  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.
