  The synchronization of different brain regions is widely observed under both
normal and pathological conditions such as epilepsy. However, the relationship
between the dynamics of these brain regions, the connectivity between them, and
the ability to synchronize remains an open question. We investigated the
problem of inter-region synchronization in networks of Wilson-Cowan/Neural
field equations with homeostatic plasticity, each of which acts as a model for
an isolated brain region. We considered arbitrary connection profiles with only
one constraint: the rows of the connection matrices are all identically
normalized. We found that these systems often synchronize to the solution
obtained from a single, self-coupled neural region. We analyze the stability of
this solution through a straightforward modification of the Master Stability
Function (MSF) approach and found that synchronized solutions lose stability
for connectivity matrices when the second largest positive eigenvalue is
sufficiently large, for values of the global coupling parameter that are not
too large. This result was numerically confirmed for ring systems and lattices
and was also robust to small amounts of heterogeneity in the homeostatic set
points in each node. Finally, we tested this result on connectomes obtained
from 196 subjects over a broad age range (4-85 years) from the Human Connectome
Project. We found that the second largest eigenvalue tended to decrease with
age, indicating an increase in synchronizability that may be related to the
increased prevalence of epilepsy with old age.
