A decaying factor accounts for contained activity in neuronal networks with no need of hierarchical or modular organization

TL;DR

This paper introduces a decay-based dynamic model that sustains contained activity in neuronal and social networks without requiring hierarchical or modular structures, challenging previous models that relied on inhibition or modularity.

Contribution

The study presents a novel decay-inspired activity mechanism that maintains activity containment without the need for network modularity or inhibition processes.

Findings

Sustained activity observed across various network types with decay dynamics.

Modularity is unnecessary for activity containment when using decay-based models.

Persistent restrained activity can occur without specific topological structures.

Abstract

The mechanisms responsible for contention of activity in systems represented by networks are crucial in various phenomena, as in diseases such as epilepsy that affects the neuronal networks, and for information dissemination in social networks. The first models to account for contained activity included triggering and inhibition processes, but they cannot be applied to social networks where inhibition is clearly absent. A recent model showed that contained activity can be achieved with no need of inhibition processes provided that the network is subdivided in modules (communities). In this paper, we introduce a new concept inspired in the Hebbian theory through which activity contention is reached by incorporating a dynamics based on a decaying activity in a random walk mechanism preferential to the node activity. Upon selecting the decay coefficient within a proper range, we observed sustained activity in all the networks tested, viz. random, Barabasi-Albert and geographical networks. The generality of this finding was confirmed by showing that modularity is no longer needed if the dynamics based on the integrate-and-fire dynamics incorporated the decay factor. Taken together, these results provide a proof of principle that persistent, restrained network activation might occur in the absence of any particular topological structure. This may be the reason why neuronal activity does not outspread to the entire neuronal network, even when no special topological organization exists.