Bifurcations and catastrophes in temporal bi-layer model of echo chambers and polarisation

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 opinion dynamics in modern era. We build upon an existing echo chambers and polarisation model and extend it onto a bi-layer topology. This new topological context allows us to indicate possible consequences of interacting groups within this model. Four different cases are presented - symmetric negative and positive couplings, an asymmetric coupling and an external bias. We show both simulation results and mean field solutions for these scenarios outlining the possible consequences of such dynamics in real world societies.Our predictions show that there are conditions in which the system can reach states of neutral consensus, a polarised consensus, polarised opposition and even opinion oscillations. Transitions between these states in terms of bifurcation theory are identified and analysed using a mean field model.