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Noise induced rhythmic phenomena

Large families of noisy interacting units (cells, individuals, components in a circuit,...) exhibiting synchronization often exhibit oscillatory behaviors too. This is a well established empirical observation that has attracted a remarkable amount of attention, notably in life sciences, because of the central role played by internally generated rhythms. This modeling effort has produced a number of elementary models that seem to capture the essence, or at least some essential features, of this phenomenon. The mathematical analysis however is still very challenging and often out of reach. The talk will focus on a class of models proposed by Kuramoto and coauthors, for which some results can be established. In spite of the fact that noise plays a crucial role, the core of the analysis is at the level of the PDE that provides an accurate description of the model in the limit of a very large number of units in interaction.

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