Stability of Synchronized Motion in Complex Networks

Abstract

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.

These lectures are based on material which was presented in the Summer school at University of São Paulo, UFABC, and Imperial College