Critical Behaviors in Contagion Dynamics

Area of Science:

• Complex systems science
• Statistical physics
• Network science

Background:

• Contagion models describe state transitions in networks.
• Previous models lacked a unifying framework for diverse dynamics.
• Understanding critical behavior is key to predicting system-level changes.

Purpose of the Study:

• To develop a unifying mean-field theory for general contagion models.
• To identify the universal critical regimes governing these dynamics.
• To resolve long-standing debates on contagion universality classes.

Main Methods:

• Derivation of a unifying mean-field theory.
• Analytical investigation of system dynamics.
• Characterization of state transitions (spontaneous, neighbor-induced, reverse).

Main Results:

• Identified three distinct critical regimes: uncorrelated spontaneous transition dynamics, contact process dynamics, and cusp catastrophes.
• Demonstrated that these three regimes encompass all possible critical behaviors.
• Showcased rich dynamics including limit cycles and random phase switching.

Conclusions:

• The critical behavior of general contagion models is limited to three universal regimes.
• The derived mean-field theory provides a comprehensive mathematical understanding.
• This work resolves debates on universality classes in complex contagion dynamics.