapunov index for short chaotic time sequences in self-oscillating chemical reactions

A method was developed for the determination of largest Lyapunov index for short chaotic time sequences with allowance for the presence of noise in the response of the system. For this purpose a simple unidimensional representation modelling the dynamics of irregular self-oscillations was investigated. Conditions were found for adequate determination of the largest Lyapunov index from the noise-distorted signals. The results were used to obtain the largest Lyapunov index for the Belousov—Zhabotinskii reaction taking place in an ideal-mixing closed reactor and in a constant-mixing flow-type reactor. Institute of Organic Chemistry, National Academy of Sciences of Ukraine. Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 33, No. 3, pp. 136–142, May–June, 1997.     

Influence of the conditions of manufacture of nanomeric zirconium dioxide,stabilized with yttrium oxide,on its catalytic properties in the oxidation of CO

The morphological and catalytic properties of samples of nanomeric zirconium dioxide, stabilized with yttrium oxide, manufactured via the effect of a UHF field during the process of drying precipitated zirconium hydroxide and calcination at temperatures from 300 to 1000 °C, were studied. It was shown that the highest activity in the oxidation of CO occurred with 40 nm particles of zirconium dioxide prepared at 1000 °C. __________ Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 43, No. 2, pp. 96–101, March–April, 2007.     

Temperature dependence of quantitative characteristics of chaotic regime in Belousov-Zhabotinskii reaction

In a Ferroin-catalyzed oscillatory Belousov-Zhabotinskii reaction, the temperature dependences of the largest Lyapunov exponent (LLE) and the induction period for a chaotic regime to appear are linear in the 285–308 interval when plotted on Arrhenius coordinates. For the LLE, the activation energies calculated for different concentrations of the catalyst are in the 82–126 kJ/mole interval, and for the induction period in the 61–95 kJ/mole interval. On the basis of the experimental data, it has been concluded that this autooscillatory chemical system, within a narrow range of catalyst concentrations, is relatively insensitive to random, small, external perturbations.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 29, No. 2, pp. 186–190, March–April, 1993.The authors wish to thank K. B. Yatsimirskii, Academician of the Academy of Sciences of Ukraine, for discussing the data obtain in this work.     

Infinite period and Hopf bifurcations for the pH-regulated oscillations in a semibatch reactor (H(2)O(2)-Cu(2+)-S(2)O(2-) (3)-NaOH system)

Dynamic behavior of the pH-regulated oscillations has been studied for the hydrogen peroxide oxidation of thiosulfate ions in the presence of trace amounts of copper(II) ions in a semibatch reactor. A solution of 0.08 M Na(2)S(2)O(3) and 0.112 M NaOH was flowed at 0.160 mL/min into 300 mL of solution containing the H(2)O(2) and Cu(2+) in a vessel. There exists a critical value of the H(2)O(2) or Cu(2+) concentrations below which the system does not oscillate. The oscillations appear due to an infinite period bifurcation at low initial concentrations of the H(2)O(2). The initial concentration of Cu(2+) may be considered as a bifurcation parameter in this case. Increase of the initial hydrogen peroxide concentration causes the pH-regulated oscillations through a nondegenerate supercritical Hopf bifurcation. The classification of bifurcations is based on the analysis of the behavior of oscillation amplitude and period at different initial concentrations of the H(2)O(2) and Cu(2+). Our results show a possibility to distinguish different scenarios for the appearance of transient oscillations in semibatch experiments. (c) 1996 American Institute of Physics.     

Structure of compounds of chromium with 2,2′-bipyridyl that participate in the Belousov-Zhabotinskii oscillating reaction

It was shown that a binuclear complex of composition [Cr₂(OH)₂(bpy)₄]³⁺ acts as a reaction catalyst in the oscillating chemical system bromate-malonic acid-compound of chromium with 2,2 bipyridyl. The catalytically active compound was investigated by fast-atom-bombardment mass spectrometry, electron and EPR spectroscopies, and cerimetric analysis. The formal redox potential of such a complex E⁰ was obtained by cyclic voltammetry as +0.72 V.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 28, No. 3, pp. 266–270, May–June, 1992.     

Influence of ion-exchange and impregnation modification of zeolite X on its catalytic properties in the alkylation of toluene with methanol

The dependence of the activity and selectivity of ion-exchanged forms of zeolite X with incorporated cesium process in alkylation of toluene with methanol in the side chain on the nature of the ion-exchanged cations (Na⁺, Cs⁺, Mg²⁺, Zn²⁺) has been established. It is shown that introduction of Mg²⁺ and Zn²⁺ in combination with Cs₂CO₃ significantly increased the yields of ethylbenzene and styrene in comparison with their yields on alkali forms of zeolite X. __________ Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 42, No. 1, pp. 33–38, January–February, 2006.     

Quantitative investigation of spatiotemporal chaos in the ferroin-catalyzed Belousov-Zhabotinskii reaction in a batch reactor

We have analyzed experimental data on the time dependence of the potentials of 16 platinum point-contact electrodes for spatiotemporal chaos in the Belousov-Zhabotinskii reaction. We show that the largest Lyapunov exponent is a convenient characteristic for spatiotemporal chaos. We found that in going from temporal to spatiotemporal chaos, the embedding dimension of the system increases by a factor of three. We have observed that as the largest Lyapunov exponent increases, we observe a decrease in the degree of spatial correlation of the process.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 31, No. 1, pp. 34–39, January–February, 1995.We would like to thank the Foundation for Basic Research of the State Science and Technology Committee of Ukraine for financial support of this work (Project 3.3/87).     

ESR study on copper(II) macrocyclic polythia complexes

ESR measurements have been made on complexes formed by copper(II) with [12]anS₄, [13]anS₄, iso-[14]anS₄, and [18]anS₆; they show intramolecular reduction for the central ion by electron transfer from the donor sulfur atoms, and free cation-radicals are formed in solution. The covalency parameter ² indicates that the copper-sulfur bonds are mainly covalent. The electronic structures are analogous to those of the active centers in copper-bearing blue proteins.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 25, No. 6, pp. 737–742, November–December, 1989.