Coevolution of dynamical states and interactions in dynamic networks

TL;DR

This paper investigates how the states of elements and their interaction networks coevolve, demonstrating that adaptive interactions promote cooperation and hierarchical, small-world network structures with critical nodes influencing global stability.

Contribution

It introduces a coupled model of state dynamics and adaptive network evolution, revealing how cooperation and hierarchical structures emerge from local interaction rules.

Findings

Adaptive networks facilitate cooperation.

Hierarchical, small-world network structures form.

Highly connected nodes influence network stability.

Abstract

We explore the coupled dynamics of the internal states of a set of interacting elements and the network of interactions among them. Interactions are modeled by a spatial game and the network of interaction links evolves adapting to the outcome of the game. As an example we consider a model of cooperation, where the adaptation is shown to facilitate the formation of a hierarchical interaction network that sustains a highly cooperative stationary state. The resulting network has the characteristics of a small world network when a mechanism of local neighbor selection is introduced in the adaptive network dynamics. The highly connected nodes in the hierarchical structure of the network play a leading role in the stability of the network. Perturbations acting on the state of these special nodes trigger global avalanches leading to complete network reorganization.