What (open) software there are for simulating behaviour of human (cortical) neurons?
No, not in the neuronal level. Because IMHO this is an ill-posed problem.


EEG combined with MRI won't have the resolution to do solve the inverse problem of neuronal network simulation. There are at least hundreds of thousands of neurons that would be involved in your specific behavioral task, and you have at most a few hundred electrodes. You'll have to make grossly simplifying assumptions about how the brain works to start any inference. You might learn something, but the claim would be somewhat weak.

Personally, I wouldn't work with EEG if you are interested in the mechanistic details of the brain. It is a very useful signal for some cognitive investigations (especially for humans), but the current technology lacks the spatial resolution.


Yes, in the coarse scale network level. (response to @sets' feedback)


If you don't care about micro-scale dynamics of the neural network, and want to model some population-wide activation that changes EEG, as @sets commented, there are various source localization &amp; dynamical system models that you can use. I am not an expert on this, so see @sets' answer, or hopefully someone else will answer in detail.