Complex Network Modeling With Power-Law Activating Patterns and Its 
Evolutionary Dynamics

Zeng, Ziyan; Feng, Minyu; Liu, Pengfei; Kurths, Jürgen

doi:10.1109/TSMC.2025.3525465

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Complex Network Modeling With Power-Law Activating Patterns and Its Evolutionary Dynamics

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Zeng, Ziyan
External Organizations;

Feng, Minyu
External Organizations;

Liu, Pengfei
External Organizations;

/persons/resource/Juergen.Kurths

Kurths, Jürgen
Potsdam Institute for Climate Impact Research;

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https://doi.org/10.48550/arXiv.2502.09768
(Preprint)

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Citation

Zeng, Z., Feng, M., Liu, P., Kurths, J. (2025): Complex Network Modeling With Power-Law Activating Patterns and Its Evolutionary Dynamics. - IEEE Transactions on Systems, Man, and Cybernetics: Systems, 55, 4, 2546-2559.
https://doi.org/10.1109/TSMC.2025.3525465

Cite as: https://publications.pik-potsdam.de/pubman/item/item_32071

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 article, 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.