On the Lyapunov Exponent of Monotone Boolean Networks †

Ilya Shmulevich
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Ilya Shmulevich: Institute for Systems Biology, Seattle, WA 98103, USA

Mathematics, 2020, vol. 8, issue 6, 1-13

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.

Keywords: lyapunov exponent; monotone boolean function; boolean network (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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