Kaplan-Yorke map

Output

(Source code, png, hires.png, pdf)

Python code

from railgun import SimObject, relpath

class KaplanYorkeMap(SimObject):
    """
    Simulating Kaplan-Yorke Map using RailGun
    """

    _clibname_ = 'libkaplan_yorke_map.so'  # name of shared library
    _clibdir_ = relpath('.', __file__)  # library directory
    _cmembers_ = [  # declaring members of struct
        'num_i',  # num_* as size of array (no need to write `int`)
        'double xt[i]',  # array with num_i elements
        'double yt[i]',  # array with num_i elements
        'double mu',
        'double lmd',
        ]
    _cfuncs_ = ["gene_seq()"]


kym = KaplanYorkeMap(num_i=10**5, mu=2, lmd=0.4, xt_0=0.1, yt_0=0.1)
kym.setv()
kym.gene_seq()
(xt, yt) = kym.getv('xt, yt')

import pylab
pylab.figure(1, figsize=(4,3))
pylab.plot(xt, yt, 'k.', markersize=0.1)
pylab.show()

C code

typedef struct kaplanyorkemap_{
  int num_i;
  double *xt;
  double *yt;
  double mu;
  double lmd;
} KaplanYorkeMap;

int KaplanYorkeMap_gene_seq(KaplanYorkeMap *self)
{
  int st;
  for (st = 1; st < self->num_i; ++st){
    self->xt[st] = 1 - self->mu * self->xt[st-1] * self->xt[st-1];
    self->yt[st] = self->lmd * self->yt[st-1] + self->xt[st-1];
  }
  return 0;
}

Definition of the map

References

• Thermodynamics of chaotic systems: an introduction By Christian Beck, Friedrich Schlögl - Google Books
• Kaplan–Yorke map - Wikipedia, the free encyclopedia