Hyperedge overlap drives synchronizability of systems with higher-order interactions
Santiago Lamata-Otín1,2, Federico Malizia3, Vito Latora4,5,6
1University of Zaragoza, Department of Condensed Matter Physics, 50009 Zaragoza, Spain.
Physical Review. E
|April 18, 2025
Summary
Higher-order interactions in dynamical systems are crucial for collective behavior. This study introduces a hyperedge overlap matrix, revealing that significant overlap hinders synchronization, especially in higher-order systems.
Area of Science:
- Complex Systems
- Network Science
- Nonlinear Dynamics
Background:
- Collective behavior in coupled dynamical systems is influenced by interaction structure.
- Higher-order interactions, involving more than two nodes, are increasingly recognized in various systems.
- Understanding the microscopic organization of these interactions is key to predicting system dynamics.
Purpose of the Study:
- To introduce a framework for investigating the impact of interaction structure on dynamical processes.
- To develop a hyperedge overlap matrix to quantify microscopic organization of higher-order interactions.
- To analyze the distinct effects of intra-order and inter-order hyperedge overlap on synchronization.
Main Methods:
- Development of a hyperedge overlap matrix.
- Analysis of nondiagonal elements for inter-order hyperedge overlap.
- Analysis of diagonal elements for intra-order hyperedge overlap.
- Investigation of the impact of these overlaps on synchronization stability in coupled chaotic oscillators.
Main Results:
- Large values of both intra-order and inter-order hyperedge overlap negatively impact synchronization stability.
- The importance of hyperedge overlap effects increases with the order of interactions.
- Intra-order overlap hinders synchronization by creating disconnected hyperedge sets.
- Inter-order overlap hinders synchronization by increasing shared nodes between diverging trajectories.
Conclusions:
- The microscopic organization of higher-order interactions, quantified by hyperedge overlap, significantly affects synchronization.
- Distinct mechanisms explain how intra-order and inter-order overlap destabilize synchronization.
- This framework provides insights into the role of network topology in the dynamics of complex systems.
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