= Normal form
{disambiguate=dynamical systems}
= Normal form of a dynamical system
{synonym}
= Normal form
{synonym}
= Normal forms of a dynamical system
{synonym}
A simplified local vector field obtained by smooth changes of state variables, and sometimes time or parameter, retaining the terms that cannot be removed at the required order. Near a simple zero eigenvalue, reduction to a <centre manifold> can give the transcritical form $\dot v=\epsilon v-v^2$ or a reflection-symmetric pitchfork form $\dot x=\epsilon x\pm x^3$. The nonzero leading coefficients and permitted coordinate changes are part of the classification.
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