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equilibrium point (of a system)

A point where a system's rate of change is exactly zero in every component.

An equilibrium point of $x'=P(x,y),\ y'=Q(x,y)$ is a point $(x^*,y^*)$ with $P(x^*,y^*)=Q(x^*,y^*)=0$ simultaneously -- a constant solution $x(t)\equiv x^*,\ y(t)\equiv y^*$ that never moves.