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  "body": "\n## Summary\n\nNumerical continuation is a family of methods that trace the solutions of a system of equations $F(x, \\lambda) = 0$ as a parameter $\\lambda$ changes.\nStarting from one known solution, it computes a chain of nearby solutions along a curve.\nEach new point usually comes from a predictor step and a [[Newton's method|07EXVNF9VP]] corrector step.\nIt is the main tool for studying how the solutions of nonlinear models depend on parameters, and for finding bifurcations.\nIt also gives a way to solve a hard system by deforming it from an easy one.\n\n## Explanations\n\n### L1 human\n\nImagine a curve of solutions drawn in space, and you stand on one point of it.\nYou take a small step along the tangent of the curve, which lands you near the curve, and then you walk back onto the curve with a few Newton steps.\nRepeating this, you follow the whole curve.\nFor example, the solutions of $x^2 + \\lambda^2 = 1$ form a circle, and continuation from $(x, \\lambda) = (1, 0)$ walks around this circle, even through the points where $\\lambda$ turns back.\n",
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