Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2010-12-03
Nonlinear Sciences
Adaptation and Self-Organizing Systems
5 pages, 3 figures
Scientific paper
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.
Boccaletti Stefano
Do Anne-Ly
Gross Thilo
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