Dynamics on network structures are fundamental models for the behaviour of complex systems, modelling physical, biological and societal systems, including the brain, food webs, epidemic diseases in populations, power grids and many others. Such dynamical networks can exhibit behavior in which deterministic chaos, exhibiting unpredictability and disorder, coexists with synchronisation, a classical paradigm of order.
In the preceding decades, our mathematical understanding of collective behavior on complex networks has increased significantly. In this winter school, we will survey the main theory behind synchronization phenomena in networks and discuss applications to secure communication, parameter estimation and the anticipation of chaos.
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