.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/brunel_alpha_nest.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_brunel_alpha_nest.py: Random balanced network (alpha synapses) connected with NEST ------------------------------------------------------------ This script simulates an excitatory and an inhibitory population on the basis of the network used in [1]_. In contrast to ``brunel-alpha-numpy.py``, this variant uses NEST's builtin connection routines to draw the random connections instead of NumPy. When connecting the network, customary synapse models are used, which allow for querying the number of created synapses. Using spike recorders, the average firing rates of the neurons in the populations are established. The building as well as the simulation time of the network are recorded. References ~~~~~~~~~~ .. [1] Brunel N (2000). Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. Journal of Computational Neuroscience 8, 183-208. .. GENERATED FROM PYTHON SOURCE LINES 48-50 Import all necessary modules for simulation, analysis and plotting. Scipy should be imported before nest. .. GENERATED FROM PYTHON SOURCE LINES 50-60 .. code-block:: default import time import numpy as np import scipy.special as sp import nest import nest.raster_plot import matplotlib.pyplot as plt .. GENERATED FROM PYTHON SOURCE LINES 61-66 Definition of functions used in this example. First, define the `Lambert W` function implemented in SLI. The second function computes the maximum of the postsynaptic potential for a synaptic input current of unit amplitude (1 pA) using the `Lambert W` function. Thus function will later be used to calibrate the synaptic weights. .. GENERATED FROM PYTHON SOURCE LINES 66-88 .. code-block:: default def LambertWm1(x): # Using scipy to mimic the gsl_sf_lambert_Wm1 function. return sp.lambertw(x, k=-1 if x < 0 else 0).real def ComputePSPnorm(tauMem, CMem, tauSyn): a = (tauMem / tauSyn) b = (1.0 / tauSyn - 1.0 / tauMem) # time of maximum t_max = 1.0 / b * (-LambertWm1(-np.exp(-1.0 / a) / a) - 1.0 / a) # maximum of PSP for current of unit amplitude return (np.exp(1.0) / (tauSyn * CMem * b) * ((np.exp(-t_max / tauMem) - np.exp(-t_max / tauSyn)) / b - t_max * np.exp(-t_max / tauSyn))) nest.ResetKernel() .. GENERATED FROM PYTHON SOURCE LINES 89-91 Assigning the current time to a variable in order to determine the build time of the network. .. GENERATED FROM PYTHON SOURCE LINES 91-95 .. code-block:: default startbuild = time.time() .. GENERATED FROM PYTHON SOURCE LINES 96-97 Assigning the simulation parameters to variables. .. GENERATED FROM PYTHON SOURCE LINES 97-102 .. code-block:: default dt = 0.1 # the resolution in ms simtime = 1000.0 # Simulation time in ms delay = 1.5 # synaptic delay in ms .. GENERATED FROM PYTHON SOURCE LINES 103-105 Definition of the parameters crucial for asynchronous irregular firing of the neurons. .. GENERATED FROM PYTHON SOURCE LINES 105-110 .. code-block:: default g = 5.0 # ratio inhibitory weight/excitatory weight eta = 2.0 # external rate relative to threshold rate epsilon = 0.1 # connection probability .. GENERATED FROM PYTHON SOURCE LINES 111-113 Definition of the number of neurons in the network and the number of neurons recorded from .. GENERATED FROM PYTHON SOURCE LINES 113-120 .. code-block:: default order = 2500 NE = 4 * order # number of excitatory neurons NI = 1 * order # number of inhibitory neurons N_neurons = NE + NI # number of neurons in total N_rec = 50 # record from 50 neurons .. GENERATED FROM PYTHON SOURCE LINES 121-122 Definition of connectivity parameters .. GENERATED FROM PYTHON SOURCE LINES 122-127 .. code-block:: default CE = int(epsilon * NE) # number of excitatory synapses per neuron CI = int(epsilon * NI) # number of inhibitory synapses per neuron C_tot = int(CI + CE) # total number of synapses per neuron .. GENERATED FROM PYTHON SOURCE LINES 128-131 Initialization of the parameters of the integrate and fire neuron and the synapses. The parameters of the neuron are stored in a dictionary. The synaptic currents are normalized such that the amplitude of the PSP is J. .. GENERATED FROM PYTHON SOURCE LINES 131-150 .. code-block:: default tauSyn = 0.5 # synaptic time constant in ms tauMem = 20.0 # time constant of membrane potential in ms CMem = 250.0 # capacitance of membrane in in pF theta = 20.0 # membrane threshold potential in mV neuron_params = {"C_m": CMem, "tau_m": tauMem, "tau_syn_ex": tauSyn, "tau_syn_in": tauSyn, "t_ref": 2.0, "E_L": 0.0, "V_reset": 0.0, "V_m": 0.0, "V_th": theta} J = 0.1 # postsynaptic amplitude in mV J_unit = ComputePSPnorm(tauMem, CMem, tauSyn) J_ex = J / J_unit # amplitude of excitatory postsynaptic current J_in = -g * J_ex # amplitude of inhibitory postsynaptic current .. GENERATED FROM PYTHON SOURCE LINES 151-155 Definition of threshold rate, which is the external rate needed to fix the membrane potential around its threshold, the external firing rate and the rate of the poisson generator which is multiplied by the in-degree CE and converted to Hz by multiplication by 1000. .. GENERATED FROM PYTHON SOURCE LINES 155-160 .. code-block:: default nu_th = (theta * CMem) / (J_ex * CE * np.exp(1) * tauMem * tauSyn) nu_ex = eta * nu_th p_rate = 1000.0 * nu_ex * CE .. GENERATED FROM PYTHON SOURCE LINES 161-165 Configuration of the simulation kernel by the previously defined time resolution used in the simulation. Setting ``print_time`` to `True` prints the already processed simulation time as well as its percentage of the total simulation time. .. GENERATED FROM PYTHON SOURCE LINES 165-172 .. code-block:: default nest.resolution = dt nest.print_time = True nest.overwrite_files = True print("Building network") .. GENERATED FROM PYTHON SOURCE LINES 173-178 Creation of the nodes using ``Create``. We store the returned handles in variables for later reference. Here the excitatory and inhibitory, as well as the poisson generator and two spike recorders. The spike recorders will later be used to record excitatory and inhibitory spikes. Properties of the nodes are specified via ``params``, which expects a dictionary. .. GENERATED FROM PYTHON SOURCE LINES 178-185 .. code-block:: default nodes_ex = nest.Create("iaf_psc_alpha", NE, params=neuron_params) nodes_in = nest.Create("iaf_psc_alpha", NI, params=neuron_params) noise = nest.Create("poisson_generator", params={"rate": p_rate}) espikes = nest.Create("spike_recorder") ispikes = nest.Create("spike_recorder") .. GENERATED FROM PYTHON SOURCE LINES 186-190 Configuration of the spike recorders recording excitatory and inhibitory spikes by sending parameter dictionaries to ``set``. Setting the property `record_to` to *"ascii"* ensures that the spikes will be recorded to a file, whose name starts with the string assigned to the property `label`. .. GENERATED FROM PYTHON SOURCE LINES 190-196 .. code-block:: default espikes.set(label="brunel-py-ex", record_to="ascii") ispikes.set(label="brunel-py-in", record_to="ascii") print("Connecting devices") .. GENERATED FROM PYTHON SOURCE LINES 197-203 Definition of a synapse using ``CopyModel``, which expects the model name of a pre-defined synapse, the name of the customary synapse and an optional parameter dictionary. The parameters defined in the dictionary will be the default parameter for the customary synapse. Here we define one synapse for the excitatory and one for the inhibitory connections giving the previously defined weights and equal delays. .. GENERATED FROM PYTHON SOURCE LINES 203-209 .. code-block:: default nest.CopyModel("static_synapse", "excitatory", {"weight": J_ex, "delay": delay}) nest.CopyModel("static_synapse", "inhibitory", {"weight": J_in, "delay": delay}) .. GENERATED FROM PYTHON SOURCE LINES 210-216 Connecting the previously defined poisson generator to the excitatory and inhibitory neurons using the excitatory synapse. Since the poisson generator is connected to all neurons in the population the default rule (``all_to_all``) of ``Connect`` is used. The synaptic properties are inserted via ``syn_spec`` which expects a dictionary when defining multiple variables or a string when simply using a pre-defined synapse. .. GENERATED FROM PYTHON SOURCE LINES 216-220 .. code-block:: default nest.Connect(noise, nodes_ex, syn_spec="excitatory") nest.Connect(noise, nodes_in, syn_spec="excitatory") .. GENERATED FROM PYTHON SOURCE LINES 221-225 Connecting the first ``N_rec`` nodes of the excitatory and inhibitory population to the associated spike recorders using excitatory synapses. Here the same shortcut for the specification of the synapse as defined above is used. .. GENERATED FROM PYTHON SOURCE LINES 225-233 .. code-block:: default nest.Connect(nodes_ex[:N_rec], espikes, syn_spec="excitatory") nest.Connect(nodes_in[:N_rec], ispikes, syn_spec="excitatory") print("Connecting network") print("Excitatory