时滞和扩散影响下社交网络谣言传播动力学

Rumor propagation dynamics in social networks under the influence of time delay and diffusion

提出了一个考虑空间扩散与发酵期时滞的社交网络谣言传播模型,重点研究了扩散与时滞对在线社交网络中谣言时空传播的影响.首先,分析了谣言传播平衡点的存在性,并得到了基本再生数R0;其次,运用Roth-Hurwitz稳定判据分析了谣言传播平衡点的局部稳定性,并讨论了扩散诱导的Turing不稳定;最后,选取时滞为分岔参数,建立了谣言传播模型的Hopf分岔条件.数值仿真结果表明,扩散和时滞的出现都能使得谣言传播模型的稳定性发生根本性改变.本文从时间和空间两个维度扩展了传统谣言传播动力学仅考虑时间演化的局限,更加真实地模拟了谣言在现实社会中的时空传播规律,为谣言传播的治理提供了全新的角度和思路.

Rumors in social networks are often referred to as infectious diseases of the Internet,because rumors spreading in networks feature strong concealment,fast transmission speed and wide spread.With the development of mobile devices,online rumors nowadays are far more harmful than before.Rumors in social networks show completely different spatiotemporal dynamics from traditional rumor spreading dynamics.A social network rumor spreading model with considering both reaction diffusion and fermentation time delay is proposed in this paper.The effects of spatial diffusion and time delay on rumor spreading in online social networks are studied.Firstly,the existence of equilibrium point of the reaction-diffusion rumor spreading model is analyzed,and the basic regeneration number Rdisappears in social networks;when R>1,the rumor persists in social networks.Secondly,the local stability of the rumor spreading equilibrium is investigated by using the Roth-Hurwitz stability criterion,and the influence of diffusion on the system stability is discussed.When the diffusion is introduced into a stable rumor spreading model without time delay,the model becomes unstable,indicating that the Turing instability is caused by diffusion.Thirdly,the Hopf bifurcation condition of the rumor spreading model is established by selecting the time delayτas the bifurcation parameter,and the expression of bifurcation thresholdτis given.Whenτ<τ,the rumor propagation model with diffusion term is stable;whenτ>τ,the model loses the stability and the Hopf bifurcation occurs.The numerical simulation results show that both diffusion and time delay play an important role in the dynamic evolution of rumor spreading.At the same time,the influence of the crowding degree of spreaders on rumor propagation is also simulated.As the crowding gets worse and worse,the rumor refuting effect weakens,the bifurcation thresholdτdecreases,and the propagation peak increases.Therefore,it is important to build an excellent social network environment to supervise the rumors that are still in the fermentation stage,improve the timeliness of the release of rumor refuting information,and strengthen the refuting of rumors among key groups.This paper breaks through the limitation considering only the time evolution,explores the spatiotemporal spreading law of rumor in real society,and provides a new perspective and idea for governing the rumor spreading.