Sufficient conditions of periodicity in reactions

The theory of oscillating reactions started with the papers by Lotka. In Lotka (1920) he provided the Lotka-Volterra model and has shown that it leads to sustained oscillations. Since then many models have been shown to lead to oscillations some papers in this area are Hsu (1976), Wolfe (1978), Kertesz (1984), Schneider et al. (1987) etc. 

It is interesting to note that several authors were able to provide sufficient conditions for classes of reactions, e.g. Schnakenberg (1979), Csaszar et ai (1981) and experts in kinetic logic (see the papers by Thomas (1979, 1981), King (1980, 1982a,b, 1983, 1986) and Glass (1977)). The problem is that all these statements are mere indications from the strictly mathematical point of view. 

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