In
mathematics, the normal form of a
dynamical system is a simplified form that can be useful in determining the system's behavior.
Normal forms are often used for determining local
bifurcations in a system. All systems exhibiting a certain type of bifurcation are locally (around the equilibrium)
topologically equivalent to the normal form of the bifurcation. For example, the normal form of a
saddle-node bifurcation is
where is the bifurcation parameter. The transcritical bifurcation