Does dynamics reflect topology in directed networks?M. Timme
Center for Applied Mathematics, Cornell University, Theoretical and Applied Mechanics Kimball Hall - Ithaca, NY 14853, USA and Max Planck Institute for Dynamics and Self-Organization (MPIDS) Bernstein Center for Computational Neuroscience (BCCN) Göttingen Bunsenstr. 10, 37073 Göttingen, Germany
received 9 May 2006; accepted in final form 12 September 2006
published online 11 October 2006
We present and analyze a topologically induced transition from ordered, synchronized to disordered dynamics in directed networks of oscillators. The analysis reveals where in the space of networks this transition occurs and its underlying mechanisms. If disordered, the dynamics of the units is precisely determined by the topology of the network and thus characteristic for it. We develop a method to predict the disordered dynamics from topology. The results suggest a new route towards understanding how the precise dynamics of the units of a directed network may encode information about its topology.
05.45.-a - Nonlinear dynamics and chaos.
87.10.+e - General theory and mathematical aspects.
89.75.-k - Complex systems.
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