Collective dynamics in sparse networks

TL;DR

This paper investigates how sparse networks with limited connectivity can sustain complex collective dynamics, demonstrating that even with few connections, large networks exhibit nontrivial behavior while maintaining extensive microscopic activity.

Contribution

It reveals that sparse networks with finite connectivity can support collective chaos and nontrivial dynamics, challenging assumptions about the necessity of dense connectivity.

Findings

Finite connectivity sustains collective dynamics in large networks.

Microscopic dynamics remain extensive despite non-additivity.

Sparse networks can exhibit complex behavior similar to dense ones.

Abstract

The microscopic and macroscopic dynamics of random networks is investigated in the strong-dilution limit (i.e. for sparse networks). By simulating chaotic maps, Stuart-Landau oscillators, and leaky integrate-and-fire neurons, we show that a finite connectivity (of the order of a few tens) is able to sustain a nontrivial collective dynamics even in the thermodynamic limit. Although the network structure implies a non-additive dynamics, the microscopic evolution is extensive (i.e. the number of active degrees of freedom is proportional to the number of network elements).