Jansen Rit - oscillations as a function of time constants

[Phillip Johnston]

Hi TVBers,

I’m trying to roughly reproduce the results of David & Friston (2003; Fig. 4) and Spiegler et al. (2010; Fig. 7) with the Jansen Rit model, specifically the rhythms generated by a single node as a function of the dendritic time constants. Using the parameters from David & Friston (2003) (but no noise) I get this:

It seems that no oscillations are produced when the inhibitory time constant is roughly equal to or less than the excitatory time constant. If I'm interpreting D&F correctly, they add noise to the input of the excitatory subpopulation, which I'm not sure how to do (if possible). But even without noise, I would expect to see oscillations as long as tau_i > 0.2*tau_e, if I'm interpreting Spiegler et al 2010 correctly.

I'm using the parameters from Table 1 in David and Friston and scaling the synaptic gains (A and B) to the time constants in the same way they did. The only parameter I'm confused about is nu_max and how it maps onto e0 (I just used the default value in TVB).

It's not imperative that I reproduce these results exactly - I'm just hoping to get a better understanding of how this model works and why my results don't agree with the literature.

Any insight much appreciated!

Phil

[Phillip Johnston]

Figures didn't seem to upload properly. I've attached them here:

[WOODMAN Michael]

Hi Phillip,

 

We have mostly verified the TVB version corresponds to the original JR 1995 paper, and not these more recent results, which require pencil and paper work to check the equations are the same before considering parameters.

 

But, as a quick guess seeing the figures, there is likely some other parameter which is different here, because those two papers show oscillations for t_e > t_i, which is not the case in TVB by default as you show.  It should be straightforward to do a stability analysis in that region to understand which terms stabilize the fixed point in the TVB/JR1995 version and not in the DF & Spiegler versions.  We don’t yet have this automated in TVB, though it could be done with e.g. sympy; so this is, as they say, an exercise left to the reader.  

 

 

Cheers,

Marmaduke

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