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Hierarchical pattern formation

Lionel Gil

Mercredi 23 avril 2014

à 11h en salle C. Brot

Our playground consists in a set of nonlinear Kuramoto’s oscillators, not necessarily identical, which are linearly coupled one with each other through a network of connections. The connections are weighted and directed such that between two coupled oscillators exists the notion of leader and follower, of master and slave.

Among the numerous dynamical regimes, we focus on the synchronized solution which is characterized by a locking in phase of all the non-linear oscillators. We investigate the dynamical and structural stability of this synchronized behavior and especially, we study the way the geometry of the connection network influences its stability.

In the framework of this model, we can then compare democratic and pyramidal organizations and explain why the latter, although less stable, may persists from an evolutionist point of view.