Opinion Dynamics Modelling: Distinct Attraction and Repulsion Topologies Highlight Quantitative Effects of Trolling

We introduce a model of opinion dynamics based on networked nonlinear differential equations. The model combines a linear attraction with a repulsive hyperbolic tangent interaction, labelled controversialness . For low controversialness, the model displays universal consensus, which is typical of opinion models. As controversialness increases, opinion behaviours such as polarisation , clustering , and dissensus emerge, dependent on the network topology. By placing attractive and repulsive interactions on distinct networks, this model is able to simulate the manipulative effects of trolls by introducing controversy, which may be associated with mis/disinformation, toxic messaging, and encouraging provocative questioning and/or emotional posting. This work offers an analytical and statistical analysis of model results, under a wide variety of topologies and initial conditions, while also generalising cluster detection algorithms typically applied to discrete models.