Berlin 2008 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 22: Statistical physics of complex networks II
DY 22.2: Talk
Wednesday, February 27, 2008, 17:00–17:15, MA 004
Dynamical Clustering in Reaction-Dispersal Processes on Complex Networks — •Vincent David1, Marc Timme1,4, Theo Geisel1,2,4, and Dirk Brockmann1,3 — 1Max-Planck-Institute for Dynamics and Self-Organization, Göttingen — 2Georg-August-Universität, Göttingen — 3Northwestern University, Evanston — 4Bernstein Center for Computational Neuroscience, Göttingen
We investigate nonlinear annihilation processes (e.g., A+A→ ∅ ) of particles that perform random walks on complex networks. In well mixed populations (mean field) this process exhibits t−1 decay behavior in the total number of particles. Additional dispersal of particles adds a second time scale and drastically changes the decay behavior.
Here we study these changes for two types of hopping processes. First, if particles independently select one of the possible exit channels at each node their exit rates are given by the sum of all outgoing weights such that the waiting times are degree-dependent. We compare this to the popular ansatz of a uniform waiting time process.
Derived mean field equations show that for large numbers of particles per node both processes exhibit nearly identical relaxation properties. However, below a critical particle number the processes deviate not only from mean field predictions but, more importantly, by orders of magnitude from one another. We attribute this to dynamical clustering effects in the uniform waiting time model, that is absent in the independent channel dynamics. We conclude that the prediction of dynamical properties of reaction-diffusion processes on complex networks drastically depend on the appropriate choice of model.