Excluding periodicity in reactions

Based upon the results of Bendixson and Dulac the investigations of Hanusse (1972), Tyson Light (1973) and Pota (1983) have shown that in two-component bimolecular systems there is only one oscillator the Lotka-Volterra model. 

Studying three-dimensional systems Pota has shown (Pota, 1985), again using Dulac-type theorems, that there only exists a single bimolecular reaction which may exhibit oscillatory behaviour, and this is the Ivanova reaction  

He has also shown that in a continuous-flow stirred tank reactor no bimolecular reaction can show sustained oscillations. 

It might be repeated here that the statements in Section 4.2 also preclude periodicity in several classes of reactions. 

---