File:Saddle-node phase portrait with central manifold.svg

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Original file ‎(SVG file, nominally 720 × 720 pixels, file size: 35 KB)

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Summary[edit]

Description
English: Sadle-node singular point phase portrait with one of possible central manifolds

This is a phase portrait of the simple saddle-node equation

Its phase flow looks like:

.

And phase curves can be represented in the form:

Русский: Фазовый портрет седлоузловой особой точки, выделено одно из возможных центральных многообразий
Date
Source Own work
Author Ilya Voyager
SVG development
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The SVG code is valid.
 
This vector image was created with  version 4.3 of GNU libplot, a free library for exporting 2-D vector graphics..
Source code
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SVG code

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);

Licensing[edit]

Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

File history

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Date/TimeThumbnailDimensionsUserComment
current20:52, 30 November 2008Thumbnail for version as of 20:52, 30 November 2008720 × 720 (35 KB)Ilya Voyager (talk | contribs){{Information |Description= |Source= |Date= |Author= |Permission= |other_versions= }}
20:44, 30 November 2008Thumbnail for version as of 20:44, 30 November 2008720 × 720 (34 KB)Ilya Voyager (talk | contribs){{Information |Description= |Source= |Date= |Author= |Permission= |other_versions= }}
20:05, 30 November 2008Thumbnail for version as of 20:05, 30 November 2008720 × 720 (35 KB)Ilya Voyager (talk | contribs){{Information |Description={{en|1=Sadle-node singular point phase portrait with one of possible central manifolds}} {{ru|1=Фазовый портрет седлоузловой особой точки, выделено одно из возможных ц

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