Multidimensional Opinion Dynamics With Private Opinions and Heterogeneous Belief Systems on the Signed Social Networks

This article proposes a new opinion dynamics model to explore the laws of opinion evolution, which fully considers social and psychological factors, such as stubbornness, cooperation and competition, differences between private and expressed opinions (PAEO), and heterogeneous belief systems. The dynamic behavior is analyzed for the proposed model by using matrix analysis techniques and graph theory. The obtained results indicate that if there are no oblivious individuals, opinions can always converge exponentially, and the final opinions depend only on the initial private opinions. If oblivious and nonoblivious individuals coexist, and the opinions of oblivious individuals converge, then opinions of nonoblivious individuals will also converge. In addition, when there exist stubborn individuals in social networks, there are always differences in the final PAEO for different initial opinions. Finally, several numerical simulation examples, including Zachary’s Karate Club network and Gahuku-Gama tribes network, are utilized to verify the effectiveness of the obtained results.