Internal character dictates phase transition dynamics between isolation and cohesive grouping

Abstract

We show that accounting for internal character among interacting, heterogeneous entities generates rich phase transition behavior between isolation and cohesive dynamical grouping. Our analytical and numerical calculations reveal different critical points arising for different character-dependent grouping mechanisms. These critical points move in opposite directions as the population's diversity decreases. Our analytical theory helps explain why a particular class of universality is so common in the real world, despite fundamental differences in the underlying entities. Furthermore, it correctly predicts the non-monotonic temporal variation in connectivity observed recently in one such system.