Regulatory Dynamics on Random Networks: Asymptotic Periodicity and Modularity

Anne Cros, Antonio Morante, Edgardo Ugalde

Published 2007-07-11, updated 2008-02-01Version 3

We study the dynamics of discrete-time regulatory networks on random digraphs. For this we define ensembles of deterministic orbits of random regulatory networks, and introduce some statistical indicators related to the long-term dynamics of the system. We prove that, in a random regulatory network, initial conditions converge almost surely to a periodic attractor. We study the subnetworks, which we call modules, where the periodic asymptotic oscillations are concentrated. We proof that those modules are dynamically equivalent to independent regulatory networks.