在线社交网络信息传播预测与调控的时空动力学反应扩散模型研究

Online social network (OSNs) is an important network platform for information spreading and sharing, which has a broad application prospect. How to describe the spatio-temporal evolution mechanism of information spreading in OSNs and establish effective forecast models for information spreading as well as regulatory decision-making models has become a key scientific problem that urgently needs to be solved. This project intends to use the biodynamic modeling method for reference to establish the spatio-temporal dynamic reaction-diffusion model of information spreading in OSNs. Aiming at the evolution process of negative (positive) information spreading in OSNs, the corrective (supplementary) information reported by mainstream media is introduced. We analyze the competition (cooperation) mechanism in the process of information spreading. By the theory of reaction-diffusion equation, the stability of the disappearing state for the negative information and the threshold for the positive information equilibrium existing are analyzed; pattern structures of information spreading as well as the influence of the competition and cooperation mechanisms on information spreading process and spatial distribution are studied; the competitive (cooperative) strategy of information is proposed to decrease (increase) the spreading speed and the spatial scope of negative (positive) information. The effectiveness of the proposed spreading and regulation models is evaluated through real data sets and numerical simulation, so as to provide advanced theoretical basis and key technical support for the prediction and regulation of information spreading trend in OSNs, which has important theoretical significance and broad application prospect.

在线社交网络(OSNs)是信息传播与共享的重要网络平台，具有广泛的应用前景。如何刻画OSNs中信息传播的时空演化机理，建立有效的信息传播趋势预测和调控决策模型已成为迫切需要解决的关键科学问题。本项目拟借鉴生物动力学建模方法，建立OSNs中信息传播的时空动力学反应扩散模型；针对负(正)面信息在OSNs中传播的演化过程，引入主流媒体报道的纠正(补充)信息，探明信息传播过程中的竞争(合作)机理；采用反应扩散方程理论，分析负面信息消失态的稳定性和正面信息平衡态存在的阈值，研究信息传播的斑图结构和竞争与合作机制对信息传播过程和空间分布的影响，提出信息竞争(合作)策略来减小负面(增加正面)信息的传播速度和空间分布范围；通过真实数据集和数值仿真评估所提出的传播与调控模型的有效性，从而为OSNs中信息传播趋势预测和调控提供先进的理论基础和关键技术支撑，具有重要的理论意义和广阔的应用前景。

反应扩散模型在很大程度上反映了“扩散”和“反应”的相互作用，它能够刻画物质时空发展的演化过程，为许多实际问题的数学建模提供了条件。本项目借助反应扩散方程理论和动力学分析方法，首先研究了几类生物模型的动力学行为；然后借鉴生物动力学和反应扩散方程建模方法，分别建立了OSNs中几类信息传播的时空动力学反应扩散模型。对这些模型主要分析了信息传播的基本再生数、平衡态稳定的阈值条件，共存解的存在性、解的长时行为、关键参数对解的时空分布的影响等。所使用方法主要包括特征值理论、分歧理论、扰动理论、拓扑度理论、空间分解技术、Lyapunov函数的构造和数值模拟等。对这些模型的动力学研究为OSNs中信息传播趋势的预测和调控决策提供理论依据和关键技术支撑，同时理论分析与数值模拟的结果也丰富和发展了反应扩散方程的动力学理论与数值计算方法。