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  "body": "\n## Definition\n\nLet $U$ be an open subset of $\\mathbb{R}^n$ and let $f : U \\to \\mathbb{R}^n$ be a function.\nA point $x^* \\in U$ is an equilibrium point of the [[autonomous system|07BNRFQ0PJ]] $x' = f(x)$ if $f(x^*) = 0$.\n\n## Remarks\n\nThe point $x^*$ is an equilibrium point exactly when the constant function $x(t) = x^*$ is a [[solution|04SW7WECS8]].\nFor the [[logistic equation|0CC4VC7KR3]] $x' = r x (1 - x/K)$ with $r, K \u003e 0$, the equilibrium points are $0$ and $K$.\nThe equilibrium points are the fixed points of the [[flow|02903SSA48]]: $\\varphi_t(x^*) = x^*$ for each $t$.\nThe behaviour of solutions near an equilibrium point is the subject of [[Lyapunov stability|092S6VBECQ]].\n\n## Explanations\n\n### L1 human\n\nAn equilibrium point is a state where the velocity is zero.\nA system that starts there stays there for all time.\n",
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