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  "body": "\n## Summary\n\nA homoclinic bifurcation is a global bifurcation in which, at one parameter value, an orbit leaves a saddle equilibrium and returns to it.\nThis orbit is a [[homoclinic orbit|6DBSQKZK4W]].\nAs the parameter crosses this value, the loop breaks, and periodic orbits can be created or destroyed near it.\nIn the plane, under nondegeneracy conditions, a single [[limit cycle|0AAQ73WRFB]] is born from the loop.\nIn three dimensions, near a saddle-focus, the bifurcation can produce chaos, as the [[Shilnikov theorem|Q134D9EMAZ]] shows.\n\n## Explanations\n\n### L1 human\n\nA saddle point has a path leading out of it and a path leading into it.\nUsually these paths miss each other, but at a special parameter value the outgoing path loops around and comes back in.\nThat loop is fragile and breaks as soon as the parameter moves.\nWhen it breaks, a closed orbit that circles around near the old loop can appear, with a period that becomes infinite as the parameter approaches the special value.\n",
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  "msc": [
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  "name": "Homoclinic bifurcation",
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