Stability of Synchronized Motion in Complex Networks

Details Stability of Synchronized Motion in Complex Networks Stability of Synchronized Motion in Complex Networks

2011-12-10

arxiv.org/abs/1112.2297v1

Nonlinear Sciences

Adaptation and Self-Organizing Systems

These lectures are based on material which was presented in the Summer school at University of S\~ao Paulo, and in the winter

Scientific paper

We give a succinct and self-contained description of the synchronized motion on networks of mutually coupled oscillators. Usually, the stability criterion for the stability of synchronized motion is obtained in terms of Lyapunov exponents. We consider the fully diffusive case which is amenable to treatment in terms of uniform contractions. This approach provides a rigorous, yet clear and concise, way to the important results.

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