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| View Original: | Saddle-node phase portrait with central manifold.svg (8x8) | |||
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| Keywords: Saddle-node phase portrait with central manifold.svg en Sadle-node singular point phase portrait with one of possible central manifolds This is a phase portrait of the simple saddle-node equation <math>\begin cases \dot x x 2\\ \dot y y\end cases </math> Its phase flow looks like <math>x t 1/ 1/x_0-t \ y t y_0 \exp t </math> And phase curves can be represented in the form <math>y x y_0\exp 1/x_0-1/x </math> ru Фазовый по т ет седлоузловой особой точки выделено одно из возможных цент альных многооб азий 2008-11-30 Own Ilya Voyager Other fields O + version 4 3 of W GNU libplot a free library for exporting 2-D vector graphics CPP import graph; import math; import metapost; size 8 inches ; defaultpen 0 45mm ; real yt real x pair z0 return z0 y exp 1/z0 x-1/x ; path trajectory pair z0 real leftmargin real rightmargin real curleftmargin leftmargin; real currightmargin rightmargin; if z0 x>0 curleftmargin 0 01; else currightmargin -0 3; return graph new real real t return yt t z0 ; curleftmargin currightmargin ; path boundary -3 -3 -- 3 -3 -- 3 3 -- -3 3 --cycle; path traj; pair inits 1 0 1 0 5 1 1 1 2 1 6 1 100 1 -0 5 1 -1 1 -2 1 -6 1 -100 -1 0 3 -1 1 -1 2 -1 3 -1 -0 3 -1 -1 -1 -2 -1 -3 -1 0 ; draw -3 0 -- 0 0 --trajectory 1 0 5 0 3 p rgb 1 0 3 0 3 +4 5 ; draw 0 -3 -- 0 3 p rgb 0 2 0 8 0 2 +4 5 ; arrowsize new real pen p currentpen return 3 5mm; ; for pair z0 inits traj trajectory z0 -3 3 ; traj lastcut traj boundary before; draw traj Arrow position 45 ; draw 0 0 1 -- 0 3 Arrow 4mm Relative 0 3 filltype NoFill Arrow 4mm Relative 0 32 filltype NoFill ; draw 0 -0 1 -- 0 -3 Arrow 4mm Relative 0 3 filltype NoFill Arrow 4mm Relative 0 32 filltype NoFill ; fill scale 0 06 unitcircle ; Dynamical systems | ||||
