Dynamics of a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise

With the development of information technology, rumors propagate faster and more widely than in the past. In this paper, a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise is proposed. The global positivity of the solution process is proved, and further the basic reproductive number R₀ is obtained. When R₀ < 1, the dynamical process of system with Lévy jump tends to the rumor-free equilibrium point of the deterministic system, and the rumor tends to extinction; when R₀ > 1, the rumor will keep spreading and the system will oscillate randomly near the rumor equilibrium point of the deterministic system. The results show that the oscillation amplitude is related to the disturbance of the system. In addition, increasing media coverage can effectively reduce the final spread of rumors. Finally, the above results are verified by numerical simulation.     

Dynamics and near-optimal control in a stochastic rumor propagation model incorporating media coverage and Lévy noise

The appearance of rumors intensifies people's panic and affects social stability. How to control the spread of rumors has become an important issue which is worth studying. In order to more accurately reflect the actual situation in the real world, a stochastic model incorporating media coverage and Lévy noise is proposed to describe the dynamic process of rumor propagation. By introducing two control strategies of popular science education and media coverage in an emergency event, an near-optimal control problem that minimizes the influence and control cost of rumor propagation is proposed. Sufficient conditions for near-optimal control of the model are established by using a Hamiltonian function. Then the necessary conditions for near-optimal control are obtained by using the Pontryagin maximum principle. Finally, the effect of popular science education, media coverage and Lévy noise on rumor propagation process control is verified by numerical simulation.     

新媒介影响下的创新产品信息扩散模型研究

随着科技的飞速发展,新媒介越来越受到关注,成为信息获取的主要途径.鉴于新媒介与传统媒介的巨大不同,为了研究新型电子商务环境下的创新产品扩散特征,基于BASS模型,构建了新媒体渠道下的两种创新产品信息扩散模型.通过仿真模拟得到新媒介影响下的两类产品信息的扩散规律及扩散状态差异.新媒介环境下的产品扩散具有非常明显的优势,企业管理者需要调整的营销渠道战略以适应时代发展步伐.     

Near-optimal control of a stochastic rumor spreading model with Holling II functional response function and imprecise parameters

In recent years, rumor spreading has caused widespread public panic and affected the whole social harmony and stability. Consequently, how to control the rumor spreading effectively and reduce its negative influence urgently needs people to pay much attention. In this paper, we mainly study the near-optimal control of a stochastic rumor spreading model with Holling II functional response function and imprecise parameters. Firstly, the science knowledge propagation and the refutation mechanism as the control strategies are introduced into a stochastic rumor spreading model. Then, some sufficient and necessary conditions for the near-optimal control of the stochastic rumor spreading model are discussed respectively. Finally, through some numerical simulations, the validity and availability of theoretical analysis is verified. Meanwhile, it shows the significance and effectiveness of the proposed control strategies on controlling rumor spreading, and demonstrates the influence of stochastic disturbance and imprecise parameters on the process of rumor spreading.     

不确定性多属性决策的新方法

本文研究了属性指标值，属性权重为L—R模糊数的多属性决策问题，首先在不同的α水平下将L—R模糊数转化为区间数，基于优化模型求出方案的区间属性值并利用α-截及区间数序关系的可能度，构造互补判断矩阵。提出一种新的排序公式，得到一族排序向量，然后对不同α水平下的排序向量集结，得出总的排序向量，以此对方案排序，最后通过实例说明了该方法的可行性和有效性。     

Dynamical behavior and optimal impulse control analysis of a stochastic rumor spreading model

The Internet era has brought great convenience to our life and communication. Meanwhile, it also makes a bunch of rumors propagate faster and causes even more harm to human life. Therefore, it is necessary to perform effective control mechanisms to minimize the negative social impact from rumors. Thereout, firstly, we formulate a rumor spreading model considering psychological factors and thinking time, then, we add white noise (i.e., stochastic interference) and two pulse control strategies which denote education mechanism and refutation mechanism into the model. Secondly, we obtain the global positive solutions and demonstrate the global exponential stability of the unique positive periodic rumor-free solution. Thirdly, we discuss the extinction and persistence of rumor. Moreover, we use Pontriagin's minimum principle to explore the optimal impulse control. Finally, several numerical simulations are carried out to verify the effectiveness and availability of the theoretical analysis. We conclude that the pulse control strategies have a great influence on controlling rumor spreading, and different control strategies should be adopted under different transmission scenarios.     

模糊多属性决策中的离差最大化方法

本文研究属性权重完全未知且属性值为L-R模糊数的多属性决策问题,提出了一种在多属性决策中,基于模糊数及α-截集理论,用离差最大化方法来估计属性权重的方法,随后研究了这种方法的相关性质,给出方程的解,得到方案排序结果。研究表明,由本文所提出的方法是有效、可行的。     

动态演化博弈视角下的“中国式过马路”问题研究

以“中国式过马路”现象中有闯红灯倾向的行人为研究对象,分析其过街行为特点,建立了行人过街的动态演化博弈模型,探讨了不同时刻、不同条件下行人的博弈选择策略;在此基础上论证了相应管理措施的有效性。结合数值模拟得到以下结论:(1)在不采取任何惩治措施条件下所有行人倾向于选择直接闯红灯;(2)轻微的惩治措施起不到显著效果,惩治措施达到一定力度后才能对“中国式过马路”现象有所改善;(3)过街行人的策略选择会受到周边行人行为的影响;(4)过长的红灯等待时间会诱发行人选择主动闯红灯的动机。综上四点得到针对性的改善措施:合理设置并优化信号配时,缩短行人过街等待时间,在此基础上加大惩治力度并提高行人总体素质和遵纪守法意识。     

基于系统动力学的谣言传播模型研究

在剖析谣言传播机理的基础上,建立了一个反映谣言传播实际情况的动力学模型,讨论了模型解的有界性和各平衡点的存在性,并利用Routh-Hurwitz判据证明了各平衡点的局部渐进稳定性,通过构造Lyapunov函数分析了平衡点的全局渐进稳定性,得到了谣言存在与否的阈值,通过传播参数以及初始条件的调整,控制谣言最终的传播状态.最后,用算例模拟试验的方法,说明方法的可行性.     

模糊多属性决策中模糊加权平均法的一种改进方法

本文针对模糊加权平均法(FWA)的应用局限性,基于α截集、区间算子改进了模糊加权平均法。该方法首先运用区间算子计算在α水平下方案的区间综合属性值,然后借助可能度对方案两两比较得到互补判断矩阵,利用模糊互补判断矩阵确定方案优先权重的参数方法确定该水平下的方案优先权重,再通过集结各个水平下的权重得到方案排序的优先权重。改进的加权平均法可以有效的处理属性值和权重以多种模糊数形式给出的模糊多属性决策,具有普遍性,值得进一步研究推广。最后用实例说明该方法的有效性与可行性。