CHAOTIC MEAN FIELD DYNAMICS OF A BOOLEAN NETWORK WITH RANDOM CONNECTIVITY

Maliackal Poulo Joy (), Donald E. Ingber () and Sui Huang ()
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Maliackal Poulo Joy: Vascular Biology Program, Children's Hospital and Harvard Medical School, 300 Longwood Ave, Boston, MA 02115, USA
Donald E. Ingber: Vascular Biology Program, Children's Hospital and Harvard Medical School, 300 Longwood Ave, Boston, MA 02115, USA
Sui Huang: Vascular Biology Program, Children's Hospital and Harvard Medical School, 300 Longwood Ave, Boston, MA 02115, USA

International Journal of Modern Physics C (IJMPC), 2007, vol. 18, issue 09, 1459-1473

Abstract: Random Boolean networks have been used as simple models of gene regulatory networks, enabling the study of the dynamic behavior of complex biological systems. However, analytical treatment has been difficult because of the structural heterogeneity and the vast state space of these networks. Here we used mean field approximations to analyze the dynamics of a class of Boolean networks in which nodes have random degree (connectivity) distributions, characterized by the mean degreekand varianceD. To achieve this we generalized the simple cellular automata rule 126 and used it as the Boolean function for all nodes. The equation for the evolution of the density of the network state is presented as a one-dimensional map for various input degree distributions, withkandDas the control parameters. The mean field dynamics is compared with the data obtained from the simulations of the Boolean network. Bifurcation diagrams and Lyapunov exponents for different parameter values were computed for the map, showing period doubling route to chaos with increasingk. Onset of chaos was delayed (occurred at higherk) with the increase in varianceDof the connectivity. Thus, the network tends to be less chaotic when the heterogeneity, as measured by the variance of connectivity, was higher.

Keywords: Boolean network; cellular automata; chaos; Lyapunov exponent; mean field theory; 82.40.Bj; 02.50.-r; 05.45.Pq; 05.50.+q; 87.10.+e (search for similar items in EconPapers)
Date: 2007
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0129183107011467

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