Hybrid universality classes of systemic cascades

Area of Science:

• Complex Systems Science
• Statistical Physics
• Network Science

Background:

• Cascades are self-reinforcing processes fundamental to systemic risk in complex systems.
• Current understanding relies on limited numerical observations and ad-hoc models.
• Identifying universal aspects of cascades is crucial for predicting and mitigating systemic failures.

Purpose of the Study:

• To develop a unifying theoretical framework for understanding cascade phenomena.
• To identify distinct universality classes of cascades based on their underlying symmetry.
• To predict critical phenomena and their characteristics in various complex systems.

Main Methods:

• Development of a unifying theoretical approach for cascade analysis.
• Application of hyperscaling arguments to predict critical exponents.
• Simulations of classic and novel cascade models across different dimensions.

Main Results:

• Identification of two distinct universality classes of cascades determined by global symmetry.
• Prediction of hybrid critical phenomena combining mean-field and d-dimensional corrections.
• Demonstration of parity invariance's influence on avalanche geometry and lifetime.

Conclusions:

• The developed theory provides a universal framework applicable to diverse networked systems.
• Revealed universal principles of cascade critical phenomena are amenable to experimental validation.
• Offers new insights into the fundamental nature of cascading failures in complex systems.