.. _sphx_glr_api_gallery_ode_dynamics_bifurcations:

Bifurcation normal forms
------------------------

Saddle-node, pitchfork, and Hopf bifurcations.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

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    <div class="sphx-glr-thumbcontainer" tooltip="Plots the closed-form fixed points (or limit-cycle radius) of the three canonical bifurcation normal forms as a function of the control parameter r, showing the characteristic collision-and-annihilation, splitting, and birth-of-a-limit-cycle shapes.">

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  .. image:: /api/gallery/ode_dynamics/bifurcations/images/thumb/sphx_glr_plot_01_normal_forms_thumb.png
    :alt:

  :doc:`/api/gallery/ode_dynamics/bifurcations/plot_01_normal_forms`

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      <div class="sphx-glr-thumbnail-title">Saddle-node, pitchfork, and Hopf bifurcation diagrams</div>
    </div>


.. thumbnail-parent-div-close

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    </div>


.. toctree::
   :hidden:

   /api/gallery/ode_dynamics/bifurcations/plot_01_normal_forms