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
can be converted to the normal form with the transformation