Multi-dimensional opinion dynamics for social networks with asynchronous updates

Multi-dimensional opinion dynamic models can often be used to describe the mutual influence of agents on different topics expressed in social networks. This paper mainly focuses on the multi-dimensional opinion dynamics on social networks with asynchronous updates, where networks include two types of agents: stubborn agents and non-stubborn agents. In the asynchronous update mechanism, the update time instants of each agent are independent and different from those of other agents, which leads to the complexity and time variance of opinion interaction among agents. This paper comprehensively analyzes the convergence of multi-dimensional opinion dynamic models under asynchronous updates, relying on the techniques of binary relation composition and infinite products of sub-stochastic matrices. The results show that the opinions of stubborn agents gradually influence the opinions of non-stubborn agents, and ultimately completely determine the stable opinions of non-stubborn agents. The theoretical results are validated through numerical simulations. • Developing a new opinion dynamics model with asynchronous update mechanism. • Extending the synchronous opinion dynamics model and including it as a special case. • Proposing a new convergence analysis method based on infinite products of substochastic matrices. • Establishing algebraic conditions for the asymptotic convergence of opinions in social networks under asynchronous scenarios.