Criticality of spreading dynamics in hierarchical cluster networks without inhibition

TL;DR

This study shows that hierarchical cluster networks can sustain stable, scalable neural activity patterns over a broader parameter range than random or small-world networks, highlighting their potential role in cortical function.

Contribution

It demonstrates that hierarchical clustering in neural networks enhances the stability and diversity of activation patterns without inhibition, unlike random networks.

Findings

Hierarchical cluster networks support persistent activation.

Critical activation range is larger in hierarchical networks.

Random networks do not sustain stable activity.

Abstract

An essential requirement for the representation of functional patterns in complex neural networks, such as the mammalian cerebral cortex, is the existence of stable network activations within a limited critical range. In this range, the activity of neural populations in the network persists between the extremes of quickly dying out, or activating the whole network. The nerve fiber network of the mammalian cerebral cortex possesses a modular organization extending across several levels of organization. Using a basic spreading model without inhibition, we investigated how functional activations of nodes propagate through such a hierarchically clustered network. The simulations demonstrated that persistent and scalable activation could be produced in clustered networks, but not in random networks of the same size. Moreover, the parameter range yielding critical activations was substantially larger in hierarchical cluster networks than in small-world networks of the same size. These findings indicate that a hierarchical cluster architecture may provide the structural basis for the stable and diverse functional patterns observed in cortical networks.