.. 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

        Click :ref:`here <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
------------------------------------------------------

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.

.. GENERATED FROM PYTHON SOURCE LINES 46-47

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

.. GENERATED FROM PYTHON SOURCE LINES 47-52

.. code-block:: default


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


.. GENERATED FROM PYTHON SOURCE LINES 53-54

Second, the simulation parameters are assigned to variables.

.. GENERATED FROM PYTHON SOURCE LINES 54-72

.. code-block:: default


    N = 1000           # number of neurons
    bias_begin = 140.  # minimal value for the bias current injection [pA]
    bias_end = 200.    # maximal value for the bias current injection [pA]
    T = 600            # simulation time (ms)

    # parameters for the alternating-current generator
    driveparams = {'amplitude': 50., 'frequency': 35.}
    # parameters for the noise generator
    noiseparams = {'mean': 0.0, 'std': 200.}
    neuronparams = {'tau_m': 20.,  # membrane time constant
                    'V_th': 20.,  # threshold potential
                    'E_L': 10.,  # membrane resting potential
                    't_ref': 2.,  # refractory period
                    'V_reset': 0.,  # reset potential
                    'C_m': 200.,  # membrane capacitance
                    'V_m': 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.

.. GENERATED FROM PYTHON SOURCE LINES 75-81

.. code-block:: default


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


.. GENERATED FROM PYTHON SOURCE LINES 82-83

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

.. GENERATED FROM PYTHON SOURCE LINES 83-87

.. code-block:: default


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


.. GENERATED FROM PYTHON SOURCE LINES 88-91

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`.

.. GENERATED FROM PYTHON SOURCE LINES 91-96

.. code-block:: default


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


.. GENERATED FROM PYTHON SOURCE LINES 97-99

Connect alternating current and noise generators as well as
`spike_recorder`s to neurons

.. GENERATED FROM PYTHON SOURCE LINES 99-104

.. code-block:: default


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


.. GENERATED FROM PYTHON SOURCE LINES 105-106

Simulate the network for time `T`.

.. GENERATED FROM PYTHON SOURCE LINES 106-109

.. code-block:: default


    nest.Simulate(T)


.. GENERATED FROM PYTHON SOURCE LINES 110-111

Plot the raster plot of the neuronal spiking activity.

.. GENERATED FROM PYTHON SOURCE LINES 111-114

.. code-block:: default


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


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

   **Total running time of the script:** ( 0 minutes  0.000 seconds)


.. _sphx_glr_download_auto_examples_BrodyHopfield.py:

.. only:: html

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


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

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

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

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


.. only:: html

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

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