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SYBN: Biological and Social Networks

SYBN 3: Biologische und Soziale Netzwerke, Postersitzung

SYBN 3.4: Poster

Monday, March 7, 2005, 14:00–15:30, Poster TU E

Dynamic Response Behavior of Random Networks — •Haijun Zhou and Reinhard Lipowsky — Max-Planck-Institute of Colloids and Interfaces, Potsdam 14424

A general class of dynamic models on random networks is studied by analytical methods and computer simulations. The networks differ in their connectivity and in their degree distribution, P(k), which represents the probability that a vertex is connected to k nearest neighbors. Each vertex can attain two internal states described by binary variables or Ising–like spins which evolve in time according to local majority rules. Scale–free networks, for which the degree distribution has the power law tail P(k)∼ k^−γ, are shown to exhibit qualitatively different response behavior for γ ≤ 5/2 and γ > 5/2. For γ ≤ 5/2, even infinite networks recover from any perturbation within a finite response time. For γ > 5/2, this time diverges with the size of the network. This different response behavior sheds new light on the empirical observation that many real-world networks are scale–free with 2 < γ <5/2.