A State Transition Matrix-Based Approach to Separation of Cooperations and Antagonisms in Opinion Dynamics
For researchers in opinion dynamics and multi-agent systems, this work provides a unified framework to analyze convergence under signed networks with switching topologies, relaxing previous assumptions on connectivity and structural balance.
This paper develops a state transition matrix-based approach to analyze opinion dynamics under signed digraphs with switching topologies, bridging the gap between signed and conventional digraphs. It shows that bipartite consensus or stability emerges if and only if the switching signed digraph is simultaneously structurally balanced or unbalanced, generalizing structural balance theory to changing topologies.
This paper is concerned with the dynamics evolution of opinions in the presence of both cooperations and antagonisms. The class of Laplacian flows is addressed through signed digraphs subject to switching topologies. Further, a state transition matrix-based approach is developed for the analysis of opinion dynamics, regardless of any assumptions on connectivity, structural balance or digon sign-symmetry of signed digraphs. It is shown that based on the separation of cooperations and antagonisms, a relationship can be bridged between opinion dynamics under signed digraphs and under conventional digraphs. This helps to solve convergence problems for opinion dynamics. In particular, bipartite consensus (or stability) emerges if and only if the associated switching signed digraph is simultaneously structurally balanced (or unbalanced), which generalizes the use of structural balance theory in opinion dynamics to the case study of changing network topologies.