On the topological sensitivity of cellular automata

Chaos

Volumn 21, Issue 2, 2011, Pages

  Baetens, Jan M ^a   De Baets, Bernard ^a  

^a GHENT UNIVERSITY   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; BIOLOGICAL MODEL; CELL;

CELLS; MODELS, BIOLOGICAL;

EID: 79960013984     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3535581     Document Type: Article

References (39)

1. Alexandridis A. Vakalis D. Siettos C. Bafas G. A cellular automata model for forest fire spread prediction: The case of the wildfire that swept through Spetses Island in 1990. Appl. Math. Comput. 2008, 204:191. 10.1016/j.amc.2008.06.046, and 201.
2. Amari S.I. A method of statistical neurodynamics. 1974, 10.1016/j.amc.2008.06.046, Kybernetik 14.
3. Atmanspacher H. Filk T. Scheingrabe H. Stability analysis of coupled map lattices at locally unstable fixed points. Eur. Phys. J. B 2005, 44:229. 10.1140/epjb/e2005-00119-2, and 239.
4. Baetens J. M. De Baets B. Phenomenological study of irregular cellular automata based on Lyapunov exponents and Jacobians. Chaos 2010, 20:033112. 10.1063/1.3460362.1, and .
5. Bagnoli F. Rechtman R. Synchronization and maximum Lyapunov exponents of cellular automata. Phys. Rev. E 1999, 59:R1307-R1310. 10.1103/PhysRevE.59.R1307, and .
6. Bagnoli F. Rechtman R. Thermodynamic entropy and chaos in a discrete hydrodynamical system. Phys. Rev. E 2009, 79:041115. 10.1103/PhysRevE.79.041115, and .
7. Bagnoli F. Rechtman R. Ruffo S. Damage spreading and Lyapunov exponents in cellular automata. Phys. Lett. A 1992, 172:34. 10.1016/0375-9601(92)90185-O, and 38.
8. Baltzer H. Braun P.W. Köhler W. Cellular automata models for vegetation dynamics. Ecol. Modell. 1998, 107:113. 10.1016/S0304-3800(97)00202-0, and 125.
9. Batty M. Cellular dynamics: Modelling urban growth as a spatial epidemic. Geocomputational Modelling 2001, 109-141. M. M. Fischer, Y. Leung, in edited by and (Springer, Berlin, Germany)
10. Berjak S.G. Hearne J.W. An improved cellular automaton model for simulating fire in a spatially heterogeneous savanna system. Ecol. Modell. 2002, 148:133-151. 10.1016/S0304-3800(01)00423-9, and .
11. Burton D.M. The History of Mathematics: An Introduction 2005, 6th ed., (McGraw-Hill, New York).
12. Chopard B. Luthi P.O. Queloz P.A. Cellular automata model of car traffic in a two-dimensional street network. J. Phys. A 1996, 29:2325-2336. 10.1088/0305-4470/29/10/012, and .
13. Courbage M. Kamiński B. Space-time directional Lyapunov exponents for cellular automata. J. Stat. Phys. 2006, 124:1499-1599. 10.1007/s10955-006-9172-1, and .
14. Courbage M. Kamiński B. On Lyapunov exponents for cellular automata. J. Cell. Autom. 2009, 4:159-168. and .
15. Deutsch A. Dormann S. Cellular Automaton Modeling of Biological Pattern Formation: Characterization, Applications, and Analysis 2005, and (Birkhäuser, Bonn).
16. Doran R.J. Laffan S.W. Simulating the spatial dynamics of foot and mouth disease outbreaks in feral pigs and livestock in Queensland, Australia, using a susceptible-infected-recovered cellular automata model. Prev. Vet. Med. 2005, 70:133-152. 10.1016/j.prevetmed.2005.03.002, and .
17. Encinas L.H. White S.H. del Rey A.M. Sánchez G.R. Modelling forest fire spread using hexagonal cellular automata. Appl. Math. Modell. 2007, 31:1213-1227. 10.1016/j.apm.2006.04.001, and .
