From cellular automaton rules to a macroscopic mean-field description

Acta Physica Polonica B, Proceedings Supplement

Volumn 3, Issue 2, 2010, Pages 399-416

  Hatzikirou, H ^a   Brusch, L ^a   Deutsch, A ^a  

^a DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BIOLOGICAL GROWTH; COMPLEX SYSTEMS; LATTICE-GAS; MEAN FIELD APPROXIMATION; MEAN-FIELD DESCRIPTION; PATTERN FORMATION; SELF ORGANIZING; SIMPLE MODEL; SPATIAL PATTERNS; SPATIOTEMPORAL PATTERNS;

ACOUSTIC WAVE VELOCITY; CELLULAR AUTOMATA; FLAME RESISTANCE; PATTERN RECOGNITION SYSTEMS; ROBOTS; SPEECH RECOGNITION; TRANSLATION (LANGUAGES);

AUTOMATA THEORY;

EID: 78651551971     PISSN: 18992358     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (19)

1. N. Boccara, Modeling Complex Systems, Springer, 2004.
2. M. Boerlijst, Math. Biosc. 200, 118 (2006).
3. J.P. Boon, D. Dab, R. Kapral, A. Lawniczak, Phys. Rep. 273, 55 (1996).
4. B. Chopard, M. Droz, Cellular Automata Modeling of Physical Systems, Cambridge University Press, Cambridge 1998.
5. A. Deutsch, S. Dormann, Cellular Automaton Modeling of Biological Pattern Formation, Birkhauser, 2005.
6. G.D. Doolen, Lattice Gas Methods for Partial Differential Equations, Addison-Wesley, New York 1990.
7. R.A. Fisher, The Genetical Theory of Natural Selection, Oxford University Press, 1930.
8. U. Frisch, D. d'Humieres, B. Hasslacher, P. Lallemand, Y. Pomeau, J.P. Rivet, Compl. Syst. 1, 649 (1987).
9. H. Hatzikirou, L. Brusch, C. Schaller, M. Simon, A. Deutsch, Comput. Math. Appl. in print.
10. H. Hatzikirou, A. Deutsch, Curr. Top. Dev. Biol. 81, 401 (2008).
11. R. Kapral, X. Wu, Physica D 103, 314 (1997).
12. A.T. Lawniczak, Transp. Theor. Stat. Phys. 29, 261 (2000).
13. J. Murray, Mathematical Biology I: An Introduction, Springer, 2001.
14. D.H. Rothman, S. Zaleski, Rev. Mod. Phys. 66(4), 1417 (1994).
15. R.F. Verhulst, Nouv. mm. de l'Academie Royale des Sci. et Belles-Lettres de Bruxelles, 18, 1 (1845).
16. J. von Neumann, Theory of Self-Reproducing Automata, Urbana, University of Illinois Press, 1966.
17. D.A. Wolf-Gladrow, Lattice-Gas Cellular Automata and Lattice Boltzmann Models - An Introduction, Springer, 2005.
18. S. Wolfram, A New Kind of Science, Wolfram Media, Inc., 2002.
19. X. Wu, R. Kapral, J. Chem. Phys. 100, 5936 (1994).