How to record xi?

Support
1

Description of problem

I added the xi variable to my neuron equation to generate noisy membrane potentials.
I would like to record the xi values as a function of time and plot it in a graph, but I failed.

If xi is not recordable, is there any other way to add a noisy current to a neuron and record the noise term?

Minimal code to reproduce problem

eqs = '''
dv/dt = (Iint-(v-v0))/tau + sigma*xi*tau**-0.5: 1 (unless refractory)
ref: second
'''
G = NeuronGroup(Nneuron, eqs, threshold='v > v_threshold', reset='v = v_reset', refractory='ref', method='Euler')
M = StateMonitor(G, ('v', 'xi'), record=True)  # record the membrane potential
run(1000*ms)
plot(M.t/ms, M.xi[0], color='black')
show()

Expected output (if relevant)

A plot with a Gaussian distributed noise as a function of time

Actual output (if relevant)

A flat line of y=0

2

Hi @cclo. I agree that this is not ideal – in particular, you should get an error message when trying to record from xi. The reason why this isn’t possible is that internally, there is no variable named xi, it is directly taken in charge as part of the numerical integration process. As an alternative, you can replace it by a variable that does the same thing manually, and which you can then record in the usual way:

eqs = '''
dv/dt = sigma*noise*tau**-0.5: 1 (unless refractory)
noise = randn()/sqrt(dt) : second**-0.5 (constant over dt)
...
'''

The value of noise might still not quite what you expect, since the values will depend on the dt that is used for the simulation. This is correct, though (see Models and neuron groups — Brian 2 2.6.0 documentation for a short explication). If you are only interested in the values of the random generator you could of course reformulate everything as, for example:

eqs = '''
dv/dt = sigma*noise/sqrt(dt)*tau**-0.5: 1 (unless refractory)
noise = randn() : 1 (constant over dt)
...
'''

You might also be interested in these comments I made in other discussions threads: