.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/geophysics/plot_13_rikitake_two_disc_dynamo.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_geophysics_plot_13_rikitake_two_disc_dynamo.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_geophysics_plot_13_rikitake_two_disc_dynamo.py:


Rikitake's two-disc dynamo (1958)
=================================

Tsuneji Rikitake coupled two disc dynamos, each driven by the same torque and
each powering the coil of the other. The currents never settle: they oscillate
about one of two steady states of opposite sign and, at irregular intervals,
jump to the other. The model was the first to show that a deterministic dynamo
can reverse its field spontaneously, without any outside trigger, with
polarity intervals of very unequal length, as in the geological record.

.. GENERATED FROM PYTHON SOURCE LINES 12-39



.. image-sg:: /api/gallery/geophysics/images/sphx_glr_plot_13_rikitake_two_disc_dynamo_001.png
   :alt: Spontaneous reversals, Two unstable centres
   :srcset: /api/gallery/geophysics/images/sphx_glr_plot_13_rikitake_two_disc_dynamo_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.geophysics import rikitake_fixed_point, simulate_rikitake_dynamo

    mu, k = 1.0, 2.0
    time = np.linspace(0, 400, 8001)
    result = simulate_rikitake_dynamo(mu, k, 1.0, time)
    x, y, z = result.values.T
    flips = np.flatnonzero(np.diff(np.sign(x)))
    assert flips.size > 10
    lengths = np.diff(time[flips])
    assert lengths.max() > 3 * np.median(lengths)
    steady = rikitake_fixed_point(mu, k)

    fig, (left, right) = plt.subplots(1, 2, figsize=(11, 4), gridspec_kw={"width_ratios": [2, 1]})
    left.plot(time, x, lw=0.8)
    left.axhline(0, color="k", lw=0.5)
    left.set(xlabel="nondimensional time", ylabel="current x (sign = polarity)", title="Spontaneous reversals")
    right.plot(x, y, lw=0.4)
    right.plot([steady[0], -steady[0]], [steady[1], -steady[1]], "r*", ms=12, label="steady states")
    right.set(xlabel="x", ylabel="y", title="Two unstable centres")
    right.legend()
    fig.tight_layout()

    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 1.846 seconds)


.. _sphx_glr_download_api_gallery_geophysics_plot_13_rikitake_two_disc_dynamo.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../lite/lab/index.html?path=api/gallery/geophysics/plot_13_rikitake_two_disc_dynamo.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_13_rikitake_two_disc_dynamo.ipynb <plot_13_rikitake_two_disc_dynamo.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_13_rikitake_two_disc_dynamo.py <plot_13_rikitake_two_disc_dynamo.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_13_rikitake_two_disc_dynamo.zip <plot_13_rikitake_two_disc_dynamo.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_