connections") .. GENERATED FROM PYTHON SOURCE LINES 234-240 Connecting the excitatory population to all neurons using the pre-defined excitatory synapse. Beforehand, the connection parameter are defined in a dictionary. Here we use the connection rule ``fixed_indegree``, which requires the definition of the indegree. Since the synapse specification is reduced to assigning the pre-defined excitatory synapse it suffices to insert a string. .. GENERATED FROM PYTHON SOURCE LINES 240-246 .. code-block:: default conn_params_ex = {'rule': 'fixed_indegree', 'indegree': CE} nest.Connect(nodes_ex, nodes_ex + nodes_in, conn_params_ex, "excitatory") print("Inhibitory connections") .. GENERATED FROM PYTHON SOURCE LINES 247-251 Connecting the inhibitory population to all neurons using the pre-defined inhibitory synapse. The connection parameter as well as the synapse parameter are defined analogously to the connection from the excitatory population defined above. .. GENERATED FROM PYTHON SOURCE LINES 251-255 .. code-block:: default conn_params_in = {'rule': 'fixed_indegree', 'indegree': CI} nest.Connect(nodes_in, nodes_ex + nodes_in, conn_params_in, "inhibitory") .. GENERATED FROM PYTHON SOURCE LINES 256-257 Storage of the time point after the buildup of the network in a variable. .. GENERATED FROM PYTHON SOURCE LINES 257-260 .. code-block:: default endbuild = time.time() .. GENERATED FROM PYTHON SOURCE LINES 261-262 Simulation of the network. .. GENERATED FROM PYTHON SOURCE LINES 262-267 .. code-block:: default print("Simulating") nest.Simulate(simtime) .. GENERATED FROM PYTHON SOURCE LINES 268-269 Storage of the time point after the simulation of the network in a variable. .. GENERATED FROM PYTHON SOURCE LINES 269-272 .. code-block:: default endsimulate = time.time() .. GENERATED FROM PYTHON SOURCE LINES 273-275 Reading out the total number of spikes received from the spike recorder connected to the excitatory population and the inhibitory population. .. GENERATED FROM PYTHON SOURCE LINES 275-279 .. code-block:: default events_ex = espikes.n_events events_in = ispikes.n_events .. GENERATED FROM PYTHON SOURCE LINES 280-284 Calculation of the average firing rate of the excitatory and the inhibitory neurons by dividing the total number of recorded spikes by the number of neurons recorded from and the simulation time. The multiplication by 1000.0 converts the unit 1/ms to 1/s=Hz. .. GENERATED FROM PYTHON SOURCE LINES 284-288 .. code-block:: default rate_ex = events_ex / simtime * 1000.0 / N_rec rate_in = events_in / simtime * 1000.0 / N_rec .. GENERATED FROM PYTHON SOURCE LINES 289-292 Reading out the number of connections established using the excitatory and inhibitory synapse model. The numbers are summed up resulting in the total number of synapses. .. GENERATED FROM PYTHON SOURCE LINES 292-297 .. code-block:: default num_synapses_ex = nest.GetDefaults("excitatory")["num_connections"] num_synapses_in = nest.GetDefaults("inhibitory")["num_connections"] num_synapses = num_synapses_ex + num_synapses_in .. GENERATED FROM PYTHON SOURCE LINES 298-300 Establishing the time it took to build and simulate the network by taking the difference of the pre-defined time variables. .. GENERATED FROM PYTHON SOURCE LINES 300-304 .. code-block:: default build_time = endbuild - startbuild sim_time = endsimulate - endbuild .. GENERATED FROM PYTHON SOURCE LINES 305-306 Printing the network properties, firing rates and building times. .. GENERATED FROM PYTHON SOURCE LINES 306-317 .. code-block:: default print("Brunel network simulation (Python)") print(f"Number of neurons : {N_neurons}") print(f"Number of synapses: {num_synapses}") print(f" Excitatory : {num_synapses_ex}") print(f" Inhibitory : {num_synapses_in}") print(f"Excitatory rate : {rate_ex:.2f} Hz") print(f"Inhibitory rate : {rate_in:.2f} Hz") print(f"Building time : {build_time:.2f} s") print(f"Simulation time : {sim_time:.2f} s") .. GENERATED FROM PYTHON SOURCE LINES 318-319 Plot a raster of the excitatory neurons and a histogram. .. GENERATED FROM PYTHON SOURCE LINES 319-322 .. code-block:: default nest.raster_plot.from_device(espikes, 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_brunel_alpha_nest.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: brunel_alpha_nest.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: brunel_alpha_nest.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_