Opinion Consensus with Multiplicative Communication Noises in Social Networks

In this paper, an opinion consensus problem with multiplicative communication noises is considered. The model considers global information, stubbornness and multiplicative random noise. The model describes the dynamic evolution of individual opinions on a topic in the network. The opinion of each individual are affected by their own opinion, global information and neighbor opinion at the previous moment. Every individual can obtain global information about the network. To be more realistic, each individual has a random stubbornness in global information. Different individuals have different multiplicative noise in the sum of difference between neighbors' opinions and their own, which is Gaussian white noise subject to normal distribution. All individuals have the same content of acceptance. For this model, we use the knowledge of multi-agent system to analysis. The results show that when the content of acceptance is within a suitable range, this range is related to the stubbornness and Gaussian white noise, and the individuals in the opinion dynamic model can converge. We validate the results by simulation.