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On the Lyapunov Exponent of Monotone Boolean Networks †

Author

Listed:
  • Ilya Shmulevich

    (Institute for Systems Biology, Seattle, WA 98103, USA)

Abstract

Boolean networks are discrete dynamical systems comprised of coupled Boolean functions. An important parameter that characterizes such systems is the Lyapunov exponent, which measures the state stability of the system to small perturbations. We consider networks comprised of monotone Boolean functions and derive asymptotic formulas for the Lyapunov exponent of almost all monotone Boolean networks. The formulas are different depending on whether the number of variables of the constituent Boolean functions, or equivalently, the connectivity of the Boolean network, is even or odd.

Suggested Citation

  • Ilya Shmulevich, 2020. "On the Lyapunov Exponent of Monotone Boolean Networks †," Mathematics, MDPI, vol. 8(6), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:1035-:d:375689
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    References listed on IDEAS

    as
    1. 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.
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