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  "body": "\n## Summary\n\nA bifurcation diagram is a picture of how the long-term behaviour of a one-parameter family of dynamical systems depends on the parameter.\nThe parameter runs along the horizontal axis, and above each value one plots the [[equilibria|0N8NGKDZDZ]], periodic orbits or [[attractor|7FWX24X5MW]] of the system.\nBranches that split, merge or end mark the bifurcations studied by [[bifurcation theory|D9TW46P19Y]].\nThe best known example is the diagram of the [[logistic map|QN9X9BNKTX]], with its cascade of period doublings.\n\n## Explanations\n\n### L1 human\n\nRun the system for many steps at one setting of the parameter and mark where it ends up.\nDo this for many settings side by side, and you get a bifurcation diagram.\nA single line means the system settles to one value; two lines mean it alternates between two values; a smeared band means chaos.\nFor the logistic map $x \\mapsto r x (1 - x)$ the single line splits into two near $r = 3$, then into four, and so on, until chaos sets in.\n",
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