考虑思考时滞的社交网络舆情最优控制模型

Optimal Control Model of Social Network Public Opinion Considering Thought Time-Lag

随着信息技术的不断发展,纷繁复杂的信息无时不刻的充斥着社交网络,这也使得负面舆情信息不断滋生并快速传播,严重影响了网络安全和社会稳定。本研究提出考虑思考时滞的舆情传播最优控制模型。首先,基于传染病模型构建引入思考者的舆情传播模型。其次,对模型中的参数进行敏感性分析,并引入对立舆论攻击机制,利用最优控制理论设计所提舆情传播最优控制模型,旨在最小化舆情采纳者密度和控制成本。实验表明,所提模型能够对社交网络中的舆情传播进行有效控制。

In the circumstance of developing information technology, various and complicated information are ubiquitous at any time on the social networks, of which the negative messages are also increasingly growing at a fast rate, having a serious impact on the network safety and social stability. As a result, it is pressing to design an effective model to control the spread of the negative information. Time lag is a common thing in nature. In the process of spreading public opinions on the social network, some users may give a response after consideration. Among the existing studies, most do not take these thinkers’ time lag into account. Because of this, an optimal control model of public sentiment spread is proposed, with time lag considered. First of all, a model of public sentiment spread, which involves thinkers, has been built based on the classical epidemic model. A systematic dynamics analysis is made in terms of steady state and local stability. At the same time, Hopf bifurcation under the extreme threshold is discussed. Secondly, sensitivity analysis is conducted for the parameters in the model. With Pontryagin maximum principle and the attack mechanism of opposing public opinion introduced, the optimal control model concerning public sentiment spread is designed according to the optimizing control theory, aiming to minimize the density of people following the negative public sentiment and the controlling cost. The experiment indicates that this model can effectively control the spread of public sentiments in social networks. The system is in a stable state when thinkers need more time to give a response as well as when the attack of opposing public opinions spread at the fastest pace via the media and experts. Besides, the optimal control model is able to let the attack information of opposite public opinion spread effectively in a short time with the minimum cost when there is an event of public opinion.