18. Eschenauer H.A. Olhoff N. Topology optimization of continuum structures: A review. Appl. Mech. Rev. 2001, 54:331-390. 10.1115/1.1388075, and .
19. Fatés N. Morvan M. Perturbing the topology of the Game of Life increases its robustness to asynchrony. Lect. Notes Comput. Sci. 2004, 3305:111-120. 10.1007/978-3-540-30479-1_12, and .
20. Ilachinski A. Cellular Automata. A Discrete Universe 2001, (World Scientific, London).
21. Langton C.G. Computation at the edge of chaos. Physica D 1990, 42:12. 10.1016/0167-2789(90)90064-V, .
22. Lyapunov A.M. The General Problem of the Stability of Motion 1992, 270. (Taylor & Francis, London)
23. Mallet D.G. De Pillis L.G. A cellular automata model of tumor-immune system interactions. J. Theor. Biol. 2006, 239:334-350. 10.1016/j.jtbi.2005.08.002, and .
24. O'Sullivan D.B. Graph-Based Cellular Automaton Models of Urban Spatial Processes. 2000, Ph.D. dissertation (University of London, London).
25. Picioreanu C. van Loosdrecht M.C. M. Heijnen J.J. Mathematical modeling of biofilm structure with a hybrid differential-discrete cellular automaton approach. Biotechnol. Bioeng. 1998, 58:101. 10.1002/(SICI)1097-0290(19980405)58:1<>1.0.CO;2-5, and .
26. Pizarro G. Griffeath D. Noguera D.R. Quantitative cellular automaton model for biofilms. J. Environ. Eng. 2001, 127:782. 10.1061/(ASCE)0733-9372(2001)127:9(782), and 789.
27. Qi A. Zheng X. Du C. An B. A cellular automaton model of cancerous growth. J. Theor. Biol. 1993, 161:1-12. 10.1006/jtbi.1993.1035, and .
28. Rouquier J.-B. Morvan M. Combined effect of topology and synchronism perturbation on cellular automata: Preliminary results. Lect. Notes Comput. Sci. 2004, 5191:220-227. 10.1007/978-3-540-79992-4_28, and .
29. Schiff J.L. Cellular Automata: A Discrete View of the World 2008, (Wiley, Chichester).
30. Shereshevsky M.A. Lyapunov exponents for one-dimensional cellular automata. J. Nonlinear Sci. 1991, 2:1-8. 10.1007/BF02429850, .
31. Tisseur P. Cellular automata and Lyapunov exponents. Nonlinearity 2000, 13:1547-1560. 10.1088/0951-7715/13/5/308, .
32. Tonguz O.K. Viriyasitavat W. Bai F. Modeling urban traffic: A cellular automata approach. IEEE Commun. Mag. 2009, 47:142-150. 10.1109/MCOM.2009.4939290, and .
33. Urías J. Rechtman R. Enciso A. Sensitive dependence on initial conditions for cellular automata. Chaos 1997, 7:688-693. 10.1063/1.166266, and .
34. Vichniac G.Y. Boolean derivatives on cellular automata. Physica D 1990, 45:63-74. 10.1016/0167-2789(90)90174-N, .
35. von Neumann J. The general and logical theory of automata. Cerebral Mechanisms in Behaviour: The Hixon Symposium 1951, 1-32. L. A. Jeffress, "z," in edited by (Wiley, New York)
36. White S.H. del Rey A.M. Sanchez G.R. Modeling epidemics using cellular automata. Appl. Math. Comput. 2007, 186:193-202. 10.1016/j.amc.2006.06.126, and .
37. Wolfram S. Statistical mechanics of cellular automata. Rev. Mod. Phys. 1983, 55:601-644. 10.1103/RevModPhys.55.601, .
38. Wolfram S. Universality and complexity in cellular automata. Physica D 1984, 10:1-35. 10.1016/0167-2789(84)90245-8, .
39. Wolfram S. Cellular Automata and Complexity 1994, (Westview Press, Boulder).