Dynamics and evolution of biological and social networks

Turing patterns in random networks

Author: Hiroya Nakao, Fritz-Haber-Institut der MPG / Kyoto Univ..

Names and affiliation of other authors:
Alexander S. Mikhailov (Fritz-Haber-Institut der MPG)

Oral presentation

We analyze diffusion-induced instability of reaction-diffusion systems on random networks. As in the ordinary Turing instability in continuous media, a homogeneous state loses its stability and gives way to inhomogeneous states when the diffusion of the inhibitor is sufficiently faster than that of the activator. We formulate linear stability of the homogeneous state using the Laplacian eigenvectors of the network, and then present numerical results of the Brusselator and Mimura-Murray models on the Erdos-Renyi and Barabasi-Albert networks. We show that the final stationary patterns are considerably different from the unstable linear modes even in the vicinity of the bifurcation point, and that those patterns can, to a certain extent, be explained based on a simple mean-field approximation of the random networks.

Dynamics and evolution of biological and social networks. February 18-20th, 2008. Mallorca, Spain.