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Limit cycle behaviour in the Belousov-Zhabotinskii oscillatory reaction

01 Jun 1980-Vol. 89, Iss: 3, pp 235-239
Abstract: Oscillations in the bromate-Mn(II)-organic substrate system are studied by following the concentrations of Mn(III) and Br2 spectrophotometrically, apart from monitoring the concentration of Br- by potentiometry. Limit cycles for the Mn(III)-Br2 combination are constructed experimentally and theoretically. The experimental results agree with the theoretical expectations based on a suggested mechanism.

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Journal ArticleDOI
Abstract: The chemical mechanism of Field, Koros, and Noyes for the oscillatory Belousov reaction has been generalized by a model composed of five steps involving three independent chemical intermediates. The behavior of the resulting differential equations has been examined numerically, and it has been shown that the system traces a stable closed trajectory in three dimensional phase space. The same trajectory is attained from other phase points and even from the point corresponding to steady state solution of the differential equations. The model appears to exhibit limit cycle behavior. By stiffly coupling the concentrations of two of the intermediates, the limit cycle model can be simplified to a system described by two independent variables; this coupled system is amenable to analysis by theoretical techniques already developed for such systems.

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1,116 citations


Book
01 Jan 1973-

401 citations


"Limit cycle behaviour in the Belous..." refers background in this paper

  • ...They are otherwise called periodic trajectories ( Pavlidis 1973 )....

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  • ...One of the reasons for such art interest stems from the fact that some of the vital biological processes are oscillatory in nature ( Pavlidis 1973 )....

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Journal ArticleDOI
Abstract: The present state of the field of chemical oscillators and the direction in which it is evolving are reviewed in this paper. A qualitative discussion of the theoretical background of chemical oscillators is presented. One section of the paper is concerned with possible mechanisms for the oscillators and the differential equations representing their dynamic behavior. The types of systems where homogeneous oscillations have been observed are indicated, and then those few reactions for which detailed mechanisms have been proposed are discussed. 111 references. (BLM)

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118 citations


Journal ArticleDOI
D. Edelson1, R. J. Field2, Richard M. Noyes2Institutions (2)
Abstract: A detailed chemical mechanism for the cerium catalyzed bromination and oxidation of malonic acid by bromate has been developed, and complete numerical solutions have been obtained for the temporal behavior of the concentrations of the intermediate species. The many points of similarity with the experimentally observed initial decay, long quiescence, and abrupt transition to sustained oscillation establish confidence in the essential validity of the proposed mechanism. Close examination of the time dependence of these species concentrations as well as the magnitude of the several reaction channels permits the clarification of the switching mechanism causing theoscillatory behavior of this system. The results appear to exhibit limit cycle behavior, in accordance with theoretical predictions.

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99 citations


Journal ArticleDOI
Abstract: General aspects of chemical oscillators are discussed using a specific model to illustrate some important concepts concerning the theory of chemical oscillators. Models for both temporal chemical oscillators and spatial chemical oscillators are presented. (BLM)

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79 citations