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# Testing the adapting exponential integrate and fire model in NEST (Brette and Gerstner Fig 2C)¶

This example tests the adaptive integrate and fire model (AdEx) according to Brette and Gerstner 1 reproduces Figure 2C of the paper. Note that Brette and Gerstner give the value for b in nA. To be consistent with the other parameters in the equations, b must be converted to pA (pico Ampere).

## References¶

1

Brette R and Gerstner W (2005). Adaptive exponential integrate-and-fire model as an effective description of neuronal activity J. Neurophysiology. https://doi.org/10.1152/jn.00686.2005

```import nest
import nest.voltage_trace
import matplotlib.pyplot as plt

nest.ResetKernel()
```

First we make sure that the resolution of the simulation is 0.1 ms. This is important, since the slop of the action potential is very steep.

```nest.resolution = 0.1
neuron = nest.Create("aeif_cond_alpha")
```

a and b are parameters of the adex model. Their values come from the publication.

```neuron.set(a=4.0, b=80.5)
```

Next we define the stimulus protocol. There are two DC generators, producing stimulus currents during two time-intervals.

```dc = nest.Create("dc_generator", 2)
dc.set(amplitude=[500.0, 800.0], start=[0.0, 500.0], stop=[200.0, 1000.0])
```

We connect the DC generators.

```nest.Connect(dc, neuron, 'all_to_all')
```

And add a `voltmeter` to sample the membrane potentials from the neuron in intervals of 0.1 ms.

```voltmeter = nest.Create("voltmeter", params={'interval': 0.1})
nest.Connect(voltmeter, neuron)
```

Finally, we simulate for 1000 ms and plot a voltage trace to produce the figure.

```nest.Simulate(1000.0)

nest.voltage_trace.from_device(voltmeter)
plt.axis([0, 1000, -80, -20])
plt.show()
```

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

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