Logistic_map.gif
Summary
Description Logistic map.gif |
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.
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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]
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