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Updated: Apr 25, 2026
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Simultaneous first- and second-order percolation transitions in interdependent networks
Dong Zhou1, Amir Bashan1, Reuven Cohen2
1Department of Physics, Bar-Ilan University, Ramat Gan 52900, Israel.
Summary
Cascading failures in interdependent networks can cause system collapse. A newly discovered second-order percolation explains the slow collapse phase, aiding in preventing catastrophic failures.
Area of Science:
- Network Science
- Complex Systems Dynamics
- Statistical Physics
Background:
- Interdependent networks are susceptible to cascading failures, potentially leading to system-wide collapse.
- Abrupt first-order transitions characterize these collapses when a critical fraction of nodes fail.
- The slow decrease of the giant component during cascading failures (plateau) and its system-size scaling remained unexplained.
Purpose of the Study:
- To elucidate the origin of the plateau phenomenon observed during cascading failures in interdependent networks.
- To understand how the plateau's length scales with the system size.
- To provide insights into the critical dynamics of cascading failures for mitigation strategies.
Main Methods:
- Analysis of cascading failure dynamics in interdependent network models.
- Identification of simultaneous phase transitions during iterative failures.
- Investigation of percolation phenomena within the failure cascade.
Main Results:
- A spontaneous second-order percolation occurs concurrently with the abrupt first-order transition during cascading failures.
- This second-order percolation explains the origin of the slow decrease plateau in the giant component.
- The length of the plateau is shown to scale with the system size due to this concurrent percolation.
Conclusions:
- The interplay between first-order collapse and second-order percolation governs cascading failures in complex networks.
- Understanding these critical dynamics is crucial for developing robust network designs and failure prevention strategies.
- Findings offer a mechanistic explanation for previously observed plateau behaviors in system collapse.
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