File:Logistic map.gif
| Uploaded by | Student298 |
|---|---|
| Upload date | 2020-08-11T18:52:33Z |
| MIME type | image/gif |
| Dimensions | 576 × 393 px |
| File size | 1.8 MB |
Summary
| Description |
English: For a logistic map, depending on your choice of the parameter r, different initial conditions will: collapse to 0, collapse on a well defined curve, show a bifurcation, get in a periodic orbit, get into an aperiodic orbit. |
| Date | |
| Source | https://twitter.com/j_bertolotti/status/1235854410493747201 |
| Author | Jacopo Bertolotti |
| Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 12.0 code
logistic[r_, x_] := r x (1 - x)
rlist = Table[r, {r, 0, 4, 0.02}];
evo = Table[NestList[logistic[r, #] &, x0, 100], {x0, 0, 1, 0.005}, {r, rlist}];
p0 =
Table[
Show[
Plot[0, {x, 0, 4}, PlotRange -> {{0, 4}, {0, 1}}, AxesLabel -> {"r", "x"}, LabelStyle -> {Bold, Black}, PlotLabel -> StringForm["Logistic map: \!\(\*SubscriptBox[\(x\), \(n + 1\)]\)=r \\!\(\*SubscriptBox[\(x\), \(n\)]\)(1-\!\(\*SubscriptBox[\(x\), \(n\)]\\)). n=``", t - 1]],Graphics[{PointSize[0.005], Opacity[0.3],
Table[Point[{rlist[[r]], evo[[x0, r, t]]}], {x0, 1, Dimensions[evo][[1]]}, {r, 1, Dimensions[evo][[2]]}]}], ImageSize -> Large]
, {t, 1, Dimensions[evo][[3]]}] ;
ListAnimate[p0]
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
 
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
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