Zhu Weiwei
Business School, University of Shanghai for Science and Technology, Shanghai, 200093, China.
Sci Rep. 2025 Aug 24;15(1):31137. doi: 10.1038/s41598-025-16369-8.
Rumor spreading has been posing a significant threat to maintain the normal social order. In this paper, we propose a ISDR rumor propagation model on scale-free networks that considers fractional-order and refutation mechanism. we acquire basic reproduction number [Formula: see text] based on the rumor equilibrium point [Formula: see text], which thoroughly characterizes the dynamics of rumor propagation. we have demonstrated that when [Formula: see text], the rumor-free equilibrium point is globally asymptotically stable; when [Formula: see text], the rumor equilibrium point is globally asymptotically stable. Numerical simulations are provided to illustrate the main theoretical results. By analyzing the existence and uniqueness of the equilibrium solution, we demonstrate the superiority of fractional-order dynamics and refutation mechanism in the rumor propagation model. Our findings are crucial for understanding the impact of network structure on the dynamics of fractional-order systems.
谣言传播对维持正常社会秩序构成了重大威胁。在本文中，我们提出了一种基于无标度网络的ISDR谣言传播模型，该模型考虑了分数阶和反驳机制。我们基于谣言平衡点[公式：见原文]获得了基本再生数[公式：见原文]，它全面刻画了谣言传播的动态特性。我们证明了，当[公式：见原文]时，无谣言平衡点是全局渐近稳定的；当[公式：见原文]时，谣言平衡点是全局渐近稳定的。提供了数值模拟以说明主要理论结果。通过分析平衡解的存在性和唯一性，我们证明了分数阶动力学和反驳机制在谣言传播模型中的优越性。我们的研究结果对于理解网络结构对分数阶系统动态特性的影响至关重要。
