Bogdanov-Takens bifurcations in the enzyme-catalyzed reaction comprising a branched network (Q2628160)

The authors investigate a planar autonomous differential system that models the dynamic behavior of substrate concentration and product in an enzyme-catalyzed reaction, where the enzyme reaction rate and the output rate of the product are both saturated. This system is orbitally equivalent to a quartic polynomial vector field with four parameters. The present work is a continuation of a preceding paper by the authors which particularly investigated bifurcations of codimension one. Now, the authors consider a two-dimensional submanifold \(M\) of the parameter space where only one positive equilibrium exists that is a cusp and thus admits bifurcations of codimension two.. The main result is the existence of Bogdanov-Takens bifurcation on \(M\) whose universal unfolding is realized within the given four-dimensional parameter space.