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The stabilizing effect of noise on the dynamics of a Boolean network

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  • Goodrich, Christopher S.
  • Matache, Mihaela T.

Abstract

In this paper, we explore both numerically and analytically the robustness of a synchronous Boolean network governed by rule 126 of cellular automata. In particular, we explore whether or not the introduction of noise into the system has any discernable effect on the evolution of the system. This noise is introduced by changing the states of a given number of nodes in the system according to certain rules. New mathematical models are developed for this purpose. We use MATLAB to run the numerical simulations including iterations of the real system and the model, computation of Lyapunov exponents (LyE), and generation of bifurcation diagrams. We provide a more in-depth fixed-point analysis through analytic computations paired with a focus on bifurcations and delay plots to identify the possible attractors. We show that it is possible either to attenuate or to suppress entirely chaos through the introduction of noise and that the perturbed system may exhibit very different long-term behavior than that of the unperturbed system.

Suggested Citation

  • Goodrich, Christopher S. & Matache, Mihaela T., 2007. "The stabilizing effect of noise on the dynamics of a Boolean network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(1), pages 334-356.
    • Handle: RePEc:eee:phsmap:v:379:y:2007:i:1:p:334-356
    DOI: 10.1016/j.physa.2006.12.043
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    References listed on IDEAS

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    1. Barabási, Albert-László & Albert, Réka & Jeong, Hawoong, 1999. "Mean-field theory for scale-free random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 272(1), pages 173-187.
    2. Fan, Jin & Li, Xiang & Fan Wang, Xiao, 2005. "On synchronous preference of complex dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(2), pages 657-666.
    3. Marr, Carsten & Hütt, Marc-Thorsten, 2005. "Topology regulates pattern formation capacity of binary cellular automata on graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 641-662.
    4. Fan, Jin & Wang, Xiao Fan, 2005. "On synchronization in scale-free dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(3), pages 443-451.
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    Cited by:

    1. Malarz, Krzysztof & Kułakowski, Krzysztof, 2021. "Heider balance of a chain of actors as dependent on the interaction range and a thermal noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    2. Beck, Gary L. & Matache, Mihaela T., 2008. "Dynamical behavior and influence of stochastic noise on certain generalized Boolean networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(19), pages 4947-4958.

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