Boolean Monomial Dynamical Systems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2004
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| _version_ | 1866912120976703488 |
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| author | Colon-Reyes, Omar Laubenbacher, Reinhard Pareigis, Bodo |
| author_facet | Colon-Reyes, Omar Laubenbacher, Reinhard Pareigis, Bodo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0403166 |
| institution | arXiv |
| publishDate | 2004 |
| record_format | arxiv |
| spellingShingle | Boolean Monomial Dynamical Systems Colon-Reyes, Omar Laubenbacher, Reinhard Pareigis, Bodo Combinatorics 05C38, 68R10, 94C10 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. |
| title | Boolean Monomial Dynamical Systems |
| topic | Combinatorics 05C38, 68R10, 94C10 |
| url | https://arxiv.org/abs/math/0403166 |