Coevolution of information processing and topology in hierarchical adaptive random Boolean networks
Faculty of Physics, Center of Excellence for Complex Systems
Research, Warsaw University of Technology, Koszykowa 75, 00-662
2 Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Palma de Mallorca, Spain
3 ITMO University, 19, Kronverkskiy av., 197101 Saint Petersburg, Russia
Received: 30 June 2015
Received in final form: 30 October 2015
Published online: 8 February 2016
Random Boolean Networks (RBNs) are frequently used for modeling complex systems driven by information processing, e.g. for gene regulatory networks (GRNs). Here we propose a hierarchical adaptive random Boolean Network (HARBN) as a system consisting of distinct adaptive RBNs (ARBNs) – subnetworks – connected by a set of permanent interlinks. We investigate mean node information, mean edge information as well as mean node degree. Information measures and internal subnetworks topology of HARBN coevolve and reach steady-states that are specific for a given network structure. The main natural feature of ARBNs, i.e. their adaptability, is preserved in HARBNs and they evolve towards critical configurations which is documented by power law distributions of network attractor lengths. The mean information processed by a single node or a single link increases with the number of interlinks added to the system. The mean length of network attractors and the mean steady-state connectivity possess minima for certain specific values of the quotient between the density of interlinks and the density of all links in networks. It means that the modular network displays extremal values of its observables when subnetworks are connected with a density a few times lower than a mean density of all links.
Key words: Statistical and Nonlinear Physics
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