Opinion consensus incorporating higher-order interactions on individual-collective networks

Abstract In the current information society, researches on the dissemination mechanisms and evolution laws of individual or collective opinions and their behaviors is one of the hot topics in the field of opinion dynamics. First, in this paper, we construct a two-layer network consisting of an individual-opinion layer and a collective-opinion layer, and propose a dissemination model of opinions incorporating higher-order interactions (i.e. OIHOI dissemination model). Furthermore, the dynamic equations of opinion dissemination for both individuals and groups are presented. Using Lyapunov's first method, some theoretical analysis of two equilibrium points, including the negative consensus point and positive consensus point, of the dynamic equations obtained for opinion dissemination, are conducted. In addition, for individual and collective opinions, some conditions to reach negative consensus and positive consensus and a theoretical expression for the dissemination threshold are put forward. Numerical simulations are carried to verify the feasibility and effectiveness of the proposed theoretical results, as well as the influence of the intra-structure, inter-connections, and higher-order interactions on the dissemination and evolution of individual opinions. The main results are as follows. (i) When the intra-structure of the collective-opinion layer meets certain characteristics, then reaching a negative or positive consensus is easier for individuals. (ii) Both negative and positive consensus perform best for mixed types of inter-connections in the two-layer network. (iii) Higher-order interactions can quickly eliminate differences among individual opinions, thereby enabling individuals to reach consensus faster.