  Equilibrium bifurcations arise from sign changes of Jacobian determinants, as
parameters are varied. Therefore we address the Jacobian determinant for
metabolic networks with general reaction kinetics. Our approach is based on the
concept of Child Selections: each (mother) metabolite is mapped, injectively,
to one of those (child) reactions that it drives as an input. Our analysis
distinguishes reaction network Jacobians with constant sign from the
bifurcation case, where that sign depends on specific reaction rates. In
particular we distinguish "good" Child Selections, which do not affect the
sign, from more interesting and mischievous "bad" children, which gang up
towards sign changes, instability, and bifurcation.
