SMALLEST CHEMICAL-REACTION SYSTEM WITH HOPF-BIFURCATION

The smallest at most bimolecular chemical reaction system with Hopf bi furcation is presented. First the notion smallest reaction system is e xplained. Since the lowest number of intermediates has the highest pri ority in this characterization and since it has already been shown tha t three-component systems can have a Hopf bifurcation[1], the smallest reaction system must contain three intermediates. On the basis of a s ufficient condition for a Hopf bifurcation in three-dimensional system s it is possible to find one reaction system which is according to the given characterization, the smallest one. In the first part of this p aper it is shortly pictured and in the second part a more extensive pr oof that this system is really the searched smallest one is given.