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Network of linear rate neuronsΒΆ
Run this example as a Jupyter notebook:
See our guide for more information and troubleshooting.
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.ResetKernel()
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
nest.Simulate(T)
Plot rates of one excitatory and one inhibitory neuron
data = mm.events
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.figure()
plt.plot(times, rate_ex, label="excitatory")
plt.plot(times, rate_in, label="inhibitory")
plt.xlabel("time (ms)")
plt.ylabel("rate (a.u.)")
plt.show()