Graphical notation reveals topological stability criteria for collective dynamics in complex networks

A.-L. Do, S. Boccaletti, T Gross

Research output: Contribution to journalArticle (Academic Journal)

16 Citations (Scopus)

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 contributionGraphical notation reveals topological stability criteria for collective dynamics in complex networks
Original languageEnglish
Article number194102
Number of pages5
JournalPhysical Review Letters
Volume108
Issue number19
DOIs
Publication statusPublished - 8 May 2012

Bibliographical note

Publisher: American Physical Society

Keywords

  • KURAMOTO MODEL
  • SYNCHRONIZATION
  • POTENTIALS
  • EQUATION
  • SYSTEMS

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