【作者】 陈晓楠；

【导师】 张素霞；

【作者基本信息】 西安理工大学 ， 数学， 2023， 硕士

【摘要】 随着互联网时代的快速发展,信息在短时间内得以快速传播.通过研究信息传播模型可以揭示信息传播机制,为促进正面信息快速传播、负面信息的及时控制等提供理论参考.本文考虑热搜效应,建立了 SICR谣言传播模型和SEIR信息传播模型,借助理论分析、数值模拟和案例应用对其传播规律进行研究,主要内容如下:首先,考虑到反谣言行为、热搜效应在网络谣言传播过程中的影响,建立了具有反谣言行为的SICR网络谣言传播模型.通过再生矩阵定义了谣言传播与否的相关阈值,利用动力学理论及方法对不同热搜效应影响下模型的各平衡点的稳定性进行分析与讨论,数值模拟验证了理论结果,同时对模型中重要参数的敏感性进行分析,结果显示增加反谣言行为或提高用户的谣言判断能力,可以有效地抑制谣言的传播.最后,基于实际的推特数据集验证了所提模型的合理性;为了刻画较为真实的推特网,基于BA网络也对该数据进行了拟合,结果表明,具有复杂网络特性的谣言传播模型拟合效果更优.其次,依据在线社交网络的结构特性,基于复杂网络考虑热搜效应建立了 SEIR信息传播模型,分别在均匀网络和异构网络中进行了动力学分析.在均匀网络中,对不同热搜效应影响下模型各平衡点的存在性和稳定性进行讨论与分析.在异构网络中,若不考虑热搜效应,其动力学性态完全由基本传播数所决定;具有热搜效应时不存在无信息平衡点,而一定阈值条件下存在唯一的信息传播平衡点.基于规则网络、WS网络、ER网络、BA网络对SEIR模型进行了数值实验,结果显示不同网络结构对可传播节点的峰值和到达峰值时间都有一定影响;同时对模型重要参数关于基本传播数和可传播节点的敏感性进行了分析.进一步地,应用微博中所采集关于信息传播的两例数据,基于BA网络模拟了信息传播的动态行为,从而验证了该模型的有效性.最后,鉴于同一信息在不同在线社交网络平台上相互渗透,考虑对双层网络中信息传播的动态行为进行建模与分析来研究所提SICR模型和SEIR模型的传播机制.在一定传播规则下,基于ER-ER、BA-BA、ER-BA三种双层耦合网络分别进行数值实验.在不同耦合网络结构下,考虑热搜效应、传谣率、反谣率、传播系数等关键参数对模型各变量的影响,并对数值结果进行了对比与分析.更多还原

【Abstract】 With the rapid development of the Internet era,information can be spread rapidly in a short period of time.By studying information dissemination models,we can reveal the mechanism of information dissemination and provide theoretical reference to promote the rapid dissemination of positive information and timely control of negative information.In this thesis,a SICR rumour propagation model and a SEIR information propagation model are developed,and their propagation patterns are studied by means of theoretical analysis,numerical simulation and case applications,the main contents are as follows:Firstly,considering the influence of anti-rumor behavior and hot search effect on the spread process of online rumors,the SICR network rumor propagation model with anti-rumor behavior was established.Through the regeneration matrix,the relevant threshold of rumor propagation is defined,the stability of each equilibrium point of the model under the influence of different hot search effects is analyzed and discussed by kinetic theory and method,and the numerical simulation verifies the theoretical results,and analyzes the sensitivity of important parameters in the model,which shows that increasing anti-rumor behavior or improving users’ rumor judgment ability can effectively inhibit the spread of rumors.Finally,based on the actual Twitter dataset,the rationality of the proposed model is verified.In order to depict a more realistic Twitter network,the data are also fitted based on the BA network,and the results show that the rumor propagation model with complex network characteristics has a better fitting effect.Secondly,according to the structural characteristics of online social networks,the SEIR information propagation model was established based on the hot search effect of complex networks,and dynamic analysis was carried out in uniform networks and heterogeneous networks.In the uniform network,the existence and stability of each equilibrium point of the model under the influence of different hot search effects are discussed and analyzed.In heterogeneous networks,if the hot search effect is not considered,its dynamic behavior is completely determined by the basic propagation number.When it has the hot search effect,there is no information balance point,but there is a unique information propagation balance point under certain threshold conditions.Based on the regular network,WS network,ER network and BA network,numerical experiments were carried out on the SEIR model,and the results showed that different network structures had a certain impact on the peak and peak time of propagable nodes.At the same time,the sensitivity of the important parameters of the model on the basic propagation number and propagable nodes is analyzed.Furthermore,using the two case data on information dissemination collected in Weibo,the dynamic behavior of information dissemination is simulated based on BA network,which verifies the effectiveness of the model.Finally,in view of the mutual penetration of the same information on different online social network platforms,the dynamic behavior of information propagation in the two-tier network is considered to study the propagation mechanism of the proposed SICR model and the SEIR model.Under certain propagation rules,numerical experiments were carried out based on three twolayer coupling networks:ER-ER,BA-BA,and ER-BA.Under different coupled network structures,the influence of key parameters such as hot search effect,rumor rate,anti-rumor rate and propagation coefficient on the variables of the model is considered,and the numerical results are compared and analyzed.更多还原