Opinion Dynamics With Competitive Relationship and Switching Topologies

In this paper, the discrete-time opinion dynamics model with competitive relationship and switching topologies is investigated. Different from the usual DeGroot model, competition between individuals and the switching topologies are considered in a social network. Furthermore, the structurally balanced and unbalanced network topologies are investigated simultaneously. It is shown that if all network topologies are structurally balanced and include a spanning tree, then there may appear polarization, neutralization or fluctuation. And we also find conditions under which the group is split into two clusters at most, specifically, opinions will reach polarization (bipartite consensus) or all individuals will remain neutrality (consensus). If there exist the structurally unbalanced network topologies in social networks, we obtain the condition in which all individuals will finally hold the neutral attitude on the discussed topic. Two examples are provided to illustrate the effectiveness of the obtained results.