Complex Network Modelling with Power-law Activating Patterns and Its Evolutionary Dynamics

TL;DR

This paper introduces a complex network model with power-law activation patterns and explores its evolutionary dynamics, revealing new insights into social physics and strategy stability in time-evolving networks.

Contribution

It presents a novel stochastic model with power-law activation, analyzes its stationary distribution, and studies evolutionary game dynamics without mutation.

Findings

Homogeneous stationary distribution of activated sizes

Critical cooperation conditions for prisoner's dilemma

Insights into strategy absorbability in networks

Abstract

Complex network theory provides a unifying framework for the study of structured dynamic systems. The current literature emphasizes a widely reported phenomenon of intermittent interaction among network vertices. In this paper, we introduce a complex network model that considers the stochastic switching of individuals between activated and quiescent states at power-law rates and the corresponding evolutionary dynamics. By using the Markov chain and renewal theory, we discover a homogeneous stationary distribution of activated sizes in the network with power-law activating patterns and infer some statistical characteristics. To better understand the effect of power-law activating patterns, we study the two-person-two-strategy evolutionary game dynamics, demonstrate the absorbability of strategies, and obtain the critical cooperation conditions for prisoner's dilemmas in homogeneous networks without mutation. The evolutionary dynamics in real networks are also discussed. Our results provide a new perspective to analyze and understand social physics in time-evolving network systems.