Universal mechanism for hybrid percolation transitions

Area of Science:

• Complex Systems Science
• Network Science
• Statistical Physics

Background:

• Hybrid percolation transitions (HPTs) are observed in various complex systems, including interdependent networks and epidemic models.
• Cascading processes are the primary drivers of HPTs across these diverse systems.

Purpose of the Study:

• To elucidate the microscopic universal mechanism underlying hybrid percolation transitions (HPTs).
• To identify the critical time window for intervention during cascading processes.

Main Methods:

• Analysis of cascading processes in complex networks.
• Identification of critical branching and supercritical process dynamics.
• Investigation of finite-size effects and large loop structures.

Main Results:

• HPTs result from a two-step process: a durable critical branching (CB) phase and a rapid, explosive supercritical (SC) phase.
• The CB phase persists for O(N^1/3) time in N-node networks, rendering remaining nodes vulnerable.
• The SC phase rapidly activates vulnerable nodes, driven by large loops in finite samples.

Conclusions:

• The identified crossover mechanism and scaling behavior are universal across different HPT systems.
• The O(N^1/3) crossover time represents a critical 'golden time' for intervention.
• Timely interventions during this window can prevent or control macroscopic cascades, such as pandemics.