  We introduce a model to study the delicate relation between the spreading of
information and the formation of opinions in social systems. For this purpose,
we propose a two-layer multiplex network model in which consensus dynamics
takes place in one layer while information spreading runs across the other one.
The two dynamical processes are mutually coupled by considering that the
control parameters that govern the dynamical evolution of the state of the
nodes inside each layer depend on the dynamical states at the other layer. In
particular, we explore the scenario in which consensus is favored by the common
adoption of information while information spreading is boosted between agents
sharing similar opinions. Numerical simulations together with some analytical
results point out that, when the coupling between the dynamics of the two
layers is strong enough, a double explosive transition, i.e. an explosive
transition both for consensus dynamics and for the information spreading
appears. Such explosive transitions lead to bi-stability regions in which the
consensus-informed stated and the disagreement-ignorant states are both stable
solutions.
