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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 μ {\displaystyle \mu } is the bifurcation parameter. The transcritical bifurcation
near x = 1 {\displaystyle x=1} can be converted to the normal form
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