Persistent Imbalance in Open Networks with Coevolutionary dynamics

TL;DR

This paper studies how external influences cause persistent imbalance in open networks with coevolutionary dynamics, revealing a transition temperature affecting network stability.

Contribution

It introduces a mean-field framework to analyze the impact of external influences on network balance and identifies a transition temperature with persistent imbalance states.

Findings

Below the transition temperature, the independent network reaches structural balance.

The open network remains in a sustained imbalance phase due to external influences.

Numerical simulations confirm the analytical predictions of the transition and imbalance states.

Abstract

Societies are quintessential open systems, shaped by internal dynamics as well as external influences. The question is how these external influences alter the collective behavior and network dynamics. To answer this, we investigate coevolutionary balance dynamics in a system of independent and open networks. Here, the system consists of two interacting networks with directed (asymmetric) coupling: an independent network evolving autonomously and an open (dependent) network whose dynamics are influenced by the former. Using a mean-field framework, we demonstrate a transition temperature: below the transition temperature, the independent network reaches a state of structural balance, while the open network is destabilized by persistent imbalance states and enters a sustained imbalance phase. This coupling also induces a measurable upward shift in the transition temperature. Direct numerical simulations robustly confirm these analytical predictions.