File:Lyapunov exponent of real quadratic map.png
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Summary
[edit]-
exponential transformation of the horizontal ( parameter ) axis
DescriptionLyapunov exponent of real quadratic map.png |
English: Real quadratic map : bifurcation diagram and Lyapunov exponent |
Date | |
Source | Own work : based on the code by Mario Rodriguez Riotorto[1] using Maxima CAS and draw package ( also by Mario Rodriguez Riotorto ) |
Author | Adam majewski |
Maxima CAS src code
[edit]/* batch file for Maxima CAS program save it as a file with mac extension and open in Maxima It creates l6.svg file in the directory path ( see below) change the path directory if you save mac file in the different location -----run ------- maxima batch("l.mac"); */ kill(all); remvalue(all); /* real quadratic diagram based on the code by Mario Rodriguez Riotorto using Maxima CAS draw packag */ pts:[]; /* points of the orbit */ ls:[]; kMax1:1000; kMax2:500; /* ------------- compute -----------------------------------*/ for c:-2.0 while c <= 0.25 step 0.001 do ( z: 0.0, l:0, /* Lyapunov exponent */ for k:1 thru kMax1 do ( z: z * z+c, /* to remove points from image compute and do not draw it */ l:l+log(abs(2*z)) ), for k:1 thru kMax2 do ( z: z * z+c, /* compute and draw it */ pts: cons([c,z], pts),/* save points to draw it later */ l:l+log(abs(2*z)) ), ls:cons([c,l/(kMax1+kMax2)],ls) /* save points to draw it later */ ); /* ================= draw ======================================*/ path:"~/maxima/batch/lyapunov/"$ /* result of pwd; to save image in the same directory as mac file */ FileName:"l6"$ /* without extension which is the terminal name */ load(draw); draw( terminal = 'svg, file_name = concat(path,FileName), dimensions=[1900,2600], /* y = x*rows */ gr2d(points_joined =false, title = "Bifurcation diagram, z[i+1] = z[i]*z[i] +c", xlabel = "c parameter", ylabel = "z ", point_type = filled_circle, point_size = 0.2, color = black, points(pts) ), gr2d(title = " Lyapunov exponent ", points_joined =true, yaxis = true, xaxis = true, xlabel = "c parameter", ylabel = " lyapunov exponent ", yrange = [-4,1], color = red, point_size = 0.5, point_type = filled_circle, points(ls)) );
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 22:13, 25 September 2016 | 1,900 × 2,600 (612 KB) | Cmdrjameson (talk | contribs) | Compressed with pngout. Reduced by 429kB (41% decrease). | |
17:30, 12 February 2014 | 1,900 × 2,600 (1.02 MB) | Soul windsurfer (talk | contribs) | User created page with UploadWizard |
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