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Gallery
=======

Examples illustrating the main features of hypersynchronization.


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States
======

Common synchronization states generated with :func:`~hypersynchronization.generate_state`.
Each example shows the phase distribution on a circle (left) and phase
values ordered by node index (right).


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    <div class="sphx-glr-thumbcontainer" tooltip="In a splay state phases are evenly distributed on the circle. The order parameter R1 = 0. Phases increase linearly with node index.">

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  .. image:: /auto_examples/states/images/thumb/sphx_glr_plot_splay_thumb.png
    :alt:

  :doc:`/auto_examples/states/plot_splay`

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      <div class="sphx-glr-thumbnail-title">Splay state</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="In a synchronized state all oscillators share the same phase. The order parameter R1 = 1.">

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  .. image:: /auto_examples/states/images/thumb/sphx_glr_plot_sync_thumb.png
    :alt:

  :doc:`/auto_examples/states/plot_sync`

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      <div class="sphx-glr-thumbnail-title">Sync state</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="In a q-twisted state the phases wind q times around the circle with node index. For q=2 the phase-vs-index plot shows two full cycles, distinguishing it from the splay state (q=1).">

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  .. image:: /auto_examples/states/images/thumb/sphx_glr_plot_2_twisted_thumb.png
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  :doc:`/auto_examples/states/plot_2_twisted`

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      <div class="sphx-glr-thumbnail-title">Two-twisted state</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="In a 2-cluster state oscillators split into two groups separated by π. The order parameter R1 reflects the imbalance between cluster sizes, and R2 = 1.">

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  .. image:: /auto_examples/states/images/thumb/sphx_glr_plot_2_cluster_thumb.png
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  :doc:`/auto_examples/states/plot_2_cluster`

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      <div class="sphx-glr-thumbnail-title">Two-cluster state</div>
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Simulate
========

End-to-end simulation examples using :func:`~hypersynchronization.simulate_kuramoto`.


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    <div class="sphx-glr-thumbcontainer" tooltip="Minimal end-to-end example: build a hypergraph, integrate the ODE from random initial conditions, and visualize the result.">

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  .. image:: /auto_examples/simulate/images/thumb/sphx_glr_plot_simulation_thumb.png
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  :doc:`/auto_examples/simulate/plot_simulation`

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      <div class="sphx-glr-thumbnail-title">Simulating Kuramoto oscillators</div>
    </div>


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Visualize
=========

Examples of the plotting functions available in hypersynchronization.


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    <div class="sphx-glr-thumbcontainer" tooltip="plot_phases_ring places oscillators on a circle and colours each node by its phase value.">

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  .. image:: /auto_examples/visualize/images/thumb/sphx_glr_plot_phases_ring_thumb.png
    :alt:

  :doc:`/auto_examples/visualize/plot_phases_ring`

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      <div class="sphx-glr-thumbnail-title">Phases on a ring</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="plot_phases shows the phase distribution on a unit circle. plot_phases_line shows phase values ordered by node index, making the state structure easier to read.">

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  .. image:: /auto_examples/visualize/images/thumb/sphx_glr_plot_phases_plots_thumb.png
    :alt:

  :doc:`/auto_examples/visualize/plot_phases_plots`

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      <div class="sphx-glr-thumbnail-title">Phase distribution plots</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="plot_summary produces a six-panel overview: time series, order parameters, phase circle snapshots, and a ring plot — all in one call.">

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  .. image:: /auto_examples/visualize/images/thumb/sphx_glr_plot_summary_panel_thumb.png
    :alt:

  :doc:`/auto_examples/visualize/plot_summary_panel`

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      <div class="sphx-glr-thumbnail-title">Summary panel</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="plot_sync combines the oscillator time series, the order parameters R1 and R2, and phase snapshots at t=0 and t=T.">

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  .. image:: /auto_examples/visualize/images/thumb/sphx_glr_plot_sync_panel_thumb.png
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  :doc:`/auto_examples/visualize/plot_sync_panel`

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      <div class="sphx-glr-thumbnail-title">Time series and order parameter</div>
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.. toctree::
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   :includehidden:


   /auto_examples/states/index.rst
   /auto_examples/simulate/index.rst
   /auto_examples/visualize/index.rst


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

      :download:`Download all examples in Python source code: auto_examples_python.zip </auto_examples/auto_examples_python.zip>`

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

      :download:`Download all examples in Jupyter notebooks: auto_examples_jupyter.zip </auto_examples/auto_examples_jupyter.zip>`


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