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Lyapunov exponents in random Boolean networks

Author

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  • Luque, Bartolo
  • Solé, Ricard V.

Abstract

A new order parameter approximation to random boolean networks (RBN) is introduced, based on the concept of Boolean derivative. A statistical argument involving an annealed approximation is used, allowing to measure the order parameter in terms of the statistical properties of a random matrix. Using the same formalism, a Lyapunov exponent is calculated, allowing to provide the onset of damage spreading through the network and how sensitive it is to minimal perturbations. Finally, the Lyapunov exponents are obtained by means of different approximations: through distance method and a discrete variant of the Wolf's method for continuous systems.

Suggested Citation

  • Luque, Bartolo & Solé, Ricard V., 2000. "Lyapunov exponents in random Boolean networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 33-45.
    • Handle: RePEc:eee:phsmap:v:284:y:2000:i:1:p:33-45
    DOI: 10.1016/S0378-4371(00)00184-9
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    Cited by:

    1. Zozor, S. & Ravier, P. & Buttelli, O., 2005. "On Lempel–Ziv complexity for multidimensional data analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 345(1), pages 285-302.
    2. Ilya Shmulevich, 2020. "On the Lyapunov Exponent of Monotone Boolean Networks †," Mathematics, MDPI, vol. 8(6), pages 1-13, June.
    3. Ballesteros, Fernando J & Luque, Bartolo, 2002. "Random Boolean networks response to external periodic signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 313(3), pages 289-300.

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