Macroscopic description of complex adaptive networks co-evolving with dynamic node states

TL;DR

This paper develops a macroscopic framework to understand how co-evolving network structures and node states influence system sustainability, with applications in social and biological systems.

Contribution

It introduces a general macroscopic description for co-evolving networks with dynamic nodes, linking microscopic interactions to macroscopic behavior.

Findings

Interaction rate and rewiring probability affect system stability.

Derived a macroscopic model applicable to various fields.

System can sustain equilibrium under certain conditions.

Abstract

In many real-world complex systems, the time-evolution of the network's structure and the dynamic state of its nodes are closely entangled. Here, we study opinion formation and imitation on an adaptive complex network which is dependent on the individual dynamic state of each node and vice versa to model the co-evolution of renewable resources with the dynamics of harvesting agents on a social network. The adaptive voter model is coupled to a set of identical logistic growth models and we show that in such systems, the rate of interactions between nodes as well as the adaptive rewiring probability play a crucial role for the sustainability of the system's equilibrium state. We derive a macroscopic description of the system which provides a general framework to model and quantify the influence of single node dynamics on the macroscopic state of the network and is applicable to many fields of study, such as epidemic spreading or social modeling.