ncts

Saddle-node bifurcations point at parameter regions where we can detect multistationarity, a property of recognized importance in biochemical systems. Saddle-node bifurcations are generic in the set of vector fields admitting an equilibrium with a singular Jacobian, thus one would expect that equilibria with singular Jacobian encountered in applications are all saddle-nodes. For vector fields arising from chemical reaction networks, though, the network structure is typically considered as fixed, while the freedom rests with the choice of the parametric reaction functions. Thus, a genericity viewpoint may apply due to the freedom of the reaction functions or may not apply due to the fixed network structure. In this talk, I will present an example of a network, whose associated system possesses either a nonsingular Jacobian or a Jacobian with algebraically multiple eigenvalue zero: this constitutes structural obstruction to standard saddle-node bifurcation.