Multilayer and multiplex networks represent a good proxy for the description of social phenomena where social structure is important and can have different origins. Here we propose a model of opinion competition where individuals are organized according to two different structures in two layers. Agents exchange opinions according to the Abrams-Strogatz model in each layer separately and opinions can be copied across layers by the same individual. In each layer a different opinion is dominant and then each layer has a different absorbing state. The consensus in one opinion is not the only possible stable solution because of the interaction between the two layers. A new mean field solution where both opinions coexist has been found. In a finite system there is a long transient time of a dynamical coexistence of both opinions, however, the system ends in a consensus state due to finite size effects. We analyze sparse topologies in the two layers and the existence of positive correlations between the layers that enables the coexistence of inter-layer groups of agents sharing the same opinion.
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