Transitions between polarization and radicalization in a temporal bilayer echo-chamber model

Echo chambers and polarization dynamics are, as of late, a very prominent topic in scientific communities around the world. As these phenomena directly affect our lives, seemingly more and more as our societies and communication channels evolve, it becomes ever so important for us to understand the intricacies of opinion dynamics in the modern era. Here we extend an existing echo-chamber model with activity-driven agents to a bilayer topology and study the dynamics of the polarized state as a function of interlayer couplings. Different cases of such couplings are presented: unidirectional coupling that can be reduced to a monolayer facing an external bias and symmetric and nonsymmetric couplings. We have assumed that initial conditions impose system polarization and agent opinions are different for both layers. Such a preconditioned polarized state can persist without explicit homophilic interactions provided the coupling strength between agents belonging to different layers is weak enough. For a strong unidirectional or attractive coupling between two layers a discontinuous transition to a radicalized state takes place when mean opinions in both layers are the same. When coupling constants between the layers are of different signs, the system exhibits sustained or decaying oscillations. Transitions between these states are analyzed using a mean field approximation and classified in the framework of bifurcation theory.