Robust Emergent Activity in Dynamical Networks

TL;DR

This paper investigates the evolution of complex nonlinear dynamical networks, revealing that the active subnetwork's size and connectivity are robust and independent of the overall network size, with implications for ecological systems.

Contribution

It introduces a macroscopic description of active subnetworks in dynamical networks, showing their size and degree distribution are robust and independent of total network size.

Findings

Active subnetwork size is independent of total network size.

Average degree of active nodes is unaffected by network size and connectivity.

Robustness of active subnetwork features across different network configurations.

Abstract

We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we develop a macroscopic description of the system in terms of the statistical features of the subnetwork of active nodes. We find the asymptotic characteristics of this subnetwork to be remarkably robust: the size of the active set is independent of the total number of nodes in the network, and the average degree of the active nodes is independent of both the network size and its connectivity. These results suggest that very different networks evolve to active subnetworks with the same characteristic features. This has strong implications for dynamical networks observed in the natural world, notably the existence of a characteristic range of links per species across ecological systems.