, Volume 17, Issue 1, pp 1-14

Smallest chemical reaction system with Hopf bifurcation

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Abstract

The smallest at most bimolecular chemical reaction system with Hopf bifurcation is presented. First the notion smallest reaction system is explained. Since the lowest number of intermediates has the highest priority in this characterization and since it has already been shown that three-component systems can have a Hopf bifurcation [1], the smallest reaction system must contain three intermediates. On the basis of a sufficient condition for a Hopf bifurcation in three-dimensional systems it is possible to find one reaction system which is according to the given characterization, the smallest one. In the first part of this paper it is shortly pictured and in the second part a more extensive proof that this system is really the searched smallest one is given.