Abstract
We propose a graphical notation by which certain spectral properties of complex systems can be rewritten concisely and interpreted topologically. Applying this notation to analyze the stability of a class of networks of coupled dynamical units, we reveal stability criteria on all scales. In particular, we show that in systems such as the Kuramoto model the Coates graph of the Jacobian matrix must contain a spanning tree of positive elements for the system to be locally stable.
| Translated title of the contribution | Graphical notation reveals topological stability criteria for collective dynamics in complex networks |
|---|---|
| Original language | English |
| Article number | 194102 |
| Number of pages | 5 |
| Journal | Physical Review Letters |
| Volume | 108 |
| Issue number | 19 |
| DOIs | |
| Publication status | Published - 8 May 2012 |
Bibliographical note
Publisher: American Physical SocietyResearch Groups and Themes
- Engineering Mathematics Research Group
Keywords
- KURAMOTO MODEL
- SYNCHRONIZATION
- POTENTIALS
- EQUATION
- SYSTEMS
Fingerprint
Dive into the research topics of 'Graphical notation reveals topological stability criteria for collective dynamics in complex networks'. Together they form a unique fingerprint.Cite this
- APA
- Author
- BIBTEX
- Harvard
- Standard
- RIS
- Vancouver