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Lee Deville : Stochastic dynamics on networks. Emergence of collective behaviors

Dynamical systems defined on networks have applications in many fields in science and engineering. In particular, it is important to understand when networks exhibit synchronous or other types of coherent collective behaviors. Other questions include whether such coherent behavior is stable with respect to random perturbation, or how to described the detailed structure of this behavior during its evolution. We will examine the mathematical challenges of understanding these questions for networked dynamical systems with a particular focus on the dynamics of the Kuramoto oscillator model.

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