Regulatory Dynamics on Random Networks: Asymptotic Periodicity and Modularity

Details Regulatory Dynamics on Random Networks: Asymptotic Periodicity and Modularity Regulatory Dynamics on Random Networks: Asymptotic Periodicity and Modularity

2007-07-11

arxiv.org/abs/0707.1551v3

Mathematics

Dynamical Systems

23 pages, 3 figures

Scientific paper

10.1088/0951-7715/21/3/009

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.

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