Objectives and summary of the book

Finally, neither the effect of external noise, which affects nonequilibrium transitions in chemical and biological systems (Lefever, 1981 Horsthemke Lefever, 1984 Lefever Turner, 1986), nor the stochastic aspects of these transitions (Nicolis, Baras Malek-Mansour, 1984) are considered - with the exception of the glycolytic system (chapter 2). Such a simplification, justified in the first approximation by the absence of systematic noise in the biological systems considered, permits us to avoid complicating from the outset the analysis of systems whose kinetics is already complex. 

Part I of the book is devoted to glycolytic oscillations. A two-variable allosteric model is analysed in chapter 2 for the phosphofructokinase reaction, which is responsible for the oscillations. The autocatalytic regulation of this reaction, which results from the cooperative activation of the multisubunit enzyme by one of its products, is at the core of the mechanism that produces the nonequilibrium instability beyond which 

Building on these results, chapters 3 and 4 present extensions of the two-variable model for glycolytic oscillations. These somewhat abstract extensions, not directly based on experimental observations, permit a detailed analysis of the transition from simple to complex oscillatory phenomena, which forms the subject of part II. 

The model analysed in chapter 3 is again that of an enzyme reaction regulated by positive feedback. To this reaction, which forms the core of the mechanism for glycolytic oscillations, is added a nonlinear recycling of product into substrate. The advantage of this extension is to keep only two variables while increasing the repertoire of dynamic behaviour. In particular, the model allows the verification of a conjee- 

The interest of the theoretical study of birhythmidty stems from the fact that the phenomenon has not been firmly demonstrated in biological systems. Some studies, however, do suggest its occurrence in the heart, as well as in a neuronal system (Hounsgaard et al, 1988). Birhythmidty has been observed in a number of chemical oscillatory systems (Alamgir Epstein, 1983 Roux, 1983 Lamba Hudson, 1985 Citri Epstein, 1988). 

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