Coeovolutionary Threshold Dynamics

TL;DR

This paper introduces a threshold model for co-evolving network structure and node states, revealing a phase transition from connected to fragmented networks influenced by initial conditions, supported by theoretical and simulation results.

Contribution

It develops a generic co-evolutionary threshold model for directed networks and derives equations describing its dynamics, highlighting a phase transition dependent on initial network configuration.

Findings

System exhibits a transition from connected to fragmented phase.

Theoretical equations accurately predict the phase transition.

Computer simulations confirm the theoretical predictions.

Abstract

We present a generic threshold model for the co-evolution of the structure of a network and the state of its nodes. We focus on regular directed networks and derive equations for the evolution of the system toward its absorbing state. It is shown that the system displays a transition from a connected phase to a fragmented phase that depends on its initial configuration. Computer simulations are performed and confirm the theoretical predictions.