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  "body": "\n## Summary\n\nA saddle-node bifurcation is a change in a family of dynamical systems at which two [[equilibrium points|0N8NGKDZDZ]] meet and disappear.\nOn one side of the critical parameter there are two equilibria, one stable and one unstable, and on the other side there are none nearby.\nIt is the most common way in which equilibria are created or destroyed as a parameter varies.\nIt is also called a fold bifurcation or a tangent bifurcation.\nSee the [[definition|TB7NBCCXJ1]].\n\n## Explanations\n\n### L1 human\n\nThe model is $x' = \\mu - x^2$ on the line.\nFor $\\mu \u003c 0$ the right side is always negative, so there is no equilibrium.\nAt $\\mu = 0$ the single equilibrium $x = 0$ appears.\nFor $\\mu \u003e 0$ it splits into a stable equilibrium at $\\sqrt{\\mu}$ and an unstable one at $-\\sqrt{\\mu}$.\nRead backwards in $\\mu$, the two equilibria collide and annihilate each other.\n",
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