Self-organized network evolution coupled to extremal dynamics

TL;DR

This paper investigates how the co-evolution of network topology and dynamics, modeled through a coupled Bak-Sneppen and fitness network process, leads to self-organized critical states with power-law behaviors.

Contribution

It introduces a novel coupled model of network evolution and extremal dynamics, revealing self-organization into complex states with emergent power-law properties.

Findings

System self-organizes into a non-trivial state

Power-law decay in dynamical and topological quantities

Feedback mechanisms influence network correlation and percolation

Abstract

The interplay between topology and dynamics in complex networks is a fundamental but widely unexplored problem. Here, we study this phenomenon on a prototype model in which the network is shaped by a dynamical variable. We couple the dynamics of the Bak-Sneppen evolution model with the rules of the so-called fitness network model for establishing the topology of a network; each vertex is assigned a fitness, and the vertex with minimum fitness and its neighbours are updated in each iteration. At the same time, the links between the updated vertices and all other vertices are drawn anew with a fitness-dependent connection probability. We show analytically and numerically that the system self-organizes to a non-trivial state that differs from what is obtained when the two processes are decoupled. A power-law decay of dynamical and topological quantities above a threshold emerges spontaneously, as well as a feedback between different dynamical regimes and the underlying correlation and percolation properties of the network.