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Boolean Monomial Dynamical Systems
Omar Colón-Reyes1, Reinhard Laubenbacher1, and Bodo Pareigis2
1Virginia Bioinformatics Institute, Virginia Tech, Blacksburg, VA 24061-0477, USA
ocolonre@calvin.math.vt.edu, reinhard@vbi.vt.edu
2Mathematisches Institut der Universität München, 80333 München, Germany
pareigis@lmu.de
Annals of Combinatorics 8 (4) p.425-439 December, 2004
AMS Subject Classification: 37F20, 37B15, 05C20, 11T06, 68R05, 68U20
Abstract:
An important problem in the theory of finite dynamical systems is to link the structure of a system with its dynamics. This paper contains such a link for a family of nonlinear systems over the field with two elements. For systems that can be described by monomials (including Boolean AND systems), one can obtain information about the limit cycle structure from the structure of the monomials. In particular, the paper contains a sufficient condition for a monomial system to have only fixed points as limit cycles. This condition depends on the cycle structure of the dependency graph of the system and can be verified in polynomial time.
Keywords: polynomial dynamical system, finite field, state space structure

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