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Chaotic Mean Field Dynamics Of A Boolean Network With Random Connectivity

Author

Listed:
  • 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)

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.

Suggested Citation

  • Maliackal Poulo Joy & Donald E. Ingber & Sui Huang, 2007. "Chaotic Mean Field Dynamics Of A Boolean Network With Random Connectivity," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 18(09), pages 1459-1473.
    • Handle: RePEc:wsi:ijmpcx:v:18:y:2007:i:09:n:s0129183107011467
    DOI: 10.1142/S0129183107011467
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    Cited by:

    1. Thomas Parmer & Luis M. Rocha & Filippo Radicchi, 2022. "Influence maximization in Boolean networks," Nature Communications, Nature, vol. 13(1), pages 1-11, December.

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