Nonlinear Dynamics of Networks
CSIC Building (#406),
Seminar Room 4122.
Directions: www.cscamm.umd.edu/directions

Dynamic networks and directed percolation
Reuven Cohen
BarIlan University

Abstract:
We introduce a model for dynamic networks, where the links or the strengths of the links change over time. We solve the model by mapping dynamic networks to the problem of directed percolation, where the direction corresponds to the time evolution of the network. We show that the dynamic network undergoes a percolation phase transition at a critical concentration p_{c}, that decreases with the rate r at which the network links are changed. The behavior near criticality is universal and independent of r. We find that for dynamic random networks fundamental laws are changed. (i) The size of the giant component at criticality scales with the network size N for all values of r, rather than as N^{2/3} in static networks. (ii) In the presence of a broad distribution of disorder, the optimal path length between two nodes in a dynamic network scales as N^{1/2}, compared to N^{1/3} in a static network. (joint work with Roni Parshani, Mark Dickison, H. Eugene Stanley and Shlomo Havlin) 
