Berlin 2012 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 20: Networks III
DY 20.2: Talk
Wednesday, March 28, 2012, 15:15–15:30, MA 004
Traveling fronts and stationary patterns in bistable reaction-diffusion systems on networks — •Nikos Kouvaris1, Hiroshi Kori2, and Alexander Mikhailov1 — 1Department of Physical Chemistry, Fritz Haber Institute of the Max Planck Society, Faradayweg 4-6, D-14195 Berlin, Germany — 2Division of Advanced Sciences, Ochadai Academic Production, Ochanomizu University, Tokyo 112-8610, Japan
We focus on activation fronts in bistable one-component systems on large complex networks. Fronts can trigger a transition from the one stable state to the other which spreads in the entire network. However, depending on the connectivity pattern of the network and the strength of diffusive coupling, the fronts can be pinned forming stationary localized patterns or can be retracted into their sources. Particularly, a front can be spread through nodes with low degrees, can be pinned at nodes with higher degrees, or can be retracted from nodes with even higher degrees. Similar behavior is observed for various values of coupling. This reach dynamical behavior can be described in terms of a mean field theory, while for the specific class of complete k-ary tree networks, saddle-node bifurcations have been found that distinguish the different dynamical regimes of traveling fronts and stationary patterns. Theoretical predictions have been verified by numerical simulations in large k-ary trees, Erdös-Rényi and scale-free networks, showing a very good agreement.