Symmetry in critical random Boolean network dynamics

Shabnam Hossein, Matthew D. Reichl, and Kevin E. Bassler
Phys. Rev. E 89, 042808 – Published 16 April 2014

Abstract

Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used both to greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. There are classes of functions that consist of Boolean functions that behave similarly. These classes are orbits of the controlling symmetry group. We find that the symmetry that controls the critical random Boolean networks is expressed through the frequency by which output functions are utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using the symmetry of the behavior of the nodes to characterize complex network dynamics, and introduce an alternative approach to the analysis of heterogeneous complex systems.

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  • Received 24 January 2014

DOI:https://doi.org/10.1103/PhysRevE.89.042808

©2014 American Physical Society

Authors & Affiliations

Shabnam Hossein1,2, Matthew D. Reichl1,2,*, and Kevin E. Bassler1,2,3,†

  • 1Department of Physics, University of Houston, Houston, Texas 77204-5005, USA
  • 2Texas Center for Superconductivity, University of Houston, Houston, Texas 77204-5002, USA
  • 3Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, Dresden D-01187, Germany

  • *Present address: Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853.
  • Permanent address: Department of Physics, University of Houston, Houston, Texas 77204-5005, USA; bassler@uh.edu

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Issue

Vol. 89, Iss. 4 — April 2014

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