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  "body": "\n## Summary\n\nA phase portrait of an autonomous system is a picture of a representative set of its [[trajectories|0BVT6VSB3S]] in the phase space, usually the [[phase plane|05VDGH129F]].\nArrows on the curves show the direction of time.\nIt shows the [[equilibrium points|0G4X36AE0X]], the periodic orbits and the long-time behaviour of the solutions.\n\n## Remarks\n\nThe [[phase line|081QSEAGEY]] is the phase portrait of a scalar autonomous equation.\nFor the undamped [[harmonic oscillator|0YG0ZJPTWG]] $x'' = -x$, the phase portrait in the $(x, x')$ plane consists of the origin and the circles around it.\n\n## Explanations\n\n### L1 human\n\nA phase portrait is a map of all the possible motions of a system.\nOne look shows where the system rests, where it cycles and where it goes in the long run.\n",
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