Equilibrium point (mathematics)

In mathematics, specifically in differential equations, an equilibrium point is a constant solution to a differential equation. == Formal definition == The point x ~ ∈ R n {\displaystyle {\tilde {\mathbf {x} }}\in \mathbb {R} ^{n}} is an equilibrium point for the differential equation d x d t = f ( t , x ) {\displaystyle {\frac {d\mathbf {x} }{dt}}=\mathbf {f} (t,\mathbf {x} )} if f ( t , x ~ ) = 0 {\displaystyle \mathbf {f} (t,{\tilde {\mathbf {x} }})=\mathbf {0} } for all t {\displaystyle t} .

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