File:Lotka-Volterra.svg
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Summary
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| Description |
English: Phase portrait of Lotka-Volterra system. Mathematica code:
Italiano: Ritratto di fase del sistema Lotka-Volterra. Codice Mathematica:
tend = 40;
Needs["VectorFieldPlots`"]
Quiet@Manipulate[
right1 = (a - b y[t]) x[t];
right2 = (c x[t] - d) y[t];
Solutions =
Table[NDSolve[{x'[t] == right1, y'[t] == right2, x[0] == d/c,
y[0] == i}, {x[t], y[t]}, {t, 0, tend}], {i, a/b,
3, (3 - a/b)/10}];
plot1 =
ParametricPlot[Evaluate[{x[t], y[t]} /. Solutions], {t, 0, tend},
ImageSize -> {300, 300}, AxesOrigin -> {0, 0},
PlotStyle -> {{Blue, Thick}}];
plot2 =
Plot[Evaluate[{x[t], y[t]} /. Solutions[[-1]]], {t, 0, tend},
ImageSize -> {300, 300}];
plot3 = ListPlot[{{0, 0}, {d/c, a/b}}, PlotMarkers -> {Automatic}];
plot4 =
VectorFieldPlot[{right1, right2} /. {x[t] -> x, y[t] -> y}, {x, 0,
3}, {y, 0, 3}];
plotLeft =
Show[plot1, plot3, plot4, PlotRange -> {{0, 3}, {0, 3}},
AxesLabel -> {x, y}, Ticks -> None];
Row[{plotLeft, plot2}]
, {{a, 1}, 0, 5}, {{b, 1}, 0, 5}, {{c, 1}, 0, 5}, {{d, 1}, 0, 5}]
|
| Date | |
| Source | Own work |
| Author | Wiso |
Licensing
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I, the copyright holder of this work, hereby publish it under the following licenses:
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. |
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported, 2.5 Generic, 2.0 Generic and 1.0 Generic license.
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 11:20, 29 May 2008 | | 512 × 512 (432 KB) | Wiso (talk | contribs) | {{Information |Description= |Source= |Date= |Author= |Permission= |other_versions= }} |
| 11:19, 29 May 2008 |  | 512 × 512 (344 KB) | Wiso (talk | contribs) | {{Information |Description= |Source= |Date= |Author= |Permission= |other_versions= }} | |
| 10:48, 29 May 2008 |  | 512 × 512 (432 KB) | Wiso (talk | contribs) | {{Information |Description={{en|1=Phase portrait of Lotka-Volterra system. Mathematica code: tend = 40; Needs["VectorFieldPlots`"] Quiet@Manipulate[][t]) x[t]; right2 = (c x[t] - d) y[t]; Solutions = Table[][][t] == right1, y'[t] == right2, x[0] |
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