Coupled dynamics on hypergraphs: Master stability of steady states and synchronization
Raffaella Mulas, Christian Kuehn, Jürgen Jost1
1Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103 Leipzig, Germany and Santa Fe Institute for the Sciences of Complexity, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA.
Physical Review. E
|July 22, 2020
Summary
This study generalizes the master stability function approach to hypergraphs, enabling analysis of higher-order interactions. This framework reveals how complex network topologies influence dynamical system stability.
Area of Science:
- Dynamical systems theory
- Network science
- Graph theory
Background:
- Analyzing dynamical systems on networks often focuses on how topology affects stability.
- The master stability function is a key tool for understanding topology's influence on stability.
- Existing methods primarily apply to simple graphs, limiting analysis of higher-order interactions.
Purpose of the Study:
- To generalize the master stability function approach to hypergraphs.
- To analyze dynamical systems with higher-order interactions using hypergraph structures.
- To provide a framework for extending graph-based dynamical system results to hypergraphs.
Main Methods:
- Generalization of the master stability function to hypergraphs.
- Study of Laplace-type interaction structures on hypergraphs.
- Analysis of spectral properties of hypergraph Laplacians.
Main Results:
- The master stability function approach is successfully extended to hypergraphs.
- Hypergraph structures reveal possibilities for novel dynamical phenomena due to richer spectral theory.
- The study provides a general blueprint for extending graph-based dynamical system concepts to hypergraphs.
Conclusions:
- The generalized master stability function for hypergraphs offers a powerful tool for studying complex systems.
- Higher-order interactions in hypergraphs can lead to distinct dynamical behaviors compared to simple graphs.
- This work lays the foundation for analyzing a wider range of complex network dynamics.
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