Stability of random brain networks with excitatory and inhibitory connections

Stability of randomly connected networks of neural populations with randomly distributed excitatory and inhibitory connections is investigated using a simplified physiologically-based model of brain electrical activity. Connections within a random network are randomly assigned to be excitatory or inhibitory, and the strengths of excitatory and inhibitory connections have two distinct distributions. Stability is shown to depend on the size of the network, the connection probability, and the mean and variance of the network's distribution of connection strengths, thus constraining these quantities. Networks with a nonzero variance for their excitatory and inhibitory strengths are less likely to be stable than networks with zero variance. The effect of changes in overall network activity on an individual population is also investigated. The maximum excitatory and inhibitory inputs into a population are constrained by stability and occur when the magnitudes of the mean excitatory and inhibitory connection strengths are equal and the proportion of connections that are inhibitory has a fixed value less than 0.5. Results consistent with experimentally determined brain networks.

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