Boolean Monomial Dynamical Systems |
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Authors: | Omar Colón-Reyes Reinhard Laubenbacher Bodo Pareigis |
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Affiliation: | (1) Virginia Bioinformatics Institute, Virginia Tech, Blacksburg, VA 24061-0477, USA;(2) Mathematisches Institut der Universität München, 80333 München, Germany |
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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.Received February 2, 2004 |
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Keywords: | 37F20 37B15 05C20 11T06 68R05 68U20 |
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