Transitions Between Polarisation and Radicalisation in a Temporal Bi-Layer Echo Chambers Model.

Echo chambers and polarisation dynamics are as of late a very prominent topic in scientific communities around the world. As these phenomena directly affect our lives and 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 chambers model with activity driven agents onto a bi-layer topology and study the dynamics of the polarised state as a function of interlayer couplings. Different cases of such couplings are presented - unidirectional coupling that can be reduced to a mono-layer facing an external bias, symmetric and non-symmetric couplings. We have assumed that initial conditions impose system polarisation and agent opinions are different for both layers. Such a pre-conditioned polarised state can sustain 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 radicalised 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 analysed using a mean field approximation and classified in the framework of bifurcation theory.