Complex Network Modelling with Power-law Activating Patterns and Its Evolutionary Dynamics
Journal:
arXiv
Published Date:
Feb 13, 2025
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.
