## Network of linear rate neurons

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 nest
import pylab
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. # 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
'mean': 2.0,
# mean of Gaussian white noise input
'std': 5.
# standard deviation of Gaussian white noise input
}
```

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.SetKernelStatus({"resolution": dt, "use_wfr": False,
"print_time": True,
"overwrite_files": True})
print("Building network")
```

Configuration of the neuron model using SetDefaults().

`nest.SetDefaults(neuron_model, neuron_params)`

Creation of the nodes using `Create`

.

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

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 associatated with a delay d (rate_connection_delayed). Connections originating from inhibitory neurons are not associatated with a delay (rate_connection_instantaneous).

```
syn_e = {'weight': w, 'delay': d_e, 'model': 'rate_connection_delayed'}
syn_i = {'weight': -g*w, '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 = nest.GetStatus(mm)[0]['events']
rate_ex = data['rate'][numpy.where(data['senders'] == n_e[0])]
rate_in = data['rate'][numpy.where(data['senders'] == n_i[0])]
times = data['times'][numpy.where(data['senders'] == n_e[0])]
pylab.figure()
pylab.plot(times, rate_ex, label='excitatory')
pylab.plot(times, rate_in, label='inhibitory')
pylab.xlabel('time (ms)')
pylab.ylabel('rate (a.u.)')
```