Temporal, Structural, and Functional Heterogeneities Extend Criticality and Antifragility in Random Boolean Networks

Area of Science:

• Complex Systems Science
• Network Theory
• Dynamical Systems

Background:

• Most complex system models assume homogeneity, where all elements share identical properties.
• Natural systems often exhibit heterogeneity, with some elements possessing distinct characteristics.
• Criticality in homogeneous systems is typically confined to a narrow parameter range near phase transitions.

Purpose of the Study:

• To investigate the impact of heterogeneity on criticality and antifragility in complex systems.
• To determine if heterogeneity can broaden the parameter space for these phenomena.
• To explore the relationship between homogeneity and heterogeneity in system dynamics.

Main Methods:

• Utilized random Boolean networks as a general model for discrete dynamical systems.
• Introduced heterogeneity in temporal, structural, and functional aspects of the networks.
• Analyzed the parameter space to identify regions of criticality and antifragility.

Main Results:

• Heterogeneity additively broadens the parameter region where criticality is observed.
• Increased heterogeneity also expands the parameter regions associated with antifragility.
• Maximum antifragility, however, was found in specific homogeneous network parameter settings.

Conclusions:

• Heterogeneity plays a significant role in expanding the operational range of criticality and antifragility in complex systems.
• The ideal balance between homogeneity and heterogeneity is not fixed but is nuanced, context-specific, and potentially dynamic.
• Findings suggest that natural systems' heterogeneity is crucial for their resilience and adaptability.