**Séminaire
Exceptionnel**

"Matière et Systèmes Complexes"

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Jeudi
27 mars 2008 à 11h

Bâtiment Condorcet, 4^{ème}
étage, salle 454 A.

Leonid
Bunimovich

(Georgia Tech)

We develop a symbolic dynamics approach to the studies of dynamical networks with arbitrary topology (structure of the graph of interactions).

This approach is a development of the one introduced by Sinai and the speaker to the studies of Coupled Map Lattices, where the graph of interactions is just a lattice. The new approach allows to analyse a combined effect of all three features which characterize a dynamical network (complexity of its topology and the strengthes if local dynamics and interactions). The networks are of the most general type, e.g. the local systems and interactions need not to be homogeneous. nor restrictions are imposed on a structure of the graph of interactions.

We obtain general conditions on stability of dynamical networks and demonstrate that some subnetworks can evolve regularly while the others evolve chaotically.