Fig. 26. Coupled neural masses at locations Xi (upper figure) are coupled via local and global pathways. The large scale network dynamics arises from the interactions of the neural mass actions y(Xi, t) at locations Xi. The computation of the complete network dynamics based upon the neural state vector Z(t) (lower figure) and neural connectivity (red squares) should ideally yield the same network dynamics as computed from y(x,t)

action ^(x,t+T) at a future time point t+T as the simulation based upon the complete network dynamics using the microscopic neuronal activity Z(x,t).

In the latter approach, once Z(x,t+T) is computed, it has to be mapped upon to the neural mass action, $ : Z(x,t + T) ^ x,t + T) to allow for a comparison between the two approaches. The inverse mapping : ^(x, t + T) ^ Z(x, t + T) generally does not exist.

4.2 Mean Field Reduction of Neuronal Activity

The mean field approximation is well-known from statistical physics (see for instance Gardiner 2004). Though its basic assumptions are mostly not rigorously justified, it often provides an astonishingly good qualitative insight into the description of many models. Hence the use of mean field approaches has

large scale network dynamics

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