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  "body": "\n## Summary\n\nA pitchfork bifurcation is a change in a family of dynamical systems with a symmetry, at which one [[equilibrium point|0N8NGKDZDZ]] splits into three.\nIt typically occurs when the system is unchanged under $x \\mapsto -x$, so equilibria come in symmetric pairs.\nIn the supercritical case, a stable equilibrium becomes unstable and two new stable equilibria appear on either side.\nSee the [[definition|TRFDEJRPAZ]].\n\n## Explanations\n\n### L1 human\n\nThe model is $x' = \\mu x - x^3$.\nFor $\\mu \\le 0$ the origin is the only equilibrium, and it attracts nearby solutions.\nFor $\\mu \u003e 0$ the origin repels, and two new stable equilibria appear at $\\pm\\sqrt{\\mu}$.\nPlotting the equilibria against $\\mu$ gives a picture shaped like a pitchfork.\nA ruler pressed at both ends that buckles to the left or to the right is a physical picture of this.\n",
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