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  "body": "\n## Summary\n\nA heteroclinic orbit is a [[trajectory|07TZ2Q4C1M]] of a dynamical system that joins two different [[equilibrium points|0N8NGKDZDZ]].\nIt tends to the first one in the past and to the second one in the future.\nIt is also called a heteroclinic connection.\nHeteroclinic orbits bound regions of different behaviour in the [[phase portrait|0T3GK0XCBC]].\nTheir breaking under perturbation is a source of complicated dynamics.\nSee the [[definition|F05PSBZP8Z]].\n\n## Explanations\n\n### L1 human\n\nPicture a landscape with two mountain passes and a ridge between them.\nA ball that leaves the first pass and rolls exactly along the ridge to the second pass follows a heteroclinic orbit.\nFor the equation $x' = 1 - x^2$ on the line, the solution $x(t) = \\tanh t$ is near $-1$ in the far past and near $1$ in the far future.\nIts orbit, the open interval $(-1, 1)$, is a heteroclinic orbit from the equilibrium $-1$ to the equilibrium $1$.\nWhen the starting and the final equilibrium are the same, the orbit is called homoclinic instead.\n",
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