Dynamic analysis of a fractional-order rumor spreading model with double time delay under higher-order interactions
Articles
Yang Xia
Xinjiang University
Haijun Jiang
Xinjiang University
Jiarong Li
Xinjiang University
Shuzhen Yu
Xinjiang Normal University
Published 2025-06-27
https://doi.org/10.15388/namc.2025.30.42681
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Keywords

rumor spreading
fractional-order model
higher-order interactions
Hopf bifurcation

How to Cite

Xia, Y. (2025) “Dynamic analysis of a fractional-order rumor spreading model with double time delay under higher-order interactions”, Nonlinear Analysis: Modelling and Control, 30(4), pp. 747–770. doi:10.15388/namc.2025.30.42681.

Abstract

Although traditional network-based models also explore higher-order interactions, they are limited in capturing the complex impacts of multibody interactions, making it difficult to characterize the reinforcement effect in rumor propagation. With this in mind, firstly, this study introduces the simplicial complexes, a higher-order mathematical tool, to model rumor propagation. Secondly, the fractional-order derivatives are employed to more accurately capture the memory effect and anomalous diffusion phenomenon in the rumor propagation process under higher-order interactions. Then propagation thresholds and the existence of model solutions are investigated. Moreover, the proposed model exhibits bistability, and the Hopf bifurcation is analysed by choosing time delay as the threshold. Numerical simulations suggest that fractional-order rumor spreading models with higher-order interactions are more consistent with actual data than network-based models and integer-order models.

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