Ring attractor model

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1

Hey everyone,

I’ve just started using brian, and I’m loving it so far, thanks for developing this great software (and documenting it so well).

I’m trying to implement a network of two populations which behaves as a ring attractor as done in this and this paper.

I have implemented a network with two populations and synapses connecting them etc, but currently I have simple LIF neurons, instead of “conductance-based synaptic transmission” ones they have.

dv/dt = (ta(t, i) - v) / tau

is the equation I’m currently using (ta is a TimedArray of inputs), but in the papers they have;

\begin{aligned} C_{m} \dot{V}_{i}(t) &=-I_{i}^{L}(t)-I_{i}^{\mathrm{Ext}}(t)-I_{i}^{\mathrm{I}}(t)-I_{i}^{\mathrm{E}}(t) \\ I_{i}^{P} &=g_{P} s_{i}^{P}\left(V_{i}(t), t\right)\left(V_{i}(t)-V_{P}\right) \end{aligned}

with P \in \{L, Ext, E, I \} and L=leaky, Ext=external inputs population, E/I=excitatory/inhibitory, g^P are gating variables, s^P are synaptic scale variables and V_P are reverse potentials.

I could implement this myself, but I was hoping someone had similar models that I could use as a starting point to save time.
Also, if anyone has an example of a ring attractor network implemented in brian2 that would be awesome and I’d love to have a look at it.

Thanks,
Federico

2

Hi Federico. I replied on gitter before reading your post here, but I think the second paper is the one that is used as an exercise in the Neuronal Dynamics book by Gerstner et al.: 12. Spatial Working Memory (Compte et. al.) — Neuronaldynamics Exercises 0.3.7.dev0+gb16ea71.d20210104 documentation The actual Brian code is a bit buried in code specific to their teaching package neurodynex that they wrap around it, but it still looks fairly useable on its own: neurodynex3/wm_model.py at master · apester/neurodynex3 · GitHub A simplified version of this code would be a welcomed contribution to our docs :slight_smile: !

3

That’s great, super useful. Thank you very much, I will dig into it and will get back if I get a minimal working example.