A universal route to explosive phenomena.

Area of Science:

• Complex Systems Science
• Statistical Physics
• Network Science

Background:

• Critical transitions, such as synchronization in coupled oscillators or epidemic emergence, are fundamental phenomena in complex systems.
• First-order transitions, particularly "explosive" types, have garnered significant interest when classical models are enhanced with additional effects.

Purpose of the Study:

• To provide a mathematical framework demonstrating that first-order transitions are a universally expected outcome in generalized complex systems.
• To explain the emergence of "explosive" transitions as a natural consequence of model generalization.

Main Methods:

• Mathematical analysis of classical models generalized by incorporating additional effects.
• Investigation of generic two-parameter families of models to observe changes in criticality.
• Application of the theoretical framework to distinct physical systems.

Main Results:

• A mathematical argument proving that varying classical models along a generic two-parameter family inevitably leads to a change in criticality.
• Demonstration that first-order transitions are not surprising but universally expected effects in generalized systems.
• Empirical validation through three distinct examples: adaptive epidemic dynamics, a generalized Kuramoto model, and a percolation transition.

Conclusions:

• The emergence of first-order transitions, including explosive ones, is a predictable consequence of generalizing classical models.
• The presented framework unifies the understanding of these transitions across diverse complex systems.
• This work provides a theoretical basis for expecting and analyzing first-order transitions in various scientific domains.