File:CircleMapOrbitDiag.png
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Summary
DescriptionCircleMapOrbitDiag.png |
English: Produced by the following Python code adapted from Wikipedia article Logistic map:
import numpy as np import math import matplotlib.pyplot as plt # - Described at: https://mathworld.wolfram.com/CircleMap.html # - Both the formula and modulo 1 trace to the above. # - Described https://en.wikipedia.org/wiki/Arnold_tongue # - The above uses "+ K/2*pi" while MathWorld uses "- K/2*pi" # - The choice of omega = 1/3 traces to the above. # - The choice of kInterval of (0, 4 * math.pi) traces to the above, except that we start at -2 # to get a more complete picture. # - Issue: the choice of omega and kInterval trace only to Wikipedia, not to other source. # - The choice of starting at 0.5 is not based on anything; it is a guess taken over # from the logistic map. preset = 1 saveFigure = True markerSize = 0.001 markerStyle = "," # . - point; , - pixel if preset == 1: kInterval = (-2, 4 * math.pi) kResolution = 0.002 mapIterationCount = 1000 lastMapIterationCountToPlot = 1000 startingIterationValue = 0.5 yLim = (-0.1, 1.1) omega = 1.0/3.0 fileName = "CircleMapOrbitDiag.png" lims = np.zeros(mapIterationCount) fig, biax = plt.subplots() fig.set_size_inches(16, 9) itemCount = 0 for K in np.arange(kInterval[0], kInterval[1], kResolution): itemCount += 1 lims[0] = startingIterationValue for i in xrange(mapIterationCount - 1): lims[i + 1] = (lims[i] + omega + K / (2 * math.pi) * math.sin(2 * math.pi * lims[i])) % 1 if itemCount % 1000 == 0: print("Parameter values processed:", itemCount) biax.plot([K] * lastMapIterationCountToPlot, lims[(mapIterationCount - lastMapIterationCountToPlot):], "b.", markersize=markerSize, marker=markerStyle) biax.set(xlabel="K", ylabel="x", title="Circle map - (x + omega - K / (2 * pi) * sin(2 * pi * x)) mod 1 - bifurcation diagram/orbit diagram" + "\n" + "K resolution: " + str(kResolution) + ", iteration count: " + str(mapIterationCount) + ", last values to plot count: " + str(lastMapIterationCountToPlot) + (", omega: %.3f" % omega)) biax.set_ylim(yLim[0], yLim[1]) if saveFigure: plt.savefig(fileName, dpi=600) else: plt.show() |
Date | |
Source | Own work |
Author | Dan Polansky |
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9 February 2024
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 08:20, 9 February 2024 | 9,600 × 5,400 (5.57 MB) | Dan Polansky | Uploaded own work with UploadWizard |
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