부산대학교 도서관

Authors' summary: ``The Field-Noyes model of the Belousov-Zhabotinskii reaction has attracted attention since it is apparently the only such model that is derived directly from detailed knowledge of a real oscillating chemical reaction. The values of most of the parameters in the model are easily assignable by analogy to the chemistry occurring in the real system. However, two parameters are only qualitatively related to this chemistry, and the behavior of the model as the values of these parameters are varied is of interest. Earlier numerical and qualitative work has shown that the model exhibits limit cycle oscillations for certain values of these parameters. The present qualitative work shows that for other values limit cycles do not appear, as the physically significant steady state is globally asymptotically stable. However, this steady state may be excitable in that a finite perturbation is greatly amplified before the system returns to rest. The size of the excursion depends upon the value of a parameter related to an autocatalytic portion of the model. The relationship between this excitability and phenomena actually observed in the reaction is discussed, and an analogy is drawn between the behavior of this model and of modifications of the Hodgkin-Huxley model for nerve impulse transmission.''