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An essential requirement for the representation of functional patterns incomplex neural networks, such as the mammalian cerebral cortex, is theexistence of stable network activations within a limited critical range. Inthis range, the activity of neural populations in the network persists betweenthe extremes of quickly dying out, or activating the whole network. The nervefiber network of the mammalian cerebral cortex possesses a modular organizationextending across several levels of organization. Using a basic spreading modelwithout inhibition, we investigated how functional activations of nodespropagate through such a hierarchically clustered network. The simulationsdemonstrated that persistent and scalable activation could be produced inclustered networks, but not in random networks of the same size. Moreover, theparameter range yielding critical activations was substantially larger inhierarchical cluster networks than in small-world networks of the same size.These findings indicate that a hierarchical cluster architecture may providethe structural basis for the stable and diverse functional patterns observed incortical networks.

Criticality of spreading dynamics in hierarchical cluster networks without inhibition