Time scale competition leading to fragmentation and recombination transitions in the coevolution of network and states

TL;DR

This paper investigates how the interplay of network restructuring and node state changes leads to phase transitions like fragmentation and recombination, driven by emergent time scales in co-evolving systems.

Contribution

It introduces a model capturing the co-evolution of network topology and node states, revealing two distinct phase transitions governed by emergent time scales.

Findings

Identifies a recombination transition separating frozen and active network states.

Discovers a fragmentation transition as an anomalous order-disorder phase change.

Provides analytical explanation for the nature of these transitions.

Abstract

We study the co-evolution of network structure and node states in a model of multiple state interacting agents. The system displays two transitions, network recombination and fragmentation, governed by time scales that emerge from the dynamics. The recombination transition separates a frozen configuration, composed by disconnected network components whose agents share the same state, from an active configuration, with a fraction of links that are continuously being rewired. The nature of this transition is explained analytically as the maximum of a characteristic time. The fragmentation transition, that appears between two absorbing frozen phases, is an anomalous order-disorder transition, governed by a crossover between the time scales that control the structure and state dynamics.