Max Planck Institute for Dynamics and Self-Organization -- Department for Nonlinear Dynamics and Network Dynamics Group
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Tuesday, 02.02.2010 17 c.t.

Spectra and synchronization of networks

by Prof. Dr. Jürgen Jost
from Complex Structures in Biology and Cognition, Max Planck Institute for Mathematics in the Sciences

Contact person: Fred Wolf


Seminarraum Haus 2, 4. Stock (Bunsenstr.)


I discuss the question fo the synchronization of coupled dynamics on networks which is important in various applications, for instance as a proposed theoretical framework for understanding neuronal coordination of the various sensory features of complex objects. The starting point for my formal investigation is the old paradigm of coupled map lattices introduced by Kaneko. It turns out that on the basis of the spectrum of the underlying network Laplacian and suitable Lyapunov type exponents, one can develop a rather general framework that can handle various coupling schemes and also transmission delays. The synchronized dynamics can become more complicated than the dynamical behavior that the individual network elements are capable of in isolation, but of course, in other situations, it can also lead to simpler coherent patterns. The network structure enters via estimates on the eigenvalues of the aforementioned Laplacian. These estimates control for instance the cohesion of the network or how close it is to being bipartite. The talk represents joint work with Fatihcan Atay and Frank Bauer.

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