Re: Help! on vector field around equilibrium of nonlinear system
- To: mathgroup at smc.vnet.net
- Subject: [mg43318] Re: [mg43261] Help! on vector field around equilibrium of nonlinear system
- From: CAP F <Ferdinand.Cap at eunet.at>
- Date: Sun, 24 Aug 2003 04:55:20 -0400 (EDT)
- References: <200308231208.IAA25084@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
sabrina wrote: > Hello, all: > I am doing some nonlinear differential equations analysis. I tried to use > plotvectorfield to plot the vector field and also find the equilibrium of > this system. It seemed to me it is not so clear to show the vector field ( > kind of jamed in my case :( ) so I decided to plot some lines and arrows > around the equilibrium so that it is easier for me to visualize if those > points are saddle points or stable points, etc. Any good ideas of how to > draw those lines and determine which direction the lines should point to? > Thanks > > Sabrina Why not use portraits ? For saddle etc points, see p 71 f in the book mentioned below in the notebooks (************** Content-type: application/mathematica ************** Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info at wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 2939, 80]*) (*NotebookOutlinePosition[ 3570, 102]*) (* CellTagsIndexPosition[ 3526, 98]*) (*WindowFrame->Normal*) Notebook[{ Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{\(c14 : \ Limit\ cycle\ of\ the\ Van\ der\ Pol\ equation\), ",", " ", \((2. .6 .61)\), ",", " ", RowBox[{ "page", " ", "78", " ", "in", "\[IndentingNewLine]", "the", " ", "book", " ", "Mathematical", " ", "Methods", " ", "in", " ", "Physics", " ", "and", " ", "Engineering", " ", "with", " ", StyleBox["Mathematica", FontSlant->"Italic"]}], StyleBox[",", FontSlant->"Italic"], StyleBox[" ", FontSlant->"Italic"], \(CRC\ Press\), ",", StyleBox[" ", FontSlant->"Italic"], \(ISBN\ 1584884029\)}], " ", "*)"}], " ", \(Clear[mu, n]\)}]], "Input"], Cell[BoxData[{ \(mu = 1. ; n = 2. ;\), "\[IndentingNewLine]", \(\(Sol = NDSolve[{\(x1'\)[t] \[Equal] x2[t], \(x2'\)[t] \[Equal] \(-x1[t]\) + mu*\((1 - \((x1[t])\)^2)\)*x2[t], x1[0] \[Equal] n, x2[0] \[Equal] 0}, \[IndentingNewLine]{x1, x2}, {t, 0, 8. *Pi}];\)\), "\[IndentingNewLine]", \(ParametricPlot[ Evaluate[{x1[t], x2[t]} /. Sol], {t, 0, 4. *Pi}]\)}], "Input"] }, FrontEndVersion->"4.1 for X", ScreenRectangle->{{0, 1280}, {0, 1024}}, WindowSize->{1072, 599}, WindowMargins->{{97, Automatic}, {Automatic, 28}} ] (******************************************************************* Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. *******************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[1705, 50, 774, 17, 101, "Input"], Cell[2482, 69, 453, 9, 124, "Input"] } ] *) (******************************************************************* End of Mathematica Notebook file. *******************************************************************) (************** Content-type: application/mathematica ************** Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info at wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 2263, 62]*) (*NotebookOutlinePosition[ 2894, 84]*) (* CellTagsIndexPosition[ 2850, 80]*) (*WindowFrame->Normal*) Notebook[{ Cell[BoxData[ \(\(\( (*\ c16 : \ Phase\ portrait\ of\ the\ DUFFING\ equation\ \((2.6 .42)\)\ \ \[IndentingNewLine]see\ Mathematical\ Methods\ in\ Physics\ and\ Engineering, \ \ ISBN01584884029*) \)\(\n\)\(Clear[a, b, n, Duff, x1, x2]; a = 1. ; b = 0.1; n = 2. ; Duff = NDSolve[{\(x1'\)[t] \[Equal] x2[t], \(x2'\)[t] \[Equal] \(-a\)*x1[t] - b*x1[t]^3, x1[0] \[Equal] n, x2[0] \[Equal] 0}, {x1, x2}, {t, 0, 8*Pi}]; ParametricPlot[ Evaluate[{x1[t], x2[t]} /. Duff], {t, 0, 4. *Pi}]\)\)\)], "Input"] }, FrontEndVersion->"4.1 for X", ScreenRectangle->{{0, 1280}, {0, 1024}}, WindowSize->{1109, 640}, WindowMargins->{{77, Automatic}, {Automatic, 28}} ] (******************************************************************* Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. *******************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[1705, 50, 554, 10, 147, "Input"] } ] *) (******************************************************************* End of Mathematica Notebook file. *******************************************************************)
- References:
- Help! on vector field around equilibrium of nonlinear system
- From: sabrina <mystery@newbie.com>
- Help! on vector field around equilibrium of nonlinear system