Regulatory dynamics on random networks: Asymptotic periodicity and modularity
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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 almost certainly converge to a periodic attractor. We study the subnetworks, which we call modules, where the periodic asymptotic oscillations are concentrated. We prove that those modules are dynamically equivalent to independent regulatory networks. © 2008 IOP Publishing Ltd and London Mathematical Society.