A mathematical analysis of the Belousov-Zhabotinskii reaction

Considerable interest in oscillating reactions has been generated by the large number of such processes observed in biological systems. Thus the existence of oscillating chemical reactions is well known. However, very few homogeneous chemical systems are known to either exhibit temporal oscillations or to develop spatial structure; that is, one which changes with respect to time and position within the reaction vessel. The only reaction presently known to exhibit both temporal and spatial oscillatory structures is the cerium ion catalyzed oxidation of malonic acid by bromate in a sulfuric acid medium.Temporal oscillations in [ce(IV)]/[ce(III)] were first reported by Belousov in 1959 and development of spatial structure by Zhabotinskii in 1967. The actual oscillations, both temporal and spatial are exhibited with the reagents oscillating from a bright blue to red. The colors whichindicate the variations in the chemical concentrations can be changed by the use of different reagents.Chemical oscillation has several physical and biological significances, particularly biochemical-oscillations at the intracellular level, which permit the organism to adapt in a flexible way to external conditions. The BelousovZhavotinskii reaction, however, is primarily an inorganic redose reaction but is important because, when coupled with the process of diffusion, it is possible to obtain spatial patterns and this can be a foundation for a biochemical theory of morphogenesis. A study of this particular reaction will also enable investigators to better understand and develop a precise theory of chemical oscillation.Several investigations have already been done on this reaction, but have all been primarily chemical in nature. The purpose of this paper therefore is primarily a mathematical analysis of the Belousov-Zhabotinskii reaction. Conditions for stability of the equilibrium solutions and the existence of oscillation will be discussed.Ball State UniversityMuncie, IN 47306Thesis (M.S.)--Ball State University, 1984