Noyes’ model

S. Vajda and T. Tur3nyi, Principal component analysis for reducing the Edelsan-Field-Noyes model of Belousov-Zhabotinsky reaction, J. Phys. Chem. 

RO, Fig. 3d) (2) higher-frequency, smaller amplitude, quasi-harmonic oscillations (QHO, Fig. 3a) and (3) double-frequency oscillations containing variable numbers of each of the two previous types. By far the most familiar feature of the BZ reaction, the relaxation oscillations of type 1 were explained by Field, Koros, and Noyes in their pioneering study of the detailed BZ reaction mechanism.15 Much less well known experimentally are the quasiharmonic oscillations of type 2,4,6 although they are more easily analyzed mathematically. The double frequency mode, first reported by Vavilin et al., 4 has been studied also by the present author and co-workers,6 who explained the phenomenon qualitatively on the basis of the Field-Noyes models of the BZ reaction. 

It appears then that small amplitude disturbances of the feed stream In the Ganapathisubramanian-Noyes model will not produce solutions as Irregular as those seen In the experiments. This of course does not mean that disturbances cannot cause chaotic behavior In general. However, It does Indicate that disturbances such as the peristaltic pump probably do not have a major effect on the behavior of this reaction system. 

S. Vajda S. and T. Turtinyi, Principal Component Analysis for Reducing the Edelson-Field-Noyes Model of the Belousov-Zhabotinsky Reaction, J. Phys. Chem. 90 (1986) 1664-1670. 

Hastings, S. P. and Murray, J. D. (1975). "The existence of oscillatory solutions in the Field-Noyes model for the Belousov-Zhabotinskii reaction." SIAM J. Appl. Math. 2Sy 678-688. 

Hsu, I.-D. and Kazarinoff, N. D. (1975). "An applicable Hopf bifurcation formula and instability of small periodic solutions of the Field-Noyes model." J. Math. Anal. Appl., in press. 

Much of the material presented here was developed for a course entitled "Temporal and spatial organization in chemical systems", given at the State University of New York at Buffalo in the Spring semester, 1975. The treatment of periodic solutions of the Field-Noyes model in the relaxation oscillator regime (pp.5 -69) s developed while writing up the lecture notes for publication. 

William, C.T. A threshold phenomenon in the Field-Noyes model of the Belousov-Zhabotinsky reaction. J. Math. Anal. Appl. 58, 233 (1977)... 

This allows the basic parameters of the model to be expressed as three distinct radii, that for the cage (p), that for the normalization (r ) and that for diffusive separation (b). One might hope that a single value of p and r would suffice for a given cage pair source in every solvent. However, consideration of the Noyes model indicates this cannot be the case. The physical basis here is the distance which a pair separates during the short time while the relative velocity vectors of the cage partners are oriented towards separation. This relative velocity orientation is intrinsic to the initiation event. Variations in combination efficiency with solvent fluidity, in Noyes model, are ascribed entirely to these small initial... 

---