Modeling of human cognition in consensus agreement on social media and its implications for smarter manufacturing

Opinion dynamics modeling has long been interesting to scientists because of its applications in the marketing industry as well as elections. Agreement, e.g., on a special product, has an affective influence on its manufacturing process. However, most of the existing opinion dynamics models are linear time invariant. In this article, eight non-linear time variant models for opinion dynamics are proposed and put to test on subjective synthetic networks. Despite all the efforts, the issues of stability and convergence in time-varying networks, which can be found in industrial contexts, have not been resolved yet and only sufficient conditions have been derived. In the proposed models, unlike in the classical ones such as the French-DeGroot model, we have taken into account each member's susceptibility to persuasion by others that is a cognitive parametric function of individuals' opinions. In addition, we have introduced a stubbornness matrix which has large values initially but shrinks to zero as the time grows. This implies that agents' susceptibilities to others, at the beginning of any experiment, are smaller than what they are at the end. We present a novel mathematical formulation for these new opinion dynamics models and prove their stability too. For evaluation, we simulated a scenario in which some people connected via a graph, voted for a product. They initially had their own stands but gradually came to a point found through interaction with the others. The results confirm the convergence and stability of the proposed models.