Bogdanov-Takens bifurcation of a polynomialdifferential system in biochemical reaction

Abstract

Consider a polynomial differential system of degree p + q, which was given from a general multimolecular reaction in biochemistry as a theoretical problem of concentration kinetics. Although its local bifurcations are investigated in [1], a bifurcation of codimension 2 at a cusp remains to be considered. In this paper, such a bifurcation, called Bogdanov-Takens bifurcation, is discussed and the corresponding universal unfolding is given so as to complete the analysis of local bifurcations for the system.