Onset of Intragroup Conflict in a Generalized Model of Social Balance

Dynamically changing interpersonal relationships lie at the core of the emergence of in-group structures, such as polarity or conflict. We explore these dynamics in a simple continuous dynamical model obtained by generalizing a previously proposed model based on Heider's balance theory from social psychology. Previous findings include a rigorous proof of the emergence of in-group harmony or bipolar conflict (global minima) and the identification of local minima called jammed states, along with their corresponding energy spectrum in terms of structural complexity. However, some unrealistic scenarios constrain our capacity to contextualize and directly apply these results to real-world social behaviors. To address these challenges, we first introduce a unified dynamical model and find that group size can be critical to the onset of in-group bipolar conflict. Using random matrix statistics, we then characterize the pathways leading to jammed states, which have previously been discussed only in stochastic models. Unexpectedly, we also show that perturbing our dynamical model can increase the chances of getting trapped in jammed states, giving rise to a novel notion called the noise-induced jammed state. We conclude this Letter by discussing possible real-world implications as well as potential contributions to the existing literature in relevant fields such as anthropology.