Equilibrium point

In mathematics, specifically in differential equations, an equilibrium point is a constant solution to a differential equation.

The point ${\displaystyle {\tilde {\mathbf {x} }}\in \mathbb {R} ^{n}}$ is an equilibrium point for the differential equation

if ${\displaystyle \mathbf {f} (t,{\tilde {\mathbf {x} }})=0}$ for all ${\displaystyle t\,\!}$.

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