  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.
