Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1897113 | Physica D: Nonlinear Phenomena | 2008 | 11 Pages |
Abstract
Discrete-time regulatory networks are dynamical systems on directed graphs with a structure that is inspired on natural systems of interacting units. Using a notion of determination between vertices, we define sets of dominant vertices, and we prove that in the asymptotic regime, the projection of the dynamics on a dominant set allows us to determine the state of the whole system at all times. We provide an algorithm to find sets of dominant vertices, and we test its accuracy on several examples. We also explore the possibility of using the dominant set characteristics as a measure of the structural complexity of networks.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Beatriz Luna, Edgardo Ugalde,