Network of linear rate neuronsΒΆ

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This script simulates an excitatory and an inhibitory population of lin_rate_ipn neurons with delayed excitatory and instantaneous inhibitory connections. The rate of all neurons is recorded using a multimeter. The resulting rate for one excitatory and one inhibitory neuron is plotted.

import matplotlib.pyplot as plt
import nest
import numpy

Assigning the simulation parameters to variables.

dt = 0.1  # the resolution in ms
T = 100.0  # Simulation time in ms

Definition of the number of neurons

order = 50
NE = int(4 * order)  # number of excitatory neurons
NI = int(1 * order)  # number of inhibitory neurons
N = int(NE + NI)  # total number of neurons

Definition of the connections

d_e = 5.0  # delay of excitatory connections in ms
g = 5.0  # ratio inhibitory weight/excitatory weight
epsilon = 0.1  # connection probability
w = 0.1 / numpy.sqrt(N)  # excitatory connection strength

KE = int(epsilon * NE)  # number of excitatory synapses per neuron (outdegree)
KI = int(epsilon * NI)  # number of inhibitory synapses per neuron (outdegree)
K_tot = int(KI + KE)  # total number of synapses per neuron
connection_rule = "fixed_outdegree"  # connection rule

Definition of the neuron model and its neuron parameters

neuron_model = "lin_rate_ipn"  # neuron model
neuron_params = {
    "linear_summation": True,
    # type of non-linearity (not affecting linear rate models)
    "tau": 10.0,
    # time constant of neuronal dynamics in ms
    "mu": 2.0,
    # mean input
    "sigma": 5.0
    # noise parameter

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.

nest.resolution = dt
nest.use_wfr = False
nest.print_time = True
nest.overwrite_files = True

print("Building network")

Creation of the nodes using Create.

n_e = nest.Create(neuron_model, NE, neuron_params)
n_i = nest.Create(neuron_model, NI, neuron_params)

To record from the rate neurons a multimeter is created and the parameter record_from is set to rate as well as the recording interval to dt

mm = nest.Create("multimeter", params={"record_from": ["rate"], "interval": dt})

Specify synapse and connection dictionaries: Connections originating from excitatory neurons are associated with a delay d (rate_connection_delayed). Connections originating from inhibitory neurons are not associated with a delay (rate_connection_instantaneous).

syn_e = {"weight": w, "delay": d_e, "synapse_model": "rate_connection_delayed"}
syn_i = {"weight": -g * w, "synapse_model": "rate_connection_instantaneous"}
conn_e = {"rule": connection_rule, "outdegree": KE}
conn_i = {"rule": connection_rule, "outdegree": KI}

Connect rate units

nest.Connect(n_e, n_e, conn_e, syn_e)
nest.Connect(n_i, n_i, conn_i, syn_i)
nest.Connect(n_e, n_i, conn_i, syn_e)
nest.Connect(n_i, n_e, conn_e, syn_i)

Connect recording device to rate units

nest.Connect(mm, n_e + n_i)

Simulate the network


Plot rates of one excitatory and one inhibitory neuron

data =
senders = data["senders"]
rate = data["rate"]
times = data["times"]

ne_0_id = n_e[0].global_id
ni_0_id = n_i[0].global_id
where_sender_is_ne_0 = numpy.where(senders == ne_0_id)
where_sender_is_ni_0 = numpy.where(senders == ni_0_id)

rate_ex = rate[where_sender_is_ne_0]
rate_in = rate[where_sender_is_ni_0]
times = times[where_sender_is_ne_0]

plt.plot(times, rate_ex, label="excitatory")
plt.plot(times, rate_in, label="inhibitory")
plt.xlabel("time (ms)")
plt.ylabel("rate (a.u.)")

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