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

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_examples_BrodyHopfield.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_BrodyHopfield.py:


Spike synchronization through subthreshold oscillation
------------------------------------------------------

.. only:: html

----

 Run this example as a Jupyter notebook:

  .. card::
    :width: 25%
    :margin: 2
    :text-align: center
    :link: https://lab.ebrains.eu/hub/user-redirect/git-pull?repo=https%3A%2F%2Fgithub.com%2Fnest%2Fnest-simulator-examples&urlpath=lab%2Ftree%2Fnest-simulator-examples%2Fnotebooks%2Fnotebooks%2FBrodyHopfield.ipynb&branch=main
    :link-alt: JupyterHub service

    .. image:: https://nest-simulator.org/TryItOnEBRAINS.png


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   :padding: 0 0 2 0

   .. grid-item::
     :class: sd-text-muted
     :margin: 0 0 3 0
     :padding: 0 0 3 0
     :columns: 4

     See :ref:`our guide <run_jupyter>` for more information and troubleshooting.

----


This script reproduces the spike synchronization behavior
of integrate-and-fire neurons in response to a subthreshold
oscillation. This phenomenon is shown in Fig. 1 of [1]_

Neurons receive a weak 35 Hz oscillation, a gaussian noise current
and an increasing DC. The time-locking capability is shown to
depend on the input current given. The result is then plotted using
matplotlib. All parameters are taken from the above paper.

References
~~~~~~~~~~

.. [1] Brody CD and Hopfield JJ (2003). Simple networks for
       spike-timing-based computation, with application to olfactory
       processing. Neuron 37, 843-852.

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First, we import all necessary modules for simulation, analysis, and plotting.

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.. code-block:: Python


    import matplotlib.pyplot as plt
    import nest
    import nest.raster_plot


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Second, the simulation parameters are assigned to variables.

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.. code-block:: Python


    N = 1000  # number of neurons
    bias_begin = 140.0  # minimal value for the bias current injection [pA]
    bias_end = 200.0  # maximal value for the bias current injection [pA]
    T = 600  # simulation time (ms)

    # parameters for the alternating-current generator
    driveparams = {"amplitude": 50.0, "frequency": 35.0}
    # parameters for the noise generator
    noiseparams = {"mean": 0.0, "std": 200.0}
    neuronparams = {
        "tau_m": 20.0,  # membrane time constant
        "V_th": 20.0,  # threshold potential
        "E_L": 10.0,  # membrane resting potential
        "t_ref": 2.0,  # refractory period
        "V_reset": 0.0,  # reset potential
        "C_m": 200.0,  # membrane capacitance
        "V_m": 0.0,
    }  # initial membrane potential


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Third, the nodes are created using ``Create``. We store the returned handles
in variables for later reference.

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.. code-block:: Python


    neurons = nest.Create("iaf_psc_alpha", N)
    sr = nest.Create("spike_recorder")
    noise = nest.Create("noise_generator")
    drive = nest.Create("ac_generator")


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Set the parameters specified above for the generators using ``set``.

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.. code-block:: Python


    drive.set(driveparams)
    noise.set(noiseparams)


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Set the parameters specified above for the neurons. Neurons get an internal
current. The first neuron additionally receives the current with amplitude
``bias_begin``, the last neuron with amplitude ``bias_end``.

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.. code-block:: Python


    neurons.set(neuronparams)
    neurons.I_e = [(n * (bias_end - bias_begin) / N + bias_begin) for n in range(1, len(neurons) + 1)]


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Connect alternating current and noise generators as well as
spike_recorders to neurons

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.. code-block:: Python


    nest.Connect(drive, neurons)
    nest.Connect(noise, neurons)
    nest.Connect(neurons, sr)


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Simulate the network for time ``T``.

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.. code-block:: Python


    nest.Simulate(T)


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Plot the raster plot of the neuronal spiking activity.

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.. code-block:: Python


    nest.raster_plot.from_device(sr, hist=True)
    plt.show()


.. _sphx_glr_download_auto_examples_BrodyHopfield.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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