Boolean monomial dynamical systems

Annals of Combinatorics

Volumn 8, Issue 4, 2005, Pages 425-439

  Colón Reyes, Omar ^a   Laubenbacher, Reinhard ^a   Pareigis, Bodo ^b  

^a VIRGINIA BIOINFORMATICS INSTITUTE   (United States)

^b UNIVERSITY OF MUNICH   (Germany)

Author keywords

Finite field; Polynomial dynamical system; State space structure

Indexed keywords

EID: 13844297775     PISSN: 02180006     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00026-004-0230-6     Document Type: Article

References (20)

1. R. Albert and H.G. Othmer, The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in Drosophila melanogaster, J. Theoret. Biol. 223 (2003) 1-18.
2. C.L. Barrett and C.M. Reidys, Elements of a theory of simulation, I: sequential CA over random graphs, Appl. Math. Comput. 98 (1999) 241-259.
3. C.L. Barrett, H.S. Mortveit, and C.M. Reidys, Elements of a theory of computer simulation II: sequential dynamical systems, Appl. Math. Comput. 107 (2-3) (1999) 121-136.
4. C.L. Barrett, H.S. Mortveit, and C.M. Reidys, Elements of a theory of computer simulation III: equivalence of SDS, Appl. Math. Comput. 122 (2001) 325-340.
5. F. Celada and P.E. Seiden, A computer model of cellular interactions in the immune system, Immunol. Today 13 (1992) 56-62.
6. P. Cull, Linear analysis of switching nets, Kybernetika 8 (1971) 31-39.
7. B. Elspas, The theory of autonomous linear sequential networks, IRE Transactions on Circuit Theory CT-6 (1959) 45-60.
8. R. Germundsson, J. Gunnarsson, and J. Plantin, Symbolic algebraic discrete systems-applied to the JAS39 fighter aircraft, technical report, Linköping University, Linköping, Sweden, December, 1994.
9. R.A. Hernández Toledo, Linear Finite Dynamical Systems, preprint, 2003.
10. S.A. Kauffman, Metabolic stability and epigenesis in randomly constructed genetic nets, J. Theoret. Biol. 22 (1969) 437-467.
11. A. Khrennikov and M. Nilsson, On the number of cycles of p-adic dynamical systems, J. Number Theory 90 (2001) 255-264.
12. R. Laubenbacher, A computer algebra approach to biological systems, Proc. Intl. Symp. Symbolic and Alg. Comp., Philadelphia, Assoc. Comp. Mach., 2003.
13. R. Laubenbacher and B. Pareigis, Equivalence relations on finite dynamical systems, Adv. Appl. Math. 26 (2001) 237-251.
14. R. Laubenbacher and B. Pareigis, Decomposition and simulation of sequential dynamical systems, Adv. Appl. Math. 30 (2003) 655-678.
15. R. Laubenbacher and B. Stigler, A computational algebra approach to the reverse-engineering of gene regulatory networks, J. Theoret. Biol. 229 (2004) 523-537.
16. R. Lidl and H. Niederreiter, Finite Fields, Encyclopedia of Math and its Appl, 20, Cambridge University Press, London, 1997.
17. H. Marchand and M. LeBorgne, On the optimal control of polynomial dynamical systems over Z/p, Fourth workshop on Discrete Event Systems, Cagliari, Italy, IEEE, 1998.
18. H. Marchand and M. LeBorgne, Partial order discrete event systems modeled as polynomial dynamical systems, IEEE Intl. Conf. on Control Applications, Trieste, Italy, 1998.
19. D.K. Milligan and M.J.D. Wilson, The behaviour of affine sequential Boolean networks, Connection Science 5 (1993) 153-167.
20. S. Wolfram, Cellular Automata and Complexity, Westview Press, 1994.