Normal form (dynamical systems)
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 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
near can be converted to the normal form
with the transformation.
See also canonical form for use of the terms canonical form, normal form, or standard form more generally in mathematics.
