Multi-dimensional opinion chaos synchronization based on multi-layer complex networks

Abstract In complex networks, the interactions of opinions are significantly affected by network structure. Moreover, multi-layer networks, which contain multiple subsystems and different types of interactions, are considered to have a stronger ability to simulate various real-world systems than traditional single-layer complex networks. Based on this motivation, this article attempts to show how to achieve complete synchronization of multi-dimensional opinions in a multi-layer network topology where the opinions of nodes have Rössler chaotic dynamics. A first step in investigating the synchronization of multi-layer complex networks is to propose a multi-dimensional opinion evolution model. In this article, the multi-layer complex network model combining the Rössler oscillation system is built, which provides us a tool for insight into the nodes complexity in multi-layer networks. Furthermore, a general criterion for globally exponentially asymptotic synchronization of multi-layer complex networks is provided using multiple Lyapunov stability theories. We illustrate the reliability of the model and the correctness of the criterion by Runge-Kutta (RK4) simulation. These findings shed new light on some interesting phenomena in society and help decision-makers predict the prevalence of hot topics and public opinions.