发表机构
School of Computing, Union University; Center for Exact and Natural Sciences, Federal University of Pernambuco（联合大学计算机学院; 伯南布哥联邦大学精确与自然科学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究在一维整数格上分析谣言传播模型，发现遗忘机制导致经典Maki-Thompson模型与变体间出现相变，并确定了临界传播速率，揭示了遗忘能创造持续信息传播的新动态。
AI 中文摘要
我们研究一维整数格上的谣言传播模型，特别关注遗忘机制对谣言长期行为的影响。我们考虑了经典Maki-Thompson模型的空间版本，以及两个包含遗忘的变体。每个模型都被表述为一个相互作用粒子系统，并通过相邻个体之间的局部相互作用来描述信息的传播。我们的结果表明，遗忘的引入从根本上改变了过程的行为。在经典Maki-Thompson模型中，谣言最终灭绝，而两个带有遗忘的模型则表现出灭绝与存活之间的非平凡相变。更确切地说，我们建立了临界传播速率的存在性，这些速率将谣言几乎必然消亡的机制与以正概率存活的机制区分开来。我们还研究了这些临界阈值对抑制速率的依赖性。结合严格论证与数值模拟，我们证明了相变的存在性，获得了临界值的估计，并探讨了相应的相图。这些发现表明，遗忘尽管作为一种移除传播者的机制，却能通过创造持续信息传播的机制，从性质上改变谣言传播的动态。我们的工作为空间谣言模型的临界行为提供了新的见解，并提出了若干未来研究的问题。
英文摘要
We study rumor-spreading models on the one-dimensional integer lattice, with particular emphasis on the effect of forgetting mechanisms on the long-term behavior of the rumor. We consider the spatial version of the classical Maki--Thompson model together with two variants that incorporate forgetting. Each model is formulated as an interacting particle system and describes the propagation of information through local interactions between neighboring individuals. Our results show that the introduction of forgetting fundamentally changes the behavior of the process. In the classical Maki--Thompson model, the rumor becomes extinct, whereas the two models with forgetting exhibit nontrivial phase transitions between extinction and survival. More precisely, we establish the existence of critical transmission rates that separate regimes in which the rumor dies out almost surely from regimes in which it survives with positive probability. We also investigate the dependence of these critical thresholds on the stifling rate. Combining rigorous arguments with numerical simulations, we prove the existence of the phase transitions, obtain estimates for the critical values, and explore the corresponding phase diagrams. These findings show that forgetting, despite acting as a mechanism that removes spreaders, can qualitatively alter the dynamics of rumor propagation by creating regimes of sustained information spread. Our work provides new insight into the critical behavior of spatial rumor models and raises several questions for future research.
CommentsAccepted for publication at Chaos, Solitons & Fractals
