Skip to content

Instantly share code, notes, and snippets.

@maedoc
Created April 29, 2014 11:44
Show Gist options
  • Save maedoc/11397773 to your computer and use it in GitHub Desktop.
Save maedoc/11397773 to your computer and use it in GitHub Desktop.
circular-cp
Display the source blob
Display the rendered blob
Raw
{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"%pylab inline"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from pylab import *\n",
"from numpy import *\n",
"from scipy import stats"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 60
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's simulate a noisy oscillator that has two \"ghost\" attractors, $\\dot{x}=sin(2*x)/3 - 1/2 + \\xi(t)$:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"x = 0.5\n",
"dt = 0.1\n",
"X = []\n",
"for i in range(100000):\n",
" dx = sin(2*x)/3 - 0.5 + randn()\n",
" x += dt*dx\n",
" if x < -pi:\n",
" x += 2*pi\n",
" X.append(x)\n",
"X = array(X)\n",
"plot(X[:1000])"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 45,
"text": [
"[<matplotlib.lines.Line2D at 0xdaead30>]"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAEACAYAAAC9Gb03AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nH0v02YHggoytAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0xdacd390>"
]
}
],
"prompt_number": 45
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"(the simulation was 100k steps, this shows only the first 1k steps)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can estimate density of next step on current step"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"nbin = 100\n",
"kde = stats.gaussian_kde(c_[X[:-1], X[1:]].T)\n",
"f = kde(mgrid[-pi:pi:nbin*1j, -pi:pi:nbin*1j].reshape((2, -1))).reshape((nbin, nbin))"
],
"language": "python",
"metadata": {},
"outputs": []
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"figure(figsize=(6, 6))\n",
"imshow(f, extent=[-pi, pi, -pi, pi], interpolation='none')\n",
"ylabel('x[t+1]'), xlabel('x[t]');"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAF6CAYAAAAavuPXAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nwYQPAJZgwgcASzDhA4Al/j+gqtqRLLGIiwAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x185cb2e8>"
]
}
],
"prompt_number": 68
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"which clearly identifies the two \"ghost\" attractors."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment