Synchronization in Networks of Neural Mass Model Populations with Discrete Couplings

The problem of synchronization in networks of neural mass model populations with discrete couplings is consid-ered. The considered network is hybrid one, therefore Mikheev approach is applied to transform it to the network with time-varying delayed couplings. Thus the problem of hybrid network synchronization is reduced to the studying of synchronization in networks with delayed couplings, which was previously solved by analytical means. It is showed that the Laplace matrix spectrum and maximum sampling interval are defining for networks dynamics. The dynamics of 5 neural mass model populations with discrete couplings was simulated for 3 different situations. The first case deal with the asymptotic synchronization, when both maximum eigenvalue of Laplacian and maximum sampling interval are small enough. The second case is about
$\varepsilon$
-synchronization, which is achieved for small enough maximum eigenvalue of Laplacian and big sampling intervals. And the last case is desynchronization of oscillations, which has been observed for big values of Laplacian eigenvalues and sampling intervals.