Coevolution of actions and opinions in social networks with signed interactions

We investigate a coevolutionary model of opinions and actions on a two-layer network, incorporating both coordinating and anti-coordinating interactions by means of a signed layer. Within this framework, we derive a general convergence result and establish conditions for the existence of consensus and polarized equilibria, characterizing their basins of attraction. Our analysis shows that consensus emerges under assumptions that are more restrictive than in the presence of purely coordinating networks, but less stringent than those for purely anti-coordinating ones. In contrast, in structurally balanced networks, polarization arises more easily in the presence of both types of interactions than in networks with only coordination or only anti-coordination interactions, as inter-group antagonism reinforces intra-group consensus.