Internal character dictates phase transition dynamics between isolation and cohesive grouping

TL;DR

This paper investigates how internal character among diverse entities influences phase transitions between isolation and group cohesion, revealing critical points and explaining universal behaviors in complex systems.

Contribution

It introduces an analytical framework that accounts for internal character, uncovering diverse critical points and explaining universal phenomena in phase transition dynamics.

Findings

Different critical points depend on character-based grouping mechanisms

Critical points shift with population diversity

The theory predicts non-monotonic connectivity variations

